abstention seeing none there's no study sessions so let's take up the meetings next and excuse me the minutes next we have one set of minutes the August 17 2023 regular meeting minutes and I'd like to now take public comment on the minutes approval if you wish to make a comment via zoom please raise your hand if you are dialing via telephone please dial star 9 to raise your hand we have no one in chamber wishing to make public comment no hands raised on zoom and no email or voicemails were received very good then thank you very much that means the minutes will be approved as submitted that takes us to staff briefings and the first half briefing would you please introduce the first half briefing acting director McNeil item 5.1 thank you vice chair Arnone I'm members of the board I'm excited to introduce Claire Nordley to talk on the water supply update thank you good afternoon vice chair Arnone and members of the board I'm Claire Nordley and I'm going to be presenting the water supply update today on behalf of deputy director Martin is out today so I know you all have seen this graph many times this is Lake Hillsbury storage right now the storage curve is about 44,000 acre feet which is about 76% of the storage curve for this time of the year it is declining at a rate of about 1500 acre feet per week PG&E has filed a variance request to reduce their releases into the east fork of the Russian River from the mandated 75 cubic feet per second to 25 cubic feet per second and potentially lower actually to the minimum critical minimum of 5 cubic feet per second if conditions warrant it as of today though for hasn't yet responded back to that variance so therefore flows still haven't changed and they're under normal operating conditions here is Lake Mendocino so again reservoirs remain very full for this time of year which is great news and Sonoma water is expecting healthy carryover to the next water year which begins October 1st Sonoma water does have an existing temporary urgency change petition in place until October 15th which does allow them to reduce the minimum in stream flows to meet the biological opinion requirements and as you see here we're about 72% of the storage curve capacity and then finally Lake Sonoma again very full it's about 92% a full of the furrow enhanced storage pool and this is actually the highest storage level ever courted in for this time of year since operations began in 1983 so that's great news for us I also wanted to provide an update while I have the floor to describe our direct install program so this is a program that we launched just a few months ago to provide free high-efficiency toilets to customers along with high efficiency fixtures the RFQ to get responsive plumbers ready to install these fixtures was released in July and the deadline was August 2nd we did get six responsive plumbers which is great news including three local plumbing companies which is exciting so since June of 2023 about 1500 toilet installations have been pre-approved and those are being installed currently and that does mean that all of our phase one funding which is one point five million dollars have been committed at this time so a lot of money committed in a very short time so there's definitely customer interest in this program additionally in mid-to-late 2024 we are going to be receiving funding from a grant that we applied for through the US Bureau of Reclamation and we're going to be receiving an additional one point eight million dollars so we'll be able to install several thousand additional toilets also while I'm up here I wanted to provide an update on a new piece of legislation well the legislation was adopted in 2018 but a new rulemaking process for this legislation this is currently draft the legislation is called making conservation a California way of life and it basically directs the state water resources control board to adopt water use efficiency standards and performance measures for commercial industrial and institutional water use it requires that urban water suppliers meet a specific water use objective beginning in 2027 and we're actually required to start reporting January 1st of 2024 so that reporting deadline is coming right up despite that reporting deadline coming up this framework is actually still in draft and I'll be sharing through some slides on the draft regulations as they're currently proposed by the state board so this urban water use objective has several components different targets basically so there's an indoor residential water use target an outdoor residential water use target a commercial industrial institutional dedicated irrigation meter target and a water loss threshold and then there's also several ways in which we could adjust our target for example if we had you know a large percentage of our service area supplied by recycled water or direct potable reuse for example the indoor residential standard is based on a gallons per capita per day target you can see currently through 2025 that standard is at 55 gallons per person per day and drops down to 42 in 2030 that standard is multiplied by our population times 365 to give us this residential budget just to clarify this target is not going to be studied under an individual parcel basis so we don't plan on confirming that each one of our customers is meeting this target but it's an overall target for our entire service area there's also a target for outdoor residential use and our dedicated irrigation meters both of those are based off of plant water factor how much water the plants need the irrigation efficiency the landscape irrigation area effective precipitation and an outdoor landscape factor that decreases over time so the square footage of irrigated area for the residential side was provided to us by the Department of Water Resources they flew over our service area in 2018 and provided aerial image to us which provided us square footage for the dedicated irrigation meters we've actually been measuring for many years all of our dedicated irrigation meter sites so we would plug that into the equation and that would be our outdoor budget again we're not looking at this and we're not going to be enforcing this on a parcel by parcel basis it's an overall target for our entire service area there's also an additional water loss standard this is based on system specific standards such as our gallons per connection per day of water loss the number of connections that we have and we've been submitting this data to the state for many years now based on another piece of legislation Senate Bill five five five so this just continues that piece of legislation there are also performance measures for our commercial industrial and institutional customers so beginning in 2025 we are going to be required to identify all disclosable buildings in that sector which means that they have more than 50,000 square feet within their commercial building so we have to identify those customers and then we have to provide the monthly water use data in a format that matches an energy star portfolio manager style which is an