The next item of business is portfolio questions, and the first portfolio today is Covid-19 recovery and parliamentary business. If a member wishes to request a supplementary question, they should press their request-to-speak button during the relevant question or indicate by entering the letters RTS in the chat function during the relevant question. As ever, I would make a plea for succinct questions and answers in order to allow as many members as possible to ask their questions. I call question number one, Collette Stevenson. To ask the Scottish Government how the expansion of the Scottish child payment will impact on delivery of its Covid recovery strategy. The Covid recovery strategy is focused on reducing systemic inequalities, tackling poverty and supporting people most affected during the pandemic, increasing financial security for low-income households and tackling child poverty essential to achieving our vision of a Covid recovery based firmly on a fairer future. The extension of the Scottish child payment to children under 16 means that over 400,000 are now potentially eligible. We have demonstrated our ambition to achieving our challenging child poverty targets by further increasing the value of the payment to £25 per child per week. Collette Stevenson, I thank the Deputy First Minister for that response and I welcome the actions in the Covid recovery strategy to address inequalities and the role the Scottish child payment will have in supporting families. However, recent analysis from the IPPR shows that removing the two child limit and benefit cap could lift 300,000 children out of poverty in the UK. Does the Deputy First Minister agree that, in the middle of a crippling cost of living crisis, it is nothing short of a scandal for the UK Government to continue prioritising bankers' bonuses rather than using the powers that they have to support families out of poverty? Time to first minister. I understand and sympathise entirely with the point that Collette Stevenson advances and the analysis that the IPPR has provided has demonstrated quite clearly the negative impact of the benefit cap and the two-child limit as being both unjust and unfair. All Governments must take actions to address the issues of child poverty. The Scottish Government has introduced, as I said in my opening answer, the Scottish child payment, which is only available in Scotland and is not available in any other part of the United Kingdom. However, our efforts to lift substantial numbers of children out of poverty would be substantially assisted by the removal of the two-child limit and the benefit cap, which could be of enormous assistance in addressing the issue of child poverty. To ask the Scottish Government when it expects the Scottish Covid-19 inquiry to conclude. Section 17 of the Inquiries Act gives an inquiry chair a loan rather than the minister's responsibility for deciding how an inquiry should operate. It will be for Lord Brailsford to determine how to strike the right balance between addressing the wide range of questions that people have and making sure that the inquiry can be delivered at speed so that we can learn and benefit from lessons as early as possible. The inquiry will provide information and updates on its website, Covid19inquiry.scot, as the inquiry progresses, as the chair considers appropriate. I thank the Deputy First Minister for that answer. From reading the terms of reference, it is not clear to me whether the Government's response to long Covid and its failure to take this issue seriously is part of this inquiry. Can the Deputy First Minister tell me if the Government's response to long Covid will be part of this inquiry or will we need to wait for another inquiry after we hear the handling of the issue? I am sorry that Mr Lumson takes that view, having read the terms of reference, but I answered a parliamentary question from Jackie Baillie, if my memory says me correct. I made clear two points. One was that the inquiry remit is set out in a fashion not to be prescriptive in that only the words that are in the remit can be addressed by the inquiry but to create the broadest scope to address the issues that are relevant to Covid. Secondly, in my judgment, the issues of long Covid are certainly at the heart of the inquiry remit and should be considered by the inquiry. It will be for Lord Brailsford properly and independently to decide what evidence he hears and considers, but I would be very surprised if the issue of long Covid was not scrutinised by the inquiry. In my view, the remit is set with sufficient breadth and scope to enable that to be the case. I hope that that reassures Mr Lumson. When Lord Brailsford was appointed, the Deputy First Minister gave me a reassurance about the centrality of bereaved families to the work of the inquiry. I wonder whether he is able to give the chamber an update on what steps have been taken to engage families. I cannot give a specific answer to that because it would clearly require me to have knowledge of the transactions of the inquiry. However, in my conversation with Lord Brailsford in the aftermath of my statement to Parliament in which I announced his appointment, he indicated to me that he was making early preparations to meet bereaved families and I am certain that will be the case. We are waiting for the Scottish Covid inquiry to conclude, but would it not be more sensible to have the details and recommendations of the inquiry before ploughing on with social care reform? Obviously, there are lots of issues to consider in relation to social care reform. As a Government, we look at all the available evidence. There is a parliamentary process under way in relation to the committee's scrutiny of the bill. That will have the ability to look at all manner of questions in relation to social care. Of course, ministers will listen with care to the evidence that is put forward. To ask the Scottish Government what its response is to the Scottish Information Commission's section 46 report for 2021-22, which reported a 29 per cent increase in freedom of information appeals. The Scottish Government notes with interest the commissioners' 2021-22 performance report recently presented to the Parliament. I recognise that this is a challenging time for the commissioners' team, and a marked increase in the number of requesters seeking information from Scottish public authorities who are exercising their right to appeal. I note that, in the report, the commissioner sets out steps that his office is taking to address the challenges associated with this, and the Scottish Government acknowledges the vital role played by the commissioner as an independent regulator of access to information laws in Scotland, appointed on the nomination in this Parliament. Donald Cameron, I thank the minister for the answer. The information commissioners' report makes clear that the 626 appeals received in 2021-22 were the highest number of appeals received since 2005-6, and 18 per cent of the valid appeals were about a public authority's failure to respond. So what action will he take now to ensure higher public authority compliance with freedom of information requests? I would like to say to Mr Cameron the action that the Government is currently taking. I would like to take that opportunity to add to what I have already said. As the Scottish Government is committed to learning from all appeals cases no matter what the outcome was, we are working to deliver on an FOI improvement plan that was launched in July 2022, helping the Scottish Government case handlers to recover from the disruption of the pandemic and to adjust to higher numbers of more complex cases. Over the past year, our response rates for FOIs in general have averaged 86.5 per cent, despite cases increasing by 48 per cent over a three-year period. We will, of course, continue to work with the commissioner and others internally to ensure that we address this and to ensure that we end up hitting the 95 per cent target. Question 4, Paul O'Kane. To ask the Scottish Government what the reduction in funding for Covid recovery will be as part of the emergency budget review. The aim of the emergency budget review was to support those in need of most help whilst also managing the nation's budget. That meant taking hard choices to further prioritise spending and finding savings. Many of the difficulties facing public finances are the result of the UK Government prematurely cutting funding intended to support our recovery from the pandemic, despite the Scottish Government warning against that action. The emergency budget review identified a further £615 million in savings. Those are not decisions that we would wish to make, but in the absence of additional funding from the UK Government, they are decisions that we are compelled to find in order to balance the books in this financial year, plus prioritising funding to help families, back business and protect the delivery of public services. Paul O'Kane. I thank the Deputy First Minister for that answer. The First Minister committed to building back better for Scotland as we recover from Covid, but what has happened to that ambition? We need investment and support for those whose lives have been fundamentally affected by the pandemic. The Office of National Statistics estimates that there are over 170,000 people in Scotland living with long Covid. The support from the Scottish Government to date has been inadequate. The Scottish Government committed £3 million in funding when the number of Scots with long Covid was estimated to be at 70,000. Even that has not been fully allocated. Funding has not increased by a proportion at well. Will the Deputy First Minister commit to working across Government to protect funding for long Covid sufferers in Scotland to help their recovery with access to physiotherapy and multidisciplinary rehab? I sympathise very much with the point that Mr O'Kane makes about the importance of ensuring that people with long Covid are able to access the support that they require to assist them in their recovery. In some cases, that will be clinical support. Of course, they should have access to that clinical support. In other respects, it may be additional assistance, which individuals require perhaps to help them on a journey into employability. I assure Mr O'Kane that the Government is working across portfolios to make sure that we put in place the support that is necessary to assist individuals in their recovery. The Scottish Government established a £25 million ventilation fund that businesses could apply to for support. The last time I checked, I think that just £1 million had been paid out from that fund. Is that still the case? Is that fund still available? If not, has that money been reallocated? If so, to where? Obviously, the figures that Mr Fraser quotes to my recollection are correct. In terms of the funding that was available there, if it is not being utilised, it will be made available to meet other budget pressures within the Government. Mr Fraser is familiar with the fact that I am wrestling with the challenge of balancing the budget. Any resources that are not needed for the purpose for which they are being allocated are being drawn into the centre so that I can meet funding pressures across the Government. It is impossible for me to give him a link between individual money that was allocated for one fund to other purposes within Government. He knows the way that Government funding works, but I remind Parliament that I am still working to balance the budget this year because of the significant and corrosive effects of inflation and the public sector pay deals. Parliament was well informed about the challenges that I faced by the Auditor General's statement that was issued last Thursday, which I think gave a fair and accurate account of the significant challenges that I faced in this financial year. To ask the Scottish Government what progress it has made on implementing the recommendations of the institutionalising participatory and deliberative democracy working group published in March. In the most recent programme for Government, we committed to publishing a response to the report of our IPDD working group. That will be set out how we can involve people in communities, Government, children and young people in democratic decision making. We are in the process of carefully considering that further, assessing the new activities and skills that could make that a success and taking account of the resource demands that are needed that would be needed to create that. I thank the minister for that answer. I have certainly read the report and the question is what happens next. People need to know that. I noticed that the minister mentioned the programme for government, but in the 2021 programme for government it stated, and I quote, We are committed to reforming council tax to make it fairer working with the Scottish Green Party and COSLA to oversee the development of effective, deliberative engagement on sources of local government funding, including council tax, that will accumulate in a citizens assembly. We have controversial issues around drugs policy, around being able to raise further funding. There are a lot of issues out there that a citizens assembly would certainly be able to grapple with and, hopefully, bring forward the views of people and communities. So what is the likelihood? When are we likely to see some announcements on this? I think that the minister has cut to the chase and just said to Mr Rowley that we are probably going to write a response to the IPTD working group's report before the end of this year. That will be the starter for us all to be able to look at this and move things forward. I am quite happy, as always, to work with Mr Rowley and meet up with Mr Rowley to discuss many of the issues, but the Government is committed to finding a fairer way to go forward with council tax and we have various other options and other participatory groups that are actually available for others to engage with as well. It might be an idea for myself, Mr Rowley, Presiding Officer, to have an offline meeting and discuss this further. To ask the Scottish Government, in light of recently reported warnings by the Bank of England that the UK is about to enter the longest recession since the 1930s, what assessment has made of the impact that this could have on its Covid recovery strategy? The current economic landscape presents us with significant challenges. The approach of the UK Government in cutting public spending risks prolonging that recession, hampering efforts to restore the public finances. There are alternatives to austerity that invest in public services and the economy, including inflationary increases to devolve Government's 2022-23 budgets. It is unfortunately inevitable that some of the savings that we need to make will have negative impacts. There are no easy decisions, but we have prior to us help for those who need it most. The Scottish Government remains committed to delivering the actions set out in our Covid recovery strategy and our internal monitoring indicates the majority of the strategy's actions remain complete or on track. There is no doubt that the war in Ukraine is having a significant impact on economies across the world. However, yesterday we saw the renewed warnings from the OECD that the UK will be the second worst performer of the world's largest economies next year as a result of the Tory Government's disastrous Brexit and shambolic economic policies. Does the First Minister share my concern that, while countries such as Ireland will see their economies growing next year, Scotland can only watch on powerless as the UK continues its decline, accelerated by Brexit, making it more difficult to recover from this pandemic? I am not quite sure why Mr McDonald's question, which is based on the substantive analysis of the OECD, was met with the groans of the Conservative benches, because we are wrestling now in the United Kingdom with the economic consequences of Brexit, which was inflicted upon us against our will by the Conservative Government. That was added to by the folly of the mini-budget in September, which is all of Conservative design and which will cause significant negative impact for many years to come. Add to that the political inertia of the United Kingdom Government since the revelation of Partygate in December last year has resulted in essentially no effective functioning domestic government in the United Kingdom over that period, with the inflationary pressures arising out of energy cost rises that were not interrupted over the course of the summer. We are dealing with very acute economic difficulties as a consequence of decisions that are voluntarily taken by the Conservative Government, and the implications are significant. I will do all that I possibly can to try to protect people from the effects of the folly of the Conservatives, but I cannot protect people from every aspect of the damage done by the United Kingdom Government. To ask the Scottish Government what assessment it has made of the impact of increasing inflation on Scotland's public services as many are still dealing with the impact of the pandemic. The current financial years budget has been significantly diminished by the corrosive effects of inflation. At the same time, demand for government support and intervention is understandably increasing, and we have not received additional funding to compensate for the reduced buying power of that funding. The emergency budget review aims to support those who need most help, whilst also managing the nation's budget, which meant taking difficult decisions to further prioritise spending and to find savings. The Covid recovery strategy focuses on reducing systemic inequalities, tackling poverty and supporting people most affected during the pandemic, and has been agreed with local government. Despite the challenges that I have outlined, we remain committed to the strategy and its achievement of its outcomes. From our NHS and social care sector to our local authority colleagues, people coming to live and work in Scotland are a huge asset and should be welcomed with open arms. Yet Labour and the Tories are an absolute lockstep with each other as they continue to ignore Scotland's needs on every serious challenge facing us right now. Can the Deputy First Minister outline what powers the Scottish Government would need to ensure an open, welcoming system of migration that supports our public sector to deliver on the Covid recovery strategy? Thank you, Deputy First Minister. Perhaps we could focus on the impact of the increase in inflation in regard to those matters. I certainly will, because the effects of inflation are undermining the purchasing power of our economy. As a consequence of that, there are acute issues that Emma Roddick raises about the migration stance of the United Kingdom Government. There is acute pressure on the availability of individuals to enter the labour market. We have historically low unemployment and historically high employment in the Scottish labour market just now. That is creating acute labour shortages and acute inflationary pressures as a consequence. For Mr Lumsden's benefit, that is causing acute inflationary pressures. If Mr Lumsden wants to ask me a supplementary question, I will go into a lot of detail about the inflationary pressures that arise out of migration challenges, because all the available evidence highlights that particular point. The Scottish Government, through the work of our ministerial population task force, tries to develop concepts such as the rural visa pilot proposal, which is designed to address some of the questions that Emma Roddick has raised with me. Of course, we need to have a fuller range of responsibilities to enable us to address the negative effects of the migration stance of the UK Government. That concludes the first portfolio. Questions on Covid-19 recovery and parliamentary business. We will now turn to the next portfolio, which is finance and the economy. Again, if any member wishes to seek to raise a supplementary question, they should please press the request and speak button during the relevant question or enter the letters RTS in the chat function during the relevant question. Again, a plea for succinct questions and answers. I call question number one, Liam McArthur. To ask the Scottish Government what discussions it has had with Orkney Islands Council regarding the Scottish budget 2022-23. The Scottish Government continues to meet with COSLA and individual local authorities on a regular basis to cover a range of topics, including current and future budget pressures. I was pleased to meet with Councillor Stockin on 31 August during my visit to South Uist, which, to the observer, will be known as not in Orkney, but it was on the occasion of a meeting with three island authority leaders in South Uist. I responded to Mr Stockin's most recent letter on 21 November, confirming that we will make arrangements to meet again at the earliest opportunity. I thank the cabinet secretary and confirm that we islanders are known to travel to different islands from time to time. Orkney Islands Council warned this week that the precarious state of the internal ferry fleet is risking, quote, life and limb, with the vulnerability of vessels exacerbated by recent repairs to ancient hulls and the grounding of the MV Varigan earlier this month. I understand that Mr Swinney will meet Councillor Stockin shortly to discuss those concerns in the context of OIC's forthcoming budget settlement. Does he accept that ferry replacement is now a matter of public safety? If so, what assurances can he offer my constituents that the Scottish Government is taking this seriously and committed to finding an urgent resolution to this long-running saga? First, I would like to say that in relation to the recent grounding of the MV Varigan, I was very pleased that everyone was safe in what was a worrying incident that took place. Councillor Stockin has raised the issues of the strength of the inter-island ferry fleet. I appreciate that it is an issue that causes significant concern to the islands council and to islanders, and there is a need to rely on regular services in that respect, and we have to make sure that those are operational and safe. It will be one of the points that Councillor Stockin and I discuss. I am aware that he has also discussed those issues with the transport minister, Jenny Gilruth. I assure Mr MacArthur that the Government is engaging constructively on the importance of renewing the ferry fleet to serve all of our island communities. I apologise that I will have to leave