energy efficiency reporting tool that was developed by the CEC then beginning in 2025 the ban on irrigation of non-functional turf for commercial industrial institutional landscapes will take effect this is already currently in place just to note through the governor's drought declaration and it doesn't expire until June of this coming year so this would just be making that current stipulation permanent then in 2026 through 2030 there's various different things that we also have to achieve we have to classify each one of our over 4,000 CII customers into 22 different categories that match the energy star portfolio manager categories and then within each one of those categories we have to target the top 2.5% and the top 20% of water users within those categories and offer them specific water use efficiency programs that match their classification type we also have to identify all of our CII large landscapes that have mixed use meters and either ask them to install a dedicated irrigation meter or employ in lieu technology for their large landscape so sort of the next steps is that this notice and the regulations were released a month or so ago in August there is going to be a public workshop on October 4th that we do plan on attending and making comments at public comments are due to the state board later on in October and the state board is set to finalize these regulations in mid to late 2024 obviously we are reviewing these regulations currently and we're determining our comments we are going to be presenting at the October 4th state board public workshop and well of course we'll continue to follow the rulemaking process and keep you all informed I'd be happy to take any questions thank you very much for the presentation do any of the board members have any questions I have a couple of questions first of all at least with the indoor residential budget there's specific numbers associated with it already and I'm wondering where we stand currently with regard to our level of usage and whether we have to make many changes to meet the potential new rules yeah we're in pretty good shape so depending on what year you look at it for determining that compliance and what methodology specifically would you use calendar years or billing years or sorry billing days or calendar days we're somewhere between 45 and 49 gallons per person per day for single family residential so we're right in that range that they're requesting and I should have mentioned as well that the goal for this legislation is that we meet the overall objective and not necessarily each individual target so we could be over say in the indoor target but as long as we're lower in another target and the overall objective is met then we are in compliance oh great okay the other question I had is that seems to be some significant monitoring and follow-up requirements at least for commercial properties and I'm wondering how much of a burden that's going to place on existing staff and resources that's a great question yes I do think that there are quite a lot of reporting burdens for that CAI part specifically and unfortunately anytime you're focused on reporting you're obviously losing time and actually working with customers to help them save water so that will probably be one of the comments that we provide to the state board to hope that they simplify the reporting requirements so that we can focus on saving water instead of just reporting excellent excellent excellent any other questions yes thank you you triggered some in me I appreciate that I have a couple questions the first is the outdoor measurement where aerial photographs were taken in 2018 so that is kind of used as the baseline is that what I'm understanding the thought was that DWR is planning on flying over our service area every few years every five years depending on what their budget allows to ensure that they're capturing new landscape as it goes in and as our landscapes change obviously we would want that to be flown as frequently as we could because people change their landscapes routinely but we are sort of beholden to DWR's budget to make that flyover happen right okay yeah because I know things change a lot there are programs out there to remove grass and put in native play you know there's a lot of stuff going on regularly so thank you the other question I had was around the CII performance measures so it was for a commercial property with 50,000 square feet of building or of footprint building so yeah excluding landscape great thank you thank you the other questions all right then we will now take a public comment on item 5.1 if you wish to make a comment via zoom please raise your hand if you're dialing in via telephone please dial star 9 to raise your hand see nobody in the chamber speaking secretary Montoya do we have anybody online there's no hands raised on zoom and no email or voicemail public comment was received thank you very much that should conclude item 5.1 as I previously thank you very much again for the report as I previously mentioned we are going to postpone consideration of item 5.2 so that moves us to the consent calendar do any board members have any questions about the item on the consent calendar okay then may I have a motion to approve I'll move the consent calendar I'll second that motion thank you it's been moved and seconded so let's now ask for a public comment we're taking public comment on the consent agenda if you wish to make a comment via zoom please raise your hand if you're dialing via telephone please dial star 9 to raise your hand and again I see nobody raising to make a comment here secretary Montoya and there are no hands raised on zoom and no email or voicemail public comment was received all right thank you very much if that's the case then can we please have a roll call vote on the adoption of the consent calendar yes board member right hi board member Walsh hi board member Barthelot hi and vice chair Nune hi and the consent calendar passes unanimously thank you that takes us to item 7.1 acting director McNeil would you please introduce that item yes thank you chair Arnone I'm happy to announce Deb Lane coming to present the recommendation to adopt proposed ordinance amending Santa Rosa city code chapters 14-21 water waste regulations good afternoon vice chair Arnone and members of the board I'm Deb Lane and I'm here to discuss our proposed revisions to the water waste regulations the regulations were originally adopted in 1999 and were last revised in 2007 to include recycled water things have changed in the past year since the last revision and we feel there is a need to modernize the water waste regulations you'll find the revisions that we were are proposing in the red line copy of the of the regulations that were included in your package and you can see here the current definition of water waste which is potable or recycled water use in outdoor areas resulting in runoff or breaks or leaks in the potable or recycled water delivery system the city can issue written warning through the director of Santa Rosa water and the city may