before the end of this session to another commitment, as I advised. The cabinet secretary will be aware that the rate-equivalent tariff, or RET, was delivered to ferry routes in northern Isles by the middle of 2018. However, during the intervening four and a half years, while Shetland has benefited from those arrangements, Orkney has been left behind, a failure to deliver on their pledge that will have clearly saved the Scottish Government considerable sums of money. Can the cabinet secretary confirm how much money the Scottish Government is estimated to have saved by not delivering RET as promised, and how will he ensure that that money will be reallocated in the budget to allow it to be used for the economic benefit of Orkney? Of course, what Mr Halcro Johnston misses out is the fact that the Government has substantially increased investment in ferry services in Scotland. When the Government came to office, or actually when the ferries plan was developed in 2012, if my member says me right, the budget was just a bit over £100 million, it's now well over £300 million, so substantial investment has been made in ferry services and in road equivalent tariff. The Government obviously works constructively with individual island authorities to maximise their economic potential, and that will continue to be the case with Orkney Islands Council. To ask the Scottish Government what discussions finance ministers have had with the Minister for Higher Education and Further Education, Youth Employment and Training to assess the number of construction apprentices and construction workers needed to support the recovery of Scotland's economy and meet its net zero targets. The Minister for Higher Education and Further Education, Youth Employment and Training and myself share the commitment to ensuring that our current and future workforce has the skills needed to support the transition to net zero. The construction sector will need over 25,000 more workers by 2026, and that includes workers with skills to support heat decarbonisation and offshore energy projects. The Scottish Government recognises that apprenticeship pathways are key to that, and we are working with the skills agencies to increase the number of apprentices back to pre-Covid levels. I'm grateful for that answer and I welcome the Minister's commitment. I did ask about specific discussions with other ministerial colleagues because the minister may be aware that last week in my capacity as a convener of the cross-party group in construction, myself and a number of industry stakeholders, including Unite the Union, met with the minister, Jamie Hepburn, because of the very serious issues affecting construction craft apprentices. The meeting was fairly positive. We hope that a solution is in sight, but there's a really serious backlog affecting around 1,700 apprentices. There's having an impact on employers, on the colleges, and we need a resolution at many to learn lessons. I get an assurance that discussions are going on behind the scenes in government and could we perhaps get a statement from the Government to Parliament by the end of the year to make sure that everyone who's waiting for good news receives it? I'll certainly convey the member's request for ministerial statement to the skills minister because I know that they had some productive discussions, as the member said just in the last week or so, and to assure the member and indeed Parliament that the climate emergency skills action plan is being refreshed, as she may be aware and will be published in 2023, and there are discussions going on across portfolios with the green skills minister, Lawrence Later, Jamie Hepburn and, of course, myself as just transition minister, and there are talks planned in the coming weeks as well to ensure that we do make sure the skills required are available. Indeed, yesterday I was in Aberdeen visiting North East Scotland College to discuss how they're using £4.5 million that they've secured from the Just Transition Fund for North East Scotland, and they're going to build a facility to ensure that apprentices are trained up as welders for offshore platforms, electricians for installing electric car charging points and so on. So there's a lot of activity across the country and I just want to assure the member that it's being co-ordinated as much as we can. We've been waiting for five years for the skills landscape reform, and the minister only acted after Audit Scotland criticised his lack of leadership in this area. The coherence and stability review for the college sector was largely delayed and in the middle of a college sector crisis. So what chance have we got of increasing the number of construction apprentices and workers if we've got this delay within the reform of the skills agenda? Well, as the economy is going to be transformed over the next 10 years to help us to get towards our net zero targets, it's clear that we have to keep our skills landscape under review given the 21st century challenges that we face and, of course, James Withers has been appointed for that skills review. This Government's got an excellent track record in delivering apprentices over the past few years. Of course, there has been a bit of a blip because of the impact of Covid, and we're making up for lost ground at the moment for that, and Skills Development Scotland has been instructed to deliver 25,000 apprentices from the start of this financial year and then build back up to 30,000 in due course. Thank you, Deputy Presiding Officer, to ask the Scottish Government what assessment it has made of the potential economic benefit to Scotland of moving to a low-carbon economy and achieving net zero. Minister Richard Lochhead. There are benefits and many opportunities are rising from our transition to net zero, not least in the key energy transition sectors such as renewables and green hydrogen, but more broadly across the whole of the economy as we reduce emissions from transport from industries of our homes and as we build our natural capital resources. Those opportunities are set out in our national strategy for economic transformation and our hydrogen action plan. They will be further developed as we bring forward our energy strategy refresh with a just transition plan for energy in the coming weeks, as well as our new climate change plan and other just transition plans in the coming years. I thank the minister for that answer. I may be aware that there was a nut west that has estimated that moving to net zero could be worth £22 billion to the Scottish economy. However, they do warn that Scotland will have to increase the support to develop services in supply chain and SME businesses by a factor of greater than two, which is much quicker than required by the rest of the United Kingdom. Given that we are behind the rest of the UK according to the nut west report, can I ask the minister what the Scottish Government is doing to support the development of our SME sector to ensure that those opportunities for our supply chain and our support services needed to achieve net zero remain here in Scotland? I am sure that a member will want to welcome the report that was out last week, independent research from Skills Development Scotland with Warwick University and Strathclyde University, saying that now there are up to 100,000 green jobs in Scotland. That is an upper estimate and it is still being researched. That is a very good indication that the green jobs revolution has started in Scotland. We are not behind the rest of the UK. There are numerous reports from Price, Waterhouse and Coopers. There was a Fraser of Islander Institute report out just last week called International Scotland that are showing in comparison to the rest of the UK, Scotland is actually making excellent progress in this agenda. I do not think that we should talk Scotland down, but I agree with the member that there is a lot more to be done and he will be aware of the supply chain work in relation to Scotland and other projects that have the potential to deliver thousands of more green jobs in Scotland. The emergency budget review cut £38 million from energy efficiency and £45 million from heat in buildings. Could the minister outline what impact that will have for our delivery of our net zero targets? The member will be aware that we face a very difficult budget environment at the moment following inflation. Indeed, the acting finance secretary outlined some of the challenges in the previous questions just a few moments ago. However, we are making good progress. There is a lot of planning in the pipeline. The just transition plans for energy in the first instance will address some of the issues that will be published for consultation, so Parliament members can submit their views to that over a 12-week period once it is published in the coming weeks. As I said, there are good positive signs that we are making progress in terms of green jobs being created and the potential for many more in the near future. To ask the Scottish Government whether it will provide an update on how it is investing to support the economy across the west of Scotland and greater Glasgow areas. The Scottish Government is a full partner in the Glasgow City region city deal, contributing £500 billion over 20 years to the infrastructure investment fund. The deal empowers Glasgow and its city region partners to identify, manage and deliver a programme of investments to stimulate economic growth and create jobs in their area. Similarly, the Scottish Government is investing £103 million in the Ayrshire growth deal, which will see transformational investments in projects across Ayrshire over the next 10 years to support long-term inclusive growth there. I thank the minister for that response. Minister, if Glasgow city region were to be awarded the Clyde Green Freeport bid, it would be a massive boost to the local economy in Glasgow and the wider region. It would provide high-quality jobs and investment opportunities in addition to accelerating net zero ambitions. Several Scottish Greens and SNP MSP have supported motions urging the Parliament to oppose the Clyde Green Freeport bid and all other Scottish freeport bids. Will the minister state his support for the Clyde Green Freeport bid and does he welcome the positive co-operation between the Scottish and UK Government? I understand that the member makes the case for her own region in terms of the bids, and she will be aware that they are under consideration at the moment from the Scottish and UK Governments in announcements, which will hopefully be in due course. Of course, there are a number of bids from across the country, but the members made her point well and she will have to wait for the final announcements that we made. To ask the Scottish Government for an update on the Advanced Manufacturing and Innovation District Scotland site in my constituency of Renfrewshire North and West, which will include two new world-class innovation centres, the National Manufacturing Institute Scotland and the Medicines Manufacturing Innovation Centre, and the projected impact that that will have on the economy of the west of Scotland and the greater Glasgow area. To Nathoddon, who, understandably, makes many of the benefits that the Scottish Government is fully supportive of this work, the Advanced Manufacturing Innovation District Scotland site is part of the £39 million city deal that is funded by Glasgow airport investment area project, and work is well under way to deliver on that ambitious project. Of course, the impact of the Glasgow city region deal will be transformational for local communities in attracting investment. Building on that investment, the Glasgow city region deal has created, as she will be aware, a regional economic strategy to help to shape the long-term, post-deal economic future of the region. To ask the Scottish Government how it is investing in rural broad brand. Minister Tom Arthur. I'm wrong indeed. Future proof digital connectivity is vital for our rural communities, and the Scottish Government delivery programmes have already connected around 1 million properties across Scotland to faster broadband. When investing more than £600 million through the R100 contracts, extending fuel fibre broadband access to some of the hardest to reach rural communities in Scotland, and our Scottish broadband voucher scheme also provides funding to connect those not part of the R100 contracts or commercial build plans. It's also imperative that we urge all the UK Government departments that are relevant to this to extend the gigabyte networks to Scotland's rural communities given telecoms is, of course, an entirely reserved matter. Alexander Stewart. I thank the minister for that response. The SNP pledged to have R100 scheme completed by 2021, but now, after failing to meet that target, the new estimate is predicted to be 2026. I have a freedom of information that shows that the R100 scheme has cost 21 million since it should have been completed last year. This is an enormous cost to the taxpayer and shows that the SNP pledge for 2021 is not going to take place. Does the minister agree with me that the failure, like the Ferris Fiascal, will ruin rural communities' chances for ever-getting transport and broadband connections that they deserve? I wish to ask Tom Arthur to answer that point. Can I just say to the member if his Tory colleagues in the UK Government who have exclusive confidence for telecommunications had acted a few years ago and got their act together, it would have been down to the Scottish Government to step in with hundreds of millions of pounds of investment to make up for lost time. The R100 project is game-changing for many parts of rural Scotland. According to Think Broadbands, which the UK Government also used to give the success of its own programmes, 95.1 per cent of premises across Scotland are now able to access superfast broadband speeds of 30 megabytes per second and above, up from just 59.3 per cent in 2014 when the deployment began. That is superb progress and the investment from the Scottish Government is making a real difference to rural communities in the south of Scotland and throughout the country. Given the disruption to EE's 4G mobile service, which my constituents in Uig have been enduring for six weeks now, effectively cutting a huge geographic area off from all broadband access and severely impacting on medical and other essential services, will the minister agree that EE's response has been truly woeful and also commit to facilitating a meeting in Uig between the R100 team and the community? I just say to the member that this is clearly a very serious issue in his constituency, and whilst on the issue of ensuring 4G mobile connectivity is maintained as a reserved part of the telecommunications legislation in the UK, which means that the Scottish Government doesn't have a mechanism to directly intervene in such matters, will certainly give consideration to the member's request, and I'll make sure that he is written back too shortly. Of course, responsibility falls upon OFCOM as the UK's telecoms regulator. However, as with the recent telecom outages that have suffered in Shetland, Col and now Uig, we urge operators to ensure that they rectify such issues as a matter of urgency. For our part, we are investing £28.75 million in the Scottish 4G infill programme, which is delivering 4G mobile infrastructure services throughout rural Scotland, including the Western Isles. To ask the Scottish Government what discussions finance ministers have had with ministerial colleagues regarding any plans to investigate the feasibility of a land value tax. Although there have been no recent discussions on the feasibility of introducing a land value tax in Scotland, we will continue to look closely at the Scottish Land Commission's recommendations on land reform and taxation, review any evidence in detail and assess that as part of our wider approach to tax policy. We are, as ever, hoping to explore how the Scottish Government could support land reform objectives using its limited powers over taxation to generate revenues to invest in our public services and to support a sustainable and inclusive wellbeing economy. Katie Clark It is estimated that 432 people own 50 per cent of the privately held land in Scotland. A record, £447 million was invested in the purchase of private Scottish estates in 2021, a 333 per cent increase from 2018. Given the financial backdrop, does the Government accept that it is now essential that we introduce a land value tax as a matter of urgency? As I said in my original answer to the member, we are considering recommendations carefully. Clearly, the introduction of any new tax is a substantial matter. For example, while the Parliament enjoys powers to introduce local taxis, national taxis do require new, devolved national taxis do require the agreement of the UK Government and the Westminster Parliament, we are considering the details carefully and any measures that we do take forward will be done so in a way that is consistent with our framework for tax. Arrianne Burgess It is clear from stakeholders and constituents that high land prices can impede regeneration efforts and hinder attempts to assemble land for community-led development. That is why the Bute House agreement commits to deliver an effective and fair mechanism for capturing for public benefit a share of the increase in land value when a development is supported through the planning system. Can I ask the minister what benefits he sees coming from that commitment and can he update on progress? Can I thank Mr Burgess for her question? We have of course been focused within planning on the preparation and delivery of our revised national planning framework. I very much look forward to appearing before the committee next week to give evidence. As we move into the new year and hopefully as we see Parliament adopt and approve the new national planning framework, we will then turn our attention and earnestly focus on the delivery of national planning framework. That will encapsulate a range of different actions, including the continued roll-out implementation of the planning act, our on-going review of planning obligations and taking forward the commitment between the Scottish Government and the Scottish Green Party on the matters that the member raised. To ask the Scottish Government what assessment has been made of the impact that the UK Government's autumn statement will have on Scotland's public finances. The autumn statement has shown that households across Scotland are paying a steep price for the economic mismanagement of the UK Government, with the OBR warning that average household disposable income will drop next year by some 7.1 per cent. Inflation is eating away at the Scottish budget, which has fallen by 10 per cent in real terms between this year and last, and due to the lack of additional funding in 2020-23 and the fiscal constraints of devolution, we have had no choice but to already make unplanned savings of more than £1 billion. The corrosive impact of inflation and turmoil caused by the UK Government's economic choices, meaning that the Scottish Government is facing very difficult choices for public spending over the next few years. Earlier this month, the Bank of England warned that the UK may be facing the longest recession in a century. Does the minister share my concern that UK Government's plans to cut public spending risks prolonging that recession, and can he advise what alternative priorities could be pursued if this Parliament had the full financial powers? I do share Jenny Mentor's concern and indeed the OBR has painted a grim outlook with the UK economy now forecast to be no bigger at the end of this UK Parliament when at its start, which means five years of stagnant economic growth. This combined with yesterday's OECD forecast predicting that the UK economy will be the worst hit of all G7 nations is a devastating indictment of the UK Government's management of the economy. We have made no secret, Presiding Officer, of our frustration at the limitations imposed on us by the current fiscal framework. Our reserve funding is capped, our tax powers are limited, and we have no legal ability to borrow to fund day-to-day spending. Not one of the three main Westminster parties support giving this Parliament the fiscal flexibilities that it requires. Consequently, the only means by which we can assume the most financial powers that are so necessary is by this Parliament assuming the powers of an independent country. To ask the Scottish Government what assets currently in public ownership it plans to privatise. The Scottish Government works on a case-by-case basis to secure the best outcome for assets in public ownership. Parliament would be notified of any future agreement to return a commercial asset to the private sector. Three weeks ago, the First Minister told the Public Audit Committee that our position with all of the commercial assets that the Government has taken ownership of is that, ultimately, we want them to be back in the private sector. Let me ask again, in the interests of openness and democracy, what assets does the Scottish Government want to privatise? I can only refer the member to my previous answer. We work on a case-by-case basis to secure the best outcome for assets in public ownership. Parliament would be notified, but it is thanks to the Government's intervention that many, many jobs have been saved. Indeed, the contribution that those industries are making to the economy has only taken place because of the actions of this Government. Ferguson's is clearly not without its challenges, but by stepping in, the SNP Government saved Scottish shipbuilding on the Clyde and hundreds of jobs that went with it. Now we see Prestwick airport turning a welcome profit. Will the minister agree that moving assets and businesses into public ownership when they are failing in the private sector can and does work? Yes, I agree. We have shown how, through our investment, we can realise benefits to communities and businesses from our strategic investments. Taking businesses into public ownership is a complex issue. For each case, we work to understand the legal, financial and policy implications. I am delighted that Prestwick airport is continuing to grow steadily, making a positive contribution to the local and regional economy, supporting 300 direct jobs and many more. Through our intervention in Ferguson Marine, we are showing how we are standing by our commitment to the shipbuilding communities in and of a Clyde, where we have rescued more than 300 jobs and supporting our island communities, but we lie on the vessels. That concludes portfolio questions on finance and the economy. There will be a short pause before we move on to the next item of business to allow front-bench teams to change positions should they wish to do so.