disconnect water service so why revise these regulations AMI and the hourly data that we now have has increased our ability to identify continuous use which is typically and often leaks our current water waste regulations are missing acknowledgement of the continuous use exceptions for enforcement based on adverse impacts on health sanitation and safety and an option to enforce the commercial industrial institutional accounts CII without disconnection it's also missing a defined appeals process so CII shut off is often not feasible there are essential services in our CII sector that need to continue operation we have schools police fire grocery etc. and shut off could also disrupt local economic activity so we need a mechanism to motivate the CIA customers to resolve their water waste this is an overview of the proposed revisions all go into a little more detail on each one and this is a result of reviewing other cities regulations like Petaluma and a year long process of reviewing a review and discussion with the city attorney's office so we have it's applicable to all customer classes CII multi-family residents single-family residents we have defied redefined water waste and added an escalating penalty although the fine would be applicable to every customer in practice we plan to primarily use this to enforce the water regulations water waste regulations for non responsive CII customers we've clarified the authority to disconnect added a process for requesting exception and a process for appeal I already went went over the current definition of water waste you can see it's a very basic definition it doesn't address equipment malfunction that can cause water waste especially in the CII sector and it doesn't put a time reference requiring the customer to find and fix the problem here's our proposed definition part a stays the same but with part B it's the escape of water through breaks or leaks or due to an equipment malfunction within a customer's plumbing or private distribution system for any substantial period of time within which such break leak or equipment malfunction should have been discovered and corrected so we've added that equipment malfunction and also a time reference requiring the customer to find and fix the leak so this is the waterways process that we currently follow for all of our customers we plan to continue to do so and provide support to every customer once staff identifies irregular use we make multiple attempts to reach the on-site decision-maker this is easier for single-family residents but when we get into CII the the billing contacts are often not the same contacts that we want to find at the facility so we do our due diligence to track down the right person and you know when we do we they they often most often respond when it's the right people so the billing the billing the bill can go out of state somewhere to a billing service so we do extra work to make sure we're finding the right person and that's very successful for us we offer a water smart checkup we provide ongoing technical analysis and support and if we get to the point where the customers being non-responsive then staff we still continue to make phone calls we send emails we a series of warning letters and door door tags before we ever disconnect service the process can take up to six weeks so customers have ample time to find and fix their leaks and disconnection is only for single-family residents we haven't disconnected CII customers and we don't disconnect any customer who's actively trying to find and fix the leak so this is the proposed penalty process should we be able to enact an administrative fine for a non-responsive customer as I mentioned it's applicable to all customers but in practice we only plan to implement this for CII and after staff have made many attempted phone calls and emails if the customer is still unresponsive we would follow the process as outlined in the revised regulations so the first violation would be a written warning the customers in violation of the regulations and has one week to respond or they will be assessed a $100 fine a letter that letter of warning will be signed by the director of Santa Rosa water or their directors designee and the customer can apply for an exception we feel this is going to be a rare situation and I'll say a little bit more about that in a moment so if staff receive no response after a week after sending the official warning letter then the formal notice of violation process would begin that second notice of violation letter would go out the customer has 72 hours to respond or a hundred dollar fine will be imposed and if we don't hear back in 72 hours the hundred dollar fine starts the third notice of violation letter goes out customer has 72 hours to respond or a $200 fine will be imposed if 72 hours goes by no response then that fourth notice of violation would go out they've got again 72 hours to respond or a $500 fine will be imposed and that $500 fine will continue every 72 hours if we don't hear back from them so this is definitely a last resort and all the customer would need to do is contact staff to try and find and fix the unexplained continuous use to stop the fine process process no matter where they are in the process the notices must be signed by the director of Santa Rosa water or the directors designee and the customer has a right to appeal the final decision so water waste fines are are common and this is these are some of the local and other cities and water districts that we've researched and looked at and you can see our proposed fine structure is in line with industry standard and we do anticipate a low need to implement the fine process with single family residents we are getting about 500 reports of water waste per year that's resulting in approximately eight shutoffs per year which is 1.5% of the cases so with CII we get about 40 reports of water waste per year if we extrapolate that 1.5% that's fewer than one customer per year so this is the the current definition of the authority to disconnect the director of utilities may issue a written warning to anyone who violates the provisions of this chapter if a customer does not correct the violation within 15 days of notification or or such other time as specified by the director the city may disconnect potable or recycled water service the proposed definition the part a is outlines the administrative fines that I've already described and under section B it clarifies the authority to disconnect as outlined in city code chapter 14-04 potable water and recycled water service so the this is a new section that we're proposing to add because disconnects disconnection or an administrative fine could have an adverse impact on health safety or hardship on the customer or the public so the customer may request an exception to a water waste regulation violation in advance of receiving a notice of violation they have that one week to do so the customer must submit a written application explaining why the exemption is justified the director of water or the director's design may grant the