Good morning, everyone. Thanks for being here. We present the party package that permits to perform a valid double dipping. And I will use, as example, deprimary data that are very important in order to understand the neural activation in the human brain. One of the most famous methods used in deprimary data analysis is the cluster-wise method. In this case, we analyze a set of continuous voxel, S. And for each of these set, called cluster, we have analysis in order to understand if the brain activation inside that cluster is significant. However, if we reject this analysis, we only know that at least one voxel is active. But we don't know how many and which ones. This is called a specificity paradox because larger the cluster, weaker the findings. And we cannot infer inside that cluster without falling into the double-dipping problem. So in this case, we can use the ARRI method that stands for a resolution inference or the party method that is the permutation version of ARRI. That these two methods permits to make inference on the number of truly active voxels. So we can associate it to each cluster the lower bound of the number of truly active voxel. And the permutation structure of ARRI permits to account for the correlation structure between tests. And both methods are based on the closing testing procedure for controlling the family-wise error rate. So every time that you want to infer inside a data-driving cluster and not, you can use ARRI, for example, in gene expression cluster analysis, in cluster AG data analysis, and so on, as many times as you want because it's a simultaneous inference. And so I will present the main function of the package, the party bring function and party function. The first one is for the fMRI framework and the second one is for the general framework. In the first case, we need the object cops that is a list of contrast parameter estimate involving bring activation difference for each subject in if the format. We need the detraction that constructs the clusters or the cluster map, the brain mask, and the alpha level. And for the general framework, we need the data matrix with dimension observation times variable, the feature set of interest, so the set of hypothesis, the alpha level, and the type of test that we want to perform. So for example, using the auditory data that you can find in the fMRI data package, in this case, we want to analyze the neural activation between vocal and vocal stimuli. And so using these three objects and using the party bring function, we can have an output like that. So the first line is for the first cluster that is the right superior temporal gyrus, plant temporale, and so on. This cluster comes from the cluster-wise method using that ratio equal to 3.2 for data statistics that form the clusters. And we can say that in this first cluster, we have at least 92% of truly active voxel. But we can also drill down. And so we can use a higher duration, for example, equal 4. And in this case, we have four subclusters inside that cluster. And we can compute the lower bound of the number of truly active voxel for each of these subclusters. We can also visualize the results in a brain map using the mapTDP function. So we can see, for example, in this case, we have a higher true discovery proportion respect to this cluster. And that's it. So I hear first question. And I want to thank the group that work on this project, the Professor Finos, Goehmann, Hamerick, and Bida. And thanks for your attention.


I think time for us to begin ok. As I understand you have already had two lectures and you have gone through the concepts of measurement, why measure, how to measure, what are the problems, what are the specifics. And then you have also looked at signals, you have gone through some idea about filtering of signals. As this course proceeds you will be using more and more signals. We will like you to learn and understand what are these signals, what do we do with these signals, what are the problems, what issues to address at various points. So, in this series we have also looked at one of the techniques which is analog to digital conversion, taking an analog voltage or analog signal converting to its digital representation and viewing it. Up to this point you have just an idea of this method, this technique. But why this is done and what are the issues involved with this and when you actually do put it to use what to expect, that is what we are going to look at in this lecture and also in the subsequent lab which will proceed you will be doing this. So, as this talk has been titled signal sampling and reconstruction, there are several additional terms which we will talk about like quantization, discretization, sampling, reconstruction and things like that. So, let us proceed. Now why do we discretize signals, where do we discretize signals, you do that routinely. For example, this is what you normally use. For example, what is there in a CD, music, mp3, wave files, what are these. These are nothing but digitized data which has originated probably most likely as an analog data either as an audio data or as a video data somewhere and it has gone through this process of the analog data being converted after sampling and digitizing and perhaps also encoding. It may or may not be encoded, some of the older formats like wave formats and all are not encoded, but the more efficient formats like mp3 and all, they compress information, they encode it so that a large amount of binary data can be compressed into a smaller volume and then put on to storage media. So, you are all familiar with this mp3. So, how does it originate? Now you see the sequence. The analog audio goes to a unit where there is some sampling happening, some digitizing happening, digitizing is what you do as A to D. After digitizing, encoding or perhaps not necessary and then storing on the some storage media and the vice-versa reading those binary bits which have been stored and reconstructing it back if required decoding and producing it back as an analog audio. Where is the ADC in this? Does anybody know? Can somebody tell me in which part of the sequence the ADC might be figuring? In the one where you are sampling and digitizing, the digitizing part is the ADC part and the DAC the digital to analog converter where might that be occurring? So, the ADC part comes here in the sampling digitizing and encode, the DAC parts come here in the reconstruction part. Let us continue. So, can we do like this? Take a source, take data from that as it is coming, digitize it, sample and digitize and make it into a digital bit stream. Send that bit stream to a DAC reconstruct and send it back to the receiver. Now obviously, you would say yes, such a thing would be possible when you can do this and save data and then retrieve it and then use it to reconstruct. Why not do it online continuously? Now, yes it is done and in many, many systems this is what is done. The digital bit stream here allows you the possibility of directly manipulating this data for your benefit so that you can remove if there are any noise elements or sometimes you can remove the expected noise elements which are going to interfere what we call interfering elements. For example, digital processing of data which is coming bit streams, input bit streams is the most common thing. So, what is an ADC? Where is it used? Most sensors produce an analog output and this analog output is used by the ADCs. It is converted by the ADCs into a digital equivalent or digital number what we might call a better way probably would be to say a digital representation of that analog voltage and what does that digital representation mean really? We will be looking that at that in a little more detail. So, ADCs invariably form the interface between analog signals and the digital world and then this digital data might either be directly used for online processing and then reconstructing and usage or it could be stored and used subsequently. What is this discretization? That is an important thing we keep on talking of discretization, digitization, quantization lot of words come keep on keep coming. So, let us look at it what does it really mean? Discretization is something that we do almost without realizing every day in a very everyday life we actually do it. Now, here is an example of what you might have already done. This is a meter which has got marking of 0 to 100 and it is marked there are some marks there. So, you are assuming that it is a voltmeter which is reading voltage between 0 to 100. Does it have 100 discrete steps? That is a question mark over there. Does it have 100 discrete steps? Can you actually measure voltage with a resolution of 1 volt? No, actually there are only 20 steps. So, when you measure voltage you are measuring a range of 100 volts, but discretizing this 100 volts over 20 steps. So, your resolution becomes only 5 volts. So, the discretization really means that while just look at the transfer function of such a possible volt meter that we might have. If the while the real data that you are measuring will vary continuously from 0 to 100, what you are observing here will only undergo 20 changes 20 steps. So, this is kind of a staircase transfer function. Now, this transfer function that we have is a typical transfer function of an analog to digital converter. An analog to digital converter will have linearly changing real world values on the x axis and the measured value the digital representation of that will be varying in discrete steps. It will be varying in quanta or it will be quantized. So, you will have only 20 numbers to represent this. Now, this is something which once again let me say that you many of you have probably been using without realizing. Let us go further. Here is a digital multimeter. This is my digital multimeter you have already used in the lab. A similar digital multimeter you might have used elsewhere. Now, let us look at what does it have. It has got the maximum indication of 1999 starting from 000. What it means is that it can indicate only 2000 distinct values. Now, how the multimeter is used? You can have different ranges with a 1 volt resolution up to 199 volts or with a 0.1 resolution 199.9 volts or with a 10 millivolt resolution and so on so forth. So, what is it that we are doing? We are actually saying that we take a domain which has only 2000 members and we simply keep on defining redefining the range of that. So, either it will the domain has numbers from 1 to 2000 0 to 199 volts or 10 times smaller or 10 times smaller the resolution keeps on changing. So, this really means that the ADC a typical ADC can be looked as this kind of a black box where you specify the maximum voltage range whether it is going to be 2000 volts or it is going to be 200 volts or 20 volts. So, you specify the maximum input range and you also specify how many steps will be required for quantization. In this case how many steps are there? How many steps? 2000 steps. It is customary to have two kinds of ADCs one kinds of ADCs will have steps which will be multiples of tenths in decade. For example, you will have 2000 20,000 200,000 some of these also come as 40,000 400,000 80,000 800,000 this is one kind of ADCs. The other kind of ADCs will give you conversion the output steps will be in the order of 2 to the power n this will be in binary range of typically let us say 8 bit, 10 bit, 12 bit, 14 bit, 16 bit, 18 bit it continues like that. Typical ADCs are available up to 24 bits, 24 bits ADCs are of course very high resolution use of very special applications. So, a typical ADC let us say 8 bit ADC will will be something which will have 2 to the power 8 steps which will be 256 steps. So, the maximum possible quantization that is possible in that case is 0 to 255 or 256 steps. So, an ADC is nothing, but a black box to which you give an input voltage and to that you specify what is going to be the maximum input voltage range and it gives you an output. Of course, it is a very very simplistic model it is not just this there is more to it how does it actually do this carry out this conversion. So, in the process of converting and analog voltage to a digital voltage are there some additional factors which have to be considered come into the picture. So, we will talk about that, but a little more about ADC measurement range. So, they would be typically measured in terms of bits where 2 to the power n where n would be the bit. Now, you can see an 8 bit ADC is gives you 256 steps what is the resolution of measurement in an 8 bit ADC in terms of percentage to be 100 by 256 approximately 0.4 percent little better than 0.5 percent. 12 bit ADC will be 2 to the power 12. So, 100 by 4096 much better 0.01 percent better than that and 16 bit even better. So, there would be a motivation for us to keep on increasing the width of representation digital width of representation of a analog number. So, why not keep on increasing, but the price that you have to pay when you start increasing the number comes in two ways one is the cost the price means the cost the other is what are called conversion delays. So, we will talk about conversion delays later. So, when you use a 8 bit ADC the range that you may specify could be a unipolar range 0 to 5 volts or a bipolar range minus 5 to plus 5 volts you can see that the overall range here is 5 volts while the overall range here is 10 volts. So, the same ADC for a 0 to 5 volt range will give you a resolution which is 0.196 while for a plus minus 5 volt half the resolution of that. So, you can use an ADC for any range, but you should realize that the resolution of measurement will keep on changing. Now, what are the conversion steps in the ADC? The first thing is whenever we use an ADC we have to sample the data why the data sampling is necessary will become clear a little later and if one ADC has to be used to measure multiple signals then we can multiplex data this multiplexing is nothing, but time multiplexing in real time we first measure data from first source then from second source then from third source and then keep on recycling. So, this is called time multiplexing since the ADC conversion is very fast. So, one really does not realize how with that there are missing points in between. Then there is a device which is which holds the data and the device which samples and holds the data as a single device called sample and hold because the ADC will take some time for doing the conversion. So, during that time the data will have has to be held and the sample and hold holds the data. The quantizing is done by the ADC and once that is over the data is available and then that encoding of an of the data could be just what we would have straight binary or it could be in a variety of ways. Now, what are the issues? One is the resolution that I talked about the other is the sampling rate. What is the sampling and we will look at it a little later. First of all let us look at a typical setup of measuring of converting an analog input voltage to a digital representation to its digital representation. Here we have a small box written as S stroke H. S stroke H is for sample and hold. So, a sample and hold is a device that whenever an ADC has to make a measurement it sends a signal to sample and hold that hold the analog voltage. Whatever analog voltage is existing at its input you hold it. Do not change that do not allow the analog voltage at its output of this of this S and H output change while the ADC is carrying out its conversion. So, when the ADC has finished its conversion it removes that hold input from the sample and hold and the sample and hold then goes automatically in sample mode. So, the sample and hold can work in sample mode. In the sample mode the input voltage flows to the output and in the hold mode the output voltage is held constant. So, let us look at how this would be working let us look at the a typical signal. The typical signal as a function of time will be a voltage varying in its amplitude and in time. So, look at this voltage at any time starting from the reference point 0 the voltage keeps on changing its amplitude keeps on changing. What does the sample and hold do at the output of the sample and hold? For every discrete time that it is sampling the output is held constant it is frozen then once again it is frozen once again it is frozen. So, this sample and hold what it what is it doing? It is breaking up the incoming signal into discrete points and at that specific point at the beginning of this the data is held. The ADC is taking some time to convert from the instant that the data is held to the instant that the data is converted the ADC takes some time which is called the conversion time and at the end of the conversion time the converted representation digital representation is available. So, you can see that this was what the signal originated as and this is what it will appear if I try to reconstruct it back by using this converted data. Now, one small thing that I would like to point out obviously, this signal does not exactly look like the input signal. Now, what is the factor in your opinion which will make the output signal as close to the input signal? The sampling rate the faster I sample and the faster I convert the closer is the output signal to the input that is one thing. The second thing is that the digital representation that I get depends upon what is the width of the word the digital width of the word the digital width of the word here is 12 bits. 12 bits means I get a resolution of 4096 in overall range that I am using. So, I am using 4096 quantization steps if I were using 10 bit it would be 1024 if I would be using 8 bits it will be 256. So, the accuracy of representation in the x axis is the representation of the amplitude that accuracy depends upon the resolution with which I am measuring it. And the accuracy of reproducing a dot a dot which I find here and the input back on this would depend upon two things the accuracy with which I am measuring the amplitude and also the speed with which the quickness with which I am measuring it. So, to put it back there I should have the data at that point I may not have the data at that point I may have data at a different point right. So, that is why ADC has got two important attributes the measurement resolution and the measurement speed how quickly we can make a measurement. Now, coming to this let me put a question to you you use PCs you listen to MP3 audio on your iPods from your PCs and all. So, obviously, that also would be digitized data that also would have gone through an ADC now tell me what will be the sampling speed of the ADC it is 44 kilohertz why is it 44 kilohertz. So, twice the maximum frequency is 22 kilohertz that is 44 kilohertz, but there are two channels. So, would not you have to do it at 88 kilohertz. So, when you do different types of measurements in MP3 for example, you have so many bit rates 128 bit rate 64 bit rate. So, what is what does that mean different bit rates. So, what is actually happening? So, these are interesting questions that you should you should ask yourself and try to find out supposing it were not 44 kilohertz it were 22 kilohertz or would anything be gained if I increase the sampling frequency from 44 to higher let us say 50, 60, 70, 80, 100 is there anything to be gained. So, some of these questions are all relevant they all related to your understanding of ADC and the sampling resampling rates and all. So, let us look at what happens to accuracy of reproduction of signals when you change the sampling interval sampling interval would be the sampling frequency. So, if you are sampling at 1 kilohertz your sampling interval is 1 millisecond if you are sampling at 100 kilohertz your sampling rate is accordingly 100 times faster. So, here is the signal now observe these dotted lines are the points of sampling the data is sampled here and then here and then here and then here then here and then here. Now, when it is reconstructed obviously, these are the points that are stored on the micropsacer or that are available to the micropsacer or the micro computer which it sends to the DAC and this is what is reconstructed. Now, in this reconstructed information you can see that the data is grossly different from what we sent for example, we have missed this peak. So, let us look at a little more supposing I am having a sine wave and I want to sample it each of these points of the sampling points. Analog frequency is 0.09 of sampling rate the analog frequency that we are sampling is much much smaller than the sampling rate. We are getting a large number of samples per cycle and we can reconstruct this signal very well. Let us go to a higher frequency and slower sampling rate the analog frequency is equal to 0.31 sampling rate you will observe that you are still getting sufficient samples to reconstruct at least the frequency information accurately if not the amplitude information. In this one you would have accurately got the amplitude information and also the frequency information. This one we are getting the frequency information right we may lose on the amplitude information So, sampling rate also affects when you are measuring your signals it also affects the accuracy with which you are making a measurement. Let us go further the analog frequency is 0.95 sampling rate this is the analog frequency and this is the sample points you can see that if I try to reconstruct the signal I will get a frequency of reconstructed signal which will be absolutely different from the input signal frequency which was digitized. So, this problem where the you get a signal reconstructed frequency or reconstructed signal component which was not present in the input is a big problem when we discretize signals and when we store them and this is called aliasing this what we are observing here is called aliasing and the frequency components are the aliases and there is a there is something called sampling theorem which tells you that what should be the minimum sampling rate for us to get the frequency information right. So, some of you may know some of you may not know and I am not telling you this is something that you are supposed to discover in this lab when you are going to do the experiment in the next lab you will actually be wearing the sampling frequency or you will be keeping the sampling frequency constant and you will be wearing the signal frequency. So, you should reconstruct this you will be reconstructing the digitized signal back. So, you should yourself from that infer that what is the right sampling rate at which you will get the frequency information correctly. Now, there is something about how the ADC works what is the what is a technique what is the mechanism what is the magic band the ADC how does the ADC give you the converted value. Now, in an ADC I will go further and then come back typically ADC has got many sub components and one of the type of ADC which is called successive approximation ADC the one which are going to use and also one of the more common and more popular ADCs not that just this is the only one which is largely used there are others also which are used integrating ADC is another one and sigma delta type of ADC is another one which are used quite a lot. But let us look at the successive approximation ADC which is probably still the largest or the widely most widely used.  