exception if necessary to avoid adverse impact on health sanitation safety of the applicant or public and or avoid undue hardship for the applicant or the public and this decision may be appealed in writing to the board of public utilities so we can identify customers with exceptions or they can self identify and then staff will assess case by case basis I think a good example of this will be schools or hospitals that are essential services and the type of customer we would grant an exception for it's likely that most of these exceptions will grant our situations where the customer has already been working with us and they've been finding and fix fixing every leak they can but there's still some unexplained continuous use I think another good example to think about let's say we have we have old school facilities here one big meter domestic meter it might you know go to many buildings there are no isolation valves it's hard to isolate some portions of the main line they can't cut in new valves and they've worked with they're working with us regularly and they they found numerous leaks and the continuous use they just can't trace out the last bit of it and they continue to work with us so this is the proposed appeals process any customer may appeal the final decision of Santa Rosa water staff regarding violations to the director of Santa Rosa water or the final decision of the director of Santa Rosa water to the board of public utilities the customer must submit a written notice of appeal and should we receive your approval today these are the proposed next steps October 24th we will go to city council to conduct a public hearing on the revised regulations November 14th city council will conduct the second reading of the regulations and December 14th is the proposed effective date which is 30 days post second reading so it is recommended by the water conservation who this is subcommittee yes and the Santa Rosa water San and Santa Rosa water that the board of public utilities by resolution recommend the city council adopt the proposed ordinance amending Santa Rosa city code chapter 14 dash 21 water waste regulations to include administrative fines provide an exception and an appeals process and make other clarifying changes and that's it if I if there any questions I'd be happy to answer them thank you for that presentation is Lane are there any questions for board members board thank you I guess my question is around I'm I'm thinking back when I was a single mom with three kids and if something had gone wrong with my outside plumbing connections I probably wouldn't have had the money to fix it and that would have been very challenging even in a week and then adding on more money to the fines as you know I continued to fail to fix it because I couldn't afford to do so and I don't know how to do it right I mean I know we're looking at eight or one and a half percent of the population who actually get shut off but is there is there any consideration for for people like that right well first of all situation we don't plan to use the administrative fine for a single-family residence customer okay and we work at great we go to great lengths to work with the customer that would have been in your situation okay to provide and you know we would come out and do an audit try and help figure out what's going on and any process of you know just finding the the easiest solution that we could you know try and identify right away it often isn't that complicated and even if it was a difficult situation the process of going toward any kind of violation takes many weeks so it does offer the customer time to figure out how to deal with it okay are there resources to help them figure out how to deal with it like I'm just curious is you know are they just kind of on their own or well I mean a half the two at our own horn for a minute I think I'm pretty good at what we do we're not plumbers we're not leak detectors but but we go out and and offer a lot of expertise to try and figure out and isolate at the best best we can of where is it is it maybe is it a leaking toilet is it something in your irrigation system you know hopefully it's going to be something like that and not a mainline that's under the driveway that's what we all don't wish for so right we do our best to try and help with that the AMI data really helps us understand what's going on when and in the worst-case scenarios you know they need to get a plumber out or maybe a leak detection company thank you sure any other questions from board members I had similar concerns as I mentioned in the subcommittee and I I'm pretty much taking staff at their word that this is not an assault on the single family but trying to control CII which we have no real way to do that without shutting their water wall off and when which point you as you point out you can't do that in many cases so yeah I mean I I've been around a long time in the in the department and I know the water use efficiency division is very conscientious and very helpful to customers but the situation is brought out there are people that are somewhat dysfunctional or have other issues and it's I don't know it's not our business to write grants to solve these people's problems but at the same time it's it's it's just a that's just a it's a troubling problem and I guess I'm what I'm saying is I'll take you it's a word that you're not gonna go after our single family for issues that might seem unsolvable by them that's that's what really I want to say I think yeah I'd also like to add that we have a number of programs in the department to support people of low-income we have the help to others program and we also in the case where if you do have a significant leak it can become very expensive very quickly and we do have a leak forgiveness program to help individuals but we do need to by law get these leaks fixed and this these are just mechanisms for staff to to meet those regulatory requirements and as board board member Wright has mentioned and as has Deb Lane we really do our best to try to work with our customers to support them and to prevent them from getting into a position where they can't afford their water and that's really where leaks really hit hard and if you're paying a lot of money for water and most of that isn't even what you're using it begins to become more expensive for you so this these tools that we're proposing for the council really help staff to help individuals get there we're identifying leaks earlier we're providing service to our customers so that they aren't we're wasting their limited resources on water that isn't really beneficial to them so I appreciate the concern I do think that that we are doing everything within the rules that we have to support all of our customers and businesses as well so just put that out there for your consideration any other questions from board members I I I guess I have a slightly different view on this and the reason I'm going to be voting on voting to approve this is not because there's a plan to not enforce this against single family residents I'm uncomfortable with adopting or recommending the adoption of an ordinance that we don't plan to use I think if the authorities in there to use power then that powers got to be dealt with and the reason I'm going to support this is because I think having that power has been dealt with with appropriate checks and balances I mean the whole issue of exemptions wasn't in the prior ordinance and and so now they have undo horde hardship exceptions that can be applied there's an appeal procedure that's been adopted so I I'm treating this as if it can be enforced against single family residents but given the new protections and checks and balances have been provided uncomfortable with that possibility that it that it would be enforced I've also had personal experience having had a leak in my backyard that we've discovered an irrigation leak we discovered it we called our contractor they came in to fix it as he was finishing the job I got a call from the city saying we detected a leak in your parcel and and you know so we're calling to help you fix this and I said well I think we just fixed it because we just had a guy out here to repair the problem and they said oh let me check so they had the ability to in real time check whether or not there was a continuation of the leaking water and said oh yeah there we see it it stopped you're done way to go so I'm from personal experience I know that you're very proactive in assisting single family residences in identifying leaks I'm glad to hear that there's programs to to to provide additional support and and I plan to support this as a as a more in a way more protective of users because before all we had was one option you know turn off the water now we have additional options that can be used with fines and other programs so I I like the way it was presented and I plan to approve it if I am even a motion to do so after we asked for well first we need a motion then public comment I guess yes right and I yes and I do believe assistance again briefly here I'm sorry go ahead but can you all hear me yes thank you I just wanted to speak somewhat to your last point and to also try to modify some of the concerns by the other board members you definitely recognize the intent in some of the language regarding the exceptions and the appeals so while I would agree that I believe staff is going to use this with the best of intentions to enforce on the high water wasters and I think the the main focus will be CII customers that I personally advise staff that it best to have the rule apply to all classes of customers and leave the enforcement discretion to staff however as you rightly point out that is counterbalanced by the exception and appeals which allows the individual customer to either proactively or after the process starts to say look I'm doing what I can I I can't do any better than this or for this and that reason I need you to grant me an exception and the the initial consideration will be done by staff by the director of water the designee but ultimately because it can be brought to the board of public utilities if some if staff wasn't using the rules in the way that the board intended when they if they support it there's always that final check of being able to go to the board of public utilities a kind of major case so I just wanted to kind of broadly speak to all the comments that were made by the board of thank you for those comments council any other questions by board members do I have a motion to approve this recommendation okay I'll a move that the board of public utilities by resolution recommend the city council adopt the proposed ordinance amending Santa Rosa city code chapter 14-21 water waste regulations to include in administrative fines provide an exception and an appeals process and make other clarifying changes thank you member right second that thank you member Bartholome we are now prepared to take public comments on item 7.1 if you wish to make a comment via zoom please raise your hand if you're dialing in via telephone please dial star 9 to raise your hand I see nobody in the chamber raising to comment secretary Montoya and there's no hands raised on zoom and no email or voicemail public comments were received thank you very much would you please do a roll call vote on the resolution yes board member right aye board member Walsh aye board member Bartholome aye and vice chair Anani and that passes unanimously thank you for the presentation again okay so now we are at the point in the agenda where we will take public comments on non-agenda matters so that's item 8 if you wish to make a comment via zoom please raise your hand if you're dialing in via telephone please dial star 9 to raise your hand and again this is on non-agenda matters nobody in the chamber is raising to speak secretary Montoya no hands raised on zoom and no email or voicemail public comments were received thank you that brings us to not item 9 referrals there are none I see no written communications either so how about subcommittee reports any subcommittee reports yes so regarding the water conservation subcommittee which met on September 12th the first item was a recommendation to discontinue the recycling hot water pump rebate program to a lack of realized water savings low customer participation market availability of eligible products and other challenges the committee unanimously recommended that recirculating hot water pump rebate program be discontinued and the second item was presented was the presentation we just saw of the proposed revision to the city code water waste regulations which you which we heard at today's board meeting the subcommittee reviewed the proposed changes provided feedback to staff and unanimously recommend the bpu consider and recommend to the city council the adoption of the proposed revisions to the city water waste regulations and that's my report thank you member right um are there any individual board member reports vice chair noni if we could do public comment for the report out on subcommittee reports please thank you for catching that omission this is now the time to give public comments on the subcommittee report if anybody would like to do so please make a comment via zoom by raising your hand if you're dialing in by telephone please dial star none to raise your hand nobody in the chamber secretary montoya no hands raised on zoom and no voicemail or email public comments were received thank you very much is there a director's report for us today acting director neal yes chair anoni i do have uh two items to present to the board today i'm pleased to announce this announce that the city of senorosa and the sonoma marine saving water partnership has been awarded two awards through our participation in the institute of local government's beacon program this city of senorosa has been actively participating in the beacon program since 2013 reporting on the adoption of voluntary policies that promote sustainability and tracking activities that reduce greenhouse gas emissions and save energy the city of senorosa will be recognized with the platinum level 