There are several components which form and the successive approximation means you make an approximation you make a guess what is the actual digital representation is guessed. So, that guessed representation is given to the DA converter and the guessed analog voltage is reconstructed and that reconstructed voltage is compared with the actual voltage which you are going to convert and if they are not matching then the next guess is made then the next guess is made. So, here is the guessing method supposing this is your range entire range and you have only 8 steps in this range. So, 8 steps would mean 2 to the power 3 or 3 bit ADC 3 bit conversion the first guess that we make is always at the mid scale and at the mid scale you check whether your value is your guess is too high or too low now here is the voltage input voltage that we want to convert the first guess will be mid scale and we will realize that we are too low. And then what we do is we make the next guess which is mid scale of this upper range. So, the next guess is here and we find that this guess is too high. So, we make the next guess which is again mid scale between this one which is here and then we find that this is the last guess that we have made we report that as the value. So, obviously, this was the input at this is what we have reported and this difference is the error in representation because of the discrete width the width is just 3 bits. If I wanted a better representation then I need at least one more bit which means 16 steps if I want even better than 32 steps. So, this is basically how a successive approximation ADC works and in the microcontroller kit that we are going to use to perform this experiment. All these components are available the D2A converter is available connected to a comparator where you can compare the guessed value with the actual value and obtain the output which will say the guess is too high or the guess is too low. And the programmer here that we have shown is actually the microcontroller. On the microcontroller you can make a guess send that guessed value to the D A cut water compare it with the value which you want to measure and then make a decision whether the value was too high or too low and make the next guess make the next guess. So, in your ADC experiment that we are going to perform in the next lab we will give you this opportunity for those who would desire to do that to build what we typically called a software successive approximation ADC using a DAC. So, it uses a DAC and the microcontroller and a comparator and runs through the successive approximation algorithm in the software. So, successively makes guesses subsequent bits are tested and so if you look at this here we are testing this bit the one on the what we call most significant bit here we are testing the next bit here we are testing the last bit the least significant bit. So, you are actually doing it by testing bit by bit. So, the successive approximation ADC output is typically whatever guess was the last guess made given to the D A converter is the digital output. Now you see that we have gone through steps in this case we have gone through three steps if it is an 8 bit converter how many steps we will go through 8 steps. So, how do we go through these steps? To go through these steps we have to use one type of digital circuits which are which are synchronized where things happen synchronized with the clock with the edge. So, they are basically synchronous digital circuits and that is why though it is not shown here a clock forms of course, it is here in the programmer it forms a most important component of an ADC and this is the clock which decides how quickly the ADC is going to make a conversion. So, we keep on increasing the clock speed we can get faster and faster ADC conversion, but yes. So, now the question is that what imposes the limit to which we can keep on increasing the clock speed. There are several steps in the series. The first one is the digital circuitry inside this. So, there is a limit to which the digital circuitry can be pushed the delays inside this, but that is usually very small it is in nanoseconds that is usually not the rate limiting step. The next comes the D A converter. The D A converter is something which we will look at the D A C a little later which takes a little time to convert. Typically it has got what is called a settling delay. The output voltage that it produces takes some time to settle. So, we cannot do go faster than that. So, there is a settling delay of the D A converter and then comes the comparator. There is a the comparator is comparing this voltage with the actual analog voltage and it is producing an output the comparator itself has a settling delay. So, all these delays cascaded together is the fastest that we can clock it and that will vary from ADC to ADC that will vary from implementation the technology. So, let us get a value of the range of physical time in conversion in successive successive approximation ADCs. Typically the simplest ones may take 50 microseconds for a conversion and the fastest ones may take may not be successive approximations, but others may take around 50 nanoseconds for a conversion. Typically successive approximation ADCs large variety of these will vary from 1 microsecond to 50 microsecond. But since the number of clocks depend upon the width of the representation of the word the conversion time will also depend upon the width of the conversion. Is it 8 bits, is it 10 bits, is it 12 bits, is it 16 bits? So, 8 bits will obviously be faster than 12 bits, which will be faster than 16 bits. Typical specifications of ADCs would be the range of input voltage, the range will also decide the resolution of measurement. It will be the input impedance, it is an electrical property of the ADC and it is not something that we want to discuss here, but it is important. Typically it ranges from kilo ohms to mega ohms. The accuracy of the ADC, the nature of successive approximation is such that you will always have a half LSB error, because the last test that we made there was some error and that error in worst case would be half LSB. So, what is the accuracy in terms of what is the half LSB in terms of percentage of full scale that is the accuracy and the conversion time. The format of digital output is also important. Many times it is what we call straight binary, sometimes it is two's complement, sometimes gray code depending upon different types of ADCs. So, here we come to we have finished with the ADC and let us just go back and try to consolidate what we have learnt. And ADC is this that we have here a black box where we give an input voltage, we specify the voltage range. This specifying the voltage range is usually done by providing a analog voltage which is called reference voltage. Most often the input voltage range is of the same magnitude as a reference voltage. So, if the reference voltage would be 5 volt the input range will also be 5 volt, where is 2.5 volt will be 2.5 volt, but it is not necessary. There may be a different relation also it could be 2 input could be 2 times the reference voltage, but there is some way whereby we specify the range of the ADC. Then it is not shown here, but the clock speed the speed at which it will do the conversion the clock speed. And there are some ADCs which will have an option that you want to do a 12 bit ADC conversion or an 8 bit ADC conversion. A single ADC could be used for both purposes 8 bits or. So, if you want low precision, but you want much faster measurements the same ADC could be used for 8 bit conversion. So, there would be an option of choice of the output width. And then in an ADC you have a start conversion, you give the start conversion pulse. And when the and then ADC becomes busy it starts converting when the conversion is over it gives you what is called an end of conversion signal. And when the end of conversion happens the sample and hold knows that end of conversion has happened I should go to sampling mode. And if there is a microprocessor or a micro controller it knows that the conversion is over I should read a read a value and go ahead and ask the ADC to make the next measurement. And the other aspect in an ADC in digital measurement says that whenever we are having a real signal and we are digitizing it and we want to reconstruct it. We may be off here which is the error because of quantization and we may be off here also in the time domain in this axis because of the sampling rate. The sampling rate is finite and the sampling rate is related to the signal frequency components. And if it is not right you may end up actually reconstructing the signal with wrong frequency component which never existed at the input. The number of frequent the number of point sampling points should be typically related to the highest frequency at the input of the signal. And you can see that as you keep on reducing the sampling rate you keep on getting more and more erroneous representation. And at one point you can get absolute aliases which never existed in the input signal. Now let us go to the DAC. A digital to analog converter is converse it is just a reverse of ADC. And just like an ADC characteristic is like this that you have an input voltage and you get a digital representation. It will be a reverse the digital input would be here the x axis would be the digital input and the y axis would be the analog output. But remember it will still be a staircase kind of a transfer function it will still be steps. You will only be if the digital input is 8 bits you will get an analog value here, but analog value will vary only in 256 steps it will not be continuously varying. So, a digital input gives you a corresponding analog representation if you are using a DAC. So, digital to analog converter is used to produce an analog voltage which is related to a proportional to the digital word that we are feeding and its characteristic is inverse of that of ADC. And this is where the DAC fits in the real world computer output is digital goes to a DAC becomes analog it can be used for controlling or whatever variety of purposes. Now how does a DAC work? How is a DAC built? Now interesting part of the DAC is that it is very different from an ADC you do not have do not seem to have much of digital electronics inside you have a op amp you have some resistors the op amp has been made into a summing amplifier. I am sure you are all familiar with the op amps some point you read. So, it is a summing amplifier and they are in no is it does not matter it is really very very simple to understand. This op amp is a device which has got a very large amplification factor if you do not put it in some kind of a feedback circuit and the moment you put it into a feedback circuit it starts behaving as an elegant device where the input and output properties are represented by very simple mathematical equations. For example, in this device that we have this point that I show here is called a summing point any current which comes here gets added. So, if current is coming from here and here and here and so many input sources it will get added and it will start flowing through this resistor. So, basically this is an adder which adds currents and the voltage at this point is equal to the voltage at this point. So, if this point is at ground potential or zero potential this point is also at zero potential or ground potential and hence this is called a virtual ground. So, what current will flow into this will be governed only by the voltage at this point and the resistor. So, supposing I give at this either a voltage of 1 volt or a voltage of 0 volt the current which will flow through this will be when it is on 1 by R 1 by 2 R 1 by 4 R or 1 by 2 to the power n minus 1 R and when it is connected to zero the current which will be flowing will be zero because you have zero here and zero here. So, really speaking this produces what is called binary weighted current sources ok. The resistors here are binary weighted this is R 2 R 4 R and in a DAC if you want to produce a if you want to convert a digital value to its analog equivalent we simply give the digital word to these switches a 1 means the switches on or connected to 1 volt a 0 means the switches off or connected to 0 volt. So, if I am giving a digital representation of the minimum least significant bit then only this will be on these will be off which means current will be flowing only through this or if I am giving the digital representation of only the most significant bit high then only one of these will be on the most significant bit will be on and only current will be flowing from this. So, this is MSB this is LSB over here. So, obviously depending upon how many of these bits have been switched on the current will flow and it will get added and the output representation here that we have will be a voltage which will be directly related to all the ones and their weights. So, this will produce a output voltage which will be related to the digital representation at the input. Just like a DAC just like a ADC had a range and you had to specify a reference voltage to set the range the DAC also apparently has can have a range. So, if you have 256 bit 8 bit DAC with 256 steps you can set the range whether the 256 steps will be 0 to 5 volts or 0 to 10 volts or minus 5 to plus 5 volts that kind of set by similarly setting here a reference voltage. So, you can also decide the range of the DAC conversion. Now, one of the issues with a typical what we call weighted resistor DAC is that it requires precision of resistors over the entire range which is usually very hard to get and these such DACs are not very common. Though the DAC that you are going to use for your laboratory experiment is actually a weighted resistor DAC, but the ones which are more common are called R2R DACs we are not going into that. The specifications of the DAC are essentially its resolution which will be the bits the linearity which really says that if the input changes linearly the output should also change linearly. It should happen I mean one would one would say why it should not happen why it should not be a linear change it really is not. So, most of these systems will have some nonlinearity into it. So, DACs will typically have nonlinearity of plus minus half Lsp. The accuracy the settling time DAC will also have a settling time problem from the instant that I want to make a change the output will take some time before it settles and this how much time will it take to settle within half Lsp is called the settling time of a DAC and that may be significant. For example, the settling time of a DAC may be the DAC that you are using is 100 nanoseconds. Now, 100 nanoseconds seems very small, but when you are working with very large frequencies that 100 nanoseconds is significant and this is only an 8 bit DAC the moment you go to 12 bit DACs this becomes worse you may get a 12 bit DAC typically with a 1 microsecond settling time 1000 nanoseconds and as the accuracy of representation or as the half Lsp size becomes smaller and smaller that is for the higher resolution DACs this settling time becomes larger and larger this is an important parameter for specifying DACs. And this is also something called temperature sensitivity of a DAC that is of course, true for all digital and analog devices and the DAC is actually an analog device. So, the temperature sensitivity of an analog device will get translated to this and it will it can mar its performance. Now, after having a look at the ADC and these DACs let us put them to some use and let us look at what is going to happen in the signal digitization and requisite construction experiment. Actually you are going to do this you are going to take a input signal may not be from a microphone may be, but perhaps from a signal generator sample it in an ADC and perhaps you can also use a sampling chip sample and hold chip outside if you wish to convert to your digital bit stream you can do something with it if you wish you can do a filtering of that or you simply routed back to the DAC and reconstructed and study that if you change the clock frequency or if you change the sampling rate what happens to the reconstructed data are you really getting those problems which I have just told. Can you find out by changing the clock frequency what would be the right clock frequency for an analog signal frequency for a given analog signal let us say 1 kilo hertz is a signal frequency or 10 kilo hertz is a signal frequency and you change your clock from 5 kilo hertz to 100 kilo hertz what is the right clock frequency for you that the DAC is giving you correctly reconstructed output. So, you should perform that experiment and this is one small detail about what is a clock signal a clock signal is actually nothing but a voltage which is varying with time 0 volts to maximum 0 1 0 depending upon the technology the digital technology that you are using the 0 and 1 will be defined in terms of that for example, the TTL would have 0 as anything below 0.8 volts and 1 as anything between 2.5 and 5. So, in a clock there are 4 things which are important it could be the low part of the clock it could be the high going edge of the clock it could be the high part of the clock or it could be the low going edge of the clock. So, things may happen when the clock is low or when the clock is high or in the positive edge or in the negative edge. So, typically in digital circuits sequential digital circuits they are sensitive to the edges only. So, things happen either on the positive edge or on the negative edge most of the circuits that you will be using will probably have will be sensitive to the negative edge. You have already used timer 555. So, we will not go through the details of this just to give you a brief overview you have you have already used. So, I presume that I do not have to describe how it works this is the stable multivibrator circuit that you will be using for clock generation which you have already used. Since you are going to change the frequency remember please note there is this resistor R A and this resistor R B you know that when the capacitor charges it charges through R A and R B and when it discharges it discharges only through this transistor and hence only through R B this transistor makes this pin 7 connects this pin 7 to ground and this discharges through this right. So, and the frequency depends upon both R A and R B. So, what you might be tempted to would be to change R A as well as R B. So, you might actually end up making if you make R A large it does not matter, but if you make R A small there is a small risk which is supposing you use R A of around 1 kilo ohm 1000 ohms and you use a VCC of 5 volts then when this transistor is on that is when the capacitor is discharging there will be 2 components of current flowing in this transistor the one which is the capacitor discharge current and the other one which is flowing from the power supply through R A resistor. So, if the supply is 5 volts this will be typically and this is 1 K this will be typically 5 milliamps 5 milliamps is fine, but if you reduce it further from 1000 ohms you reduce it to 500 ohms to 200 ohms to 100 ohms this will get damaged the transistor this transistor will blow. So, what I want to caution you is you if you want to change the frequency change R B or change the capacitor of C choose a value of R A which should be the smallest acceptable value I would suggest 1 kilo ohm or 1000 ohm and change only R B and C for changing the frequency ok. And this is the frequency relation which I am sure you must have used the description of the laboratory experiment is you have to make the 5 5 based clock generator measure clock frequency during the experiment the clock frequency may be changed by altering component values. You can also observe the duty cycle and keep that check that I told you that do not change R A only change R B. The ADC circuit output can be seen on the LEDs which are available on the you are you are going to work on a kit micro controller kit which has got the ADC and DAC also on the board. And there are there is a way whereby you can observe the output converted output of the ADC on LED. So, you should observe the output also set up the DAC circuit which is for which you do not really have to do anything there are some jumpers which have to remove that will route the converted ADC output to DAC. And you can observe the reconstructed output on your scope and you should find out what is the discretization error by giving a known input to the ADC. Now give a AC waveform to ADC reconstruct using DAC and see the effect of ADC sampling frequency. This is what you are going to set up eventually the function generator which is which will be your PC scope only output going to the ADC which is getting a clock which you will be wearing the output going to the DAC observed on a PC scope and compared with the original data. The PC scope has got two channels will be comparing these two right. So, that is about all if you have questions let us have them yes. I do not know the resolution of the ADC DAC inside the PC scope, but I presume that this will be at least 1 megabits I do not know somebody we can find out you can ask the TAs they will tell you. I think it will be probably at least 1 megabit maybe more no no no only successive approximation ADCs have a DAC as a part of them others like sigma delta they are based on a totally different technique and the integrating ADC is also on a totally different technique integrating ADC is made of like a DAC it is made of some integrators basically there are there are op amps inside. Any more questions regarding what is it that? So, you are all clear about what is going to be performed in the lab ok.