2023 beacon spotlight award for achieving a 21 percent natural gas savings compared to our baseline year in 2013 in addition to the spotlight award senorosa water has been awarded the 2023 beacon leadership and innovation award for our cross agency collaboration with the sonoma marine saving water partnership during the recent 2021 to 2023 drought the partnership's drought is here save water campaign was heavily augmented by senorosa water and the campaign was recognized for providing a unique yet simple and cohesive drought message throughout the russian river watershed that resulted in measurable water savings the second item is uh that um our current water and sewer rate schedule was approved by city council on may 25th 2021 the current rate schedule began july 1 2021 and concludes on july 1 2024 we are beginning the process of developing the next multi-year rate schedule for fiscal year 25 through 26 through 29 30 the first step requires hiring a consultant to compile and complete a full rate study to assure rates are designed to meet all regulatory requirements of proposition 218 we issued a request for proposals on august 17th and it closed on september 14th over the next several weeks staff will be evaluating the submitted proposals and anticipate making a recommendation for a contract award to the board likely in november and beginning work with the selected consultant sometime in december the development of the report and draft rate schedule is estimated to take one year to complete staff will review the proposed final report and new rate schedule with the budget reviews subcommittee of the bpu and the bpu in detail prior to the bpu's recommendation on the rate study and new rate schedule to the city council the council will review and provide direction in study session prior to the proposition 218 notice being sent to all water and sewer customers we are planning to hold a public hearing at city council to consider adoption of the new rate schedule in march 2025 and the new rate schedule would be implemented on july 1 2025 that concludes directors thank you for that report we will now take public questions from board members about the report we will now take public comment on item 13 if you wish to make a comment via zoom please raise your hand if you are dialing in via telephone please dial star nine to raise your hand nobody's in the chamber and miss secretary montoya there are no hands raised on zoom and no email or voicemail public comment was received very good that concludes our business for this meeting today so thank you all for your participation and that will uh we'll adjourn the meeting


Japan and Korea. Over the past couple years, the world has fallen in love with their music, movies and media. With a combined GDP of 6.6 trillion dollars, both are powerhouses in this world's economy. Together, they have a combined population of 177 million people. Representing 2.2% of the global population. But what if Japan and Korea were to somehow vanish? Today's video is sponsored by Bokksu. What is Bokksu? You know that Japan is great. But you know what also is great? Snacks from Japan. And if you're like me and you live in America, Japanese snacks aren't exactly selling on every street corner. But that's where Bokksu comes in. Bokksu is a subscription service that will send you delicious yummy treats shipped straight from Japan. And what's cute is they come in monthly themed boxes. So I'm actually really excited that it's April because, well, I got the best box. April is spring, so this Bokksu is all cherry blossom themed. Bokksu is great because every month you have a new box of treats, candies and tea delivered straight to your door. So let me help you out. Get 10% off your own authentic Japanese snack box from Bokksu and save up to $47 using my code and link in the description box. So this also supports my channel, so you're also helping me. Enjoy! For the first time in its history, South Korea's population has fallen and Japan is already on its ninth straight year. Just last year, Japan's population dropped 487,000. Is it possible for a country to go extinct? First is the incredibly low birth rate. Korea leads the world with the lowest birth rate at 1.0 which would mean that the expected number of children born per woman in her childbearing years is only one child. Japan isn't far behind at 1.4 for comparison, the world's average is 2.4. Raising kids is expensive especially in Japan and Korea from childbirth until adulthood estimates range from 250,000 to 500,000 and it's true that the single life is easy, at least monetarily. Why spend thousands of dollars a month on another human being when you can spend it on yourself? Sometimes you just gotta look out for number one. With Japan being the 8th most expensive country in the world and South Korea being 16th, children just not a viable option sometimes. In fact, about 15% of Japanese men said they don't want children which is up 8% from 10 years ago. Additionally, the work environment makes it very stressful to find a partner. Japan and Korea are both notorious for hard work environments.  South Korea ranked 3rd among all countries for most hours worked and if you're in the office all day working, how are you supposed to meet anyone? Maybe there's a reason dating sims are so popular in Japan. Hello, I'm David Koon. Lastly, people just aren't dying. What I mean is that Japan and Korea are just getting older. Thanks to modern medicine, a clean diet and healthy living, by the two countries The life expectancy is much higher than the rest of the world with Japan and Korea averaging 84 and 83 years, respectively, taking the number one and three spots. Next step, immortality? When I was first in Korea in the 60s and 70s, Korea was very, very big on small families, on ZPG. Zero population growth. And they had the slogans all over, have one child, have two, and raise them well. And that propaganda really worked well. Everybody thought, well, two children. Now they're saying they're encouraging people to have more children and it's not working so well. People aren't having more children. But I think the first phase of this was the population control in general, which worked out to be fairly effective, but now it's too effective. Well, long term, if Korea continues on this pace of not marrying, not having children, the economy can really decline. Economies are built on growing populations. And if the economy starts to decline, it could be trouble for everyone. I think it's going to be a phase. I think and I'm hopeful that in a short while, people will see that this is a dead end street and that really people, number one, are happier in family groups. And number two, it's better for society that they have children and the society can go on and prosper. So what needs to be done to ensure that Japan and Korea don't disappear? Japan has tried several government measures to increase their fertility rate, like building more nurseries and funding more childcare services. Japan even has plans to invest millions of dollars into a matchmaking project that uses AI. I'm guessing this is like some high-tech government-funded Tinder or something? Well, for me, it's an easy fix. We just need to hire the casting director from Crash Lightning on YouTube oversee the whole program. All the single men and women would be married within 16 episodes. So what's going to happen to Japan and Korea if their population continues to decline? And what needs to be done to fix this problem? Is it a problem? Maybe Thanos was right.


Everybody Matt here for late and sports cards are up in 2022 Panini contenders football hobby six bucks half case break number 53 pick your team We have Andre v. Saints and Margie Falcons Texans Kato H. Dolphins Cowboys Charles a bucks Browns Colby C Ravens Jags See Hawkins Seahawks Isuke M Titans Felix in Cardinals John K Eagles Kevin S Steelers Jets Kyle M Niners Lou F Broncos Mike K chiefs and commanders Minkou K Panthers Next bar in a Patriots Richard G Raiders Ryan F Bengals Chargers Sean P Vikings Thomas R. Bill's Lions Packers Colts Giants and Bears William B Rams. All right, let's do it 2022 contenders football hobby Just getting the checklist pulled up here. It's game day ticket to 99 Ricky Williams Brady, this is Titans Playoff ticket auto to 99 Hassan Haskins on card.  All right power players Derwin James, and this is Giants rookie auto Micah McFadden Michael Vick my homes James Cook rookie of the year Pulled like a two-card pack. It's a one-card pack gladiators Ray Lewis All right, I Mean Regular base and contenders isn't really sought after so you probably do that across the board Super Naturals TJ Watt That is Justin Jefferson This one called die-cut Justin Jefferson Vikings and Debo Contenders yeah My homes and Kelsey Yeah, when you mentioned something there's a rookie auto Raiders Chase Garbers When you mentioned something yesterday about it, I didn't have any clue what you were talking about Today Charles Woodson commanders rookie auto Colt Turner Herbert and Williams. What's up, Joshua. How's it going? What up, Josh? How you been?  This is chiefs rookie auto Chris all the dokoon Something looks like he's in a Steelers uniform Signed by the chiefs South Dakota State round numbers bills and cults dice Yeah All right, I'm gonna roll a single die for these Unless it's an auto relic or a one-of-one we'll do top one two three bottom four five six That is five duels go bottom Yeah, that's fine Double auto pack. I think this is Niners rookie auto Jordan Mason and Texans rookie auto teaking cue Quatoriano All right. Well, all right. We have a left-right duel now. Yeah, so we've got Colt Steelers here We'll do a dice roll for the left-right duels left one two three right four five six unless it's an auto relic or one-of-one That is two These duels go left duels go Bottom and left It's lamb jack Dylan today. Are you been playing poker a little bit here? We're gonna end up Cutting the Kyle's time So Josh dolphins No way this is Packers rookie auto Romeo doves You go Green Bay on card auto and Joe burrow Bobby Wagner It's chiefs rookie auto George Carl Optus round numbers They take it Desmond Ritter rookie insert Ravens playoff ticket rookie auto to 99 Anthony Brown T-roging Garrett 99 Tom Brady game day ticket Nice one bucks This is Titans rookie auto Roger McCreary There a Kenry Josh Allen bears rookie auto Trenton Gill Day ticket. Let's get the second six boxer filled up. We have Lions Packers Texans Colt Saints Bucks and Commanders That sounded like seven I'm going with it. Can you pick it rookie of the year contenders? When I first started with LSE we were ripping 2018 contenders. It was TJ Watt and Josh Allen, Baker Mayfield, Sam Darnold, Amjack, Saifan Yeah, Raiders rookie auto Darian Butler and Joe Montana, so Anyways, I Pulled the Super Bowl ticket one auto one-on-one of Saquon Garrett Wilson super natural rookie insert and then like the next time I broke pretty sure I Pulled the golden ticket redemption for Saquon So I got like both Saquon and one of them It's a crazy Saquon Magnet What's that? Saquon Magnet our players Montgomery Cowboys ticket stub auto to 80 Brandon Smith, Tremac Bride Chubb Justin Herbert and his Titans rookie auto Ryan Stonehouse Campbell John Elway Mac Jones MVP contenders it is Armani Rogers rookie auto commanders and Montana and Rice this is Bengals Jamar Chase Championship ticket to 99 for us Buckner. Who do you think who wanted a foot race? For us Buckner or DeForest Raker? Let's get that next one filled up redemption That is rookie ticket variation RPS Zemir White Yeah, that sounds right. Raiders and well, there he is right back It's my first time written contenders So I don't have my rhythm down yet usually I can get through these pretty quickly nice This is three of ten NFL Inc auto Justin Herbert for the Chargers Crats Chargers yeah, it is that's awesome looking Brown numbers Justin Jefferson Justin Herbert Cowboys rookie auto Isaac Taylor Stewart Skymore rookie insert Brady and Evans Kyle will be live at five with evening group breaks. We have five to go for the day Packers Texan Saints Bucks and Commanders if they didn't do a draft who you're really boring Raiders rookie auto chase Garvers Jim Kelly Just signing like free agents Ticket kiddle. This is Rams rookie horizontal rookie auto Kyron Williams I'll see I'm really gonna be mad as I or Williams.  I don't know why I have it stuck in my head. His name is Isaac Lions Rookie out of Malcolm Rodriguez Xbox nice that is Jets to 20 ticket stub Horizontal rookie auto 19 of 20 breeze hall Jets crush it. Who have the Jets? Kevin S. Congrats on that jet spot. Nice grab man. Appreciate you.  That's jets rookie auto Jeremy Ruckert Like whoever made that trade with seriously overpay You know Smith, I mean you have to really believe Yeah, yeah do that dude as a almost He's one foot five inches taller than me I guess I'm not really happy anymore. I was gonna say he was the same weight, but I'm not very funny more. Yeah Packers rookie auto Tyler Goodson I mean Long was like a big dude, but he wasn't You're younger than me I think Yeah One day all cowboys playoff take it out out to 49 Jake Ferguson Shot white rookie eagles rookie auto Britain Covey Players can chance player We have Packers Texan Saints bucks and commanders five to go. Here's a link for that. Let's get it filled up It's Jalen Hertz Take it Christian McCaffrey Jay Watt and Pierce rookie It's Tyree to 25 MVP contenders and supernatural Garrett Wilson last box We have one more six boxer and that'll be it for the day John Riggins 99 Jay Watt and it is Packers showcase ticket rookie auto Romeo Dobbs Here you go Green Bay Tyree Texans playoff ticket rookie auto Derek Stingley Jr. to 99 Traylon Burks rookie Kelly Eagles rookie auto Nicobi Dean Anthony Munoz We have just the Texans bucks and commanders three to go on the next grade. This is Rams Rookie ticket auto Kyron Williams second Kyron auto round numbers Williams Romeo Dobbs rookie insert cowboys rookie auto Peyton Hinder shot. I'm white Sounds like he was starting to say his name. He was starting to tell some of his name in a bar and stopped and like tried to Homes this is Texans rookie auto taking cue Kirk Cousins Ray Lewis All right, here we go. We had redemption. It was a mere white Raiders All autos in this I'm pretty sure Texans taking cue Cowboys Peyton Hinder shot Eagles to Kobe Dean Eagles Bryant Britt and Kobe Packers Tyler Goodson Jets Jeremy Rucker Lyons Malcolm Rodriguez Cardinals Jesse Locata Falcons John Fitzpatrick Cowboys Isaac Taylor Stewart Raiders Chase Garber's commanders Armani Rogers Titans Ryan Stonehouse Raiders Darian Butler Bears Trenton Gill Titans Roger McCreary chiefs George Carl Optus Texans Tegan Cue Niners Jordan Mason Chiefs Chris Oh, like a lot of cone a lot of coon a lot of oh lot of coon there we go I'm going with it Commanders Cole Turner Raiders Chase Garber's I'm gonna pull four of his autos and that's great Giants Micah McFadden Rams Kyron Williams twice Packers Romeo Dobbs Packers showcase ticket rookie auto Romeo Dobbs. That's Titans rookie auto playoff ticket to 99 Hassan Haskins Texans rookie playoff ticket auto to 99 Derek Stingley Ravens rookie playoff ticket auto to 99 Anthony Brown That's Cowboys ticket stop rookie auto to 80 Brandon Smith Cowboys playoff ticket rookie auto to 49 Jake Ferguson And we had Jets showcase ticket rookie auto Garrett Wilson Jets ticket stop rookie auto to 20 Breeze Hall and Chargers NFL Inc auto to 10 Justin Herbert. That'll do it for the break. Good stuff. Appreciate it. Everybody number 54 is coming up


Haribu sana tanokali. Thank you so much. How are you feeling? I'm feeling good. DJ Fana has been threatened by the fact that you have a guitar. Yeah, DJ is just, I don't understand. There's something in you Fanya. Kitu gani. No, I'm too question. I have to tell her now, gai. I think something is happening. To someone, lakinis mkwanapia dek. I doubt. I doubt. I doubt. Anyway. I'm being done by Joey. All right, yes. So tell us a bit about your Afropop artist. Yes. So tell us a bit about that and how you got into the genre you're in. Is it something you always wanted to do? Amoli skiza, all sorts of genres, and then you settled on something. Okay, first of all, my name is Gaduto. That is my stage name. Afropop was more of something I really loved from Kitambo. Yeah, I enjoy African music and especially Kenyan music. So I wanted to find a way in which I can do music in such a way that I can make it international, but in a Kenyan way. Yes, that's the goal. Also international with the bit of Kenyan. Yes. International and home coming together. Okay, so then when you were getting into the music, what was that experience like getting people who can help you along the music journey? Probably building a team, getting someone to help you produce music. Is this something you did all by yourself? Mama, you got people to come and tell what Shabang happened. It was a bit of an interesting journey. I think I learned most of the things myself, production and everything. So I produced my own music most of the time, but also up with certain producers here and there, but I tried to learn from them. And I think I started music seriously when I started playing the guitar. That's when I started. When you started playing the guitar? In 2020, during COVID, at the time when you were all at home doing nothing. Right. Right, but only when they learned. And I'm always like, if people learn how to play guitar, what did you learn, Jayfa, you know? Me? I actually remember when I was about to miss it. You learned how to play guitar literally 2-3 years ago. Yes. Before then, but you had an interest in music then and then the guitar once you learned, it went all the way. Yes, yes. Okay, my interest in music is dance. And then I started rapping and started singing. And then now the guitar came afterwards. After I learnt a bit of singing in Kwaia, Zapa Napale, I was in Red Fort Kwaia. So, yeah, I didn't know much about it. And then now the guitar came in 2020. Right. So basically it's literally been a journey from dance to this and that. Yes, yes. So now writing your music, some of the songs that you've released so far, what was the writing process like?  It's a bit of both. Most of the time I draw from my own personal experiences and also the experiences of those around me. Or people like here, or Lipitiahi na hi.  Sometimes I write with fellow artists. Sometimes you have sessions with Makachini. Actually those are the easier ones. Okatim Kowengi and you're writing together. But yeah, I do both. I write on my own and also write with friends. So speaking of writing, I believe you have an album coming up. Yes. Tell us a bit more about that. What the process has been like with you coming up with the features, collaborations. This is my first album. Thank you. Yes, it's called Nija Ziliye. Nija Ziliye means fill me with more and more and more. So it was an album in which I did not do any collaborations. So I did everything myself. It was more of a challenge. I wanted to see if I can compose, write, produce all of it. I did it myself, except one song that we wrote with someone. But I performed it alone also. So it's a debut album where I do everything as a solo artist on my own. But maybe in future albums I plan to consider collaborations and stuff. So it will be dropping on April. I have an album launch event. So all of you are invited. It will be at NIMPA. That's Nairobi Institute of Music and Performing Arts. Where is NIMPA? It's located at Kano Pizimaman. Kano Pizimaman? Yes. Do we have ticket sales? Yes. You can get your tickets at Hazelsasa. Just type Gazuto. Hazelsasa Gazuto. You can also get the tickets in my bio. Instagram, TikTok, everywhere. The poster is there. If you search Gazuto, you'll find everything you need. Okay. So let me ask, within now you would the upcoming album. Your debut album. What is that point in time where you learnt making, not just making music for it being a passion. The realities of making music a music business. Like you wanting to get money out of it and get chose and stuff like that. What was that switch like we could realize? Okay, I like this but I want to make some money out of it. What happened is, there was a time I was under management. I was managed by a friend of mine. He taught me these things about making your music into something more professional. Something that can get to earn me more money. But unfortunately he passed on in 2022. But from then on I've been an independent artist using the things I learnt from him. Was it heavy having to do this by yourself knowing you had someone that was along the way? Yes. It's been difficult but I'd say I got to learn a lot from him. His name was Ali. He rest in peace. He taught me so much. We worked together for a few months in the year 2022. So by the time he passed on I'd learnt so much that I just decided to apply these things on my own. It's been difficult yes because there are things I still don't know yet. But I'm getting there slowly by slowly. So what would be for you since I know it's such a huge personal loss for you because of that. But how would it work if at all in the future you'd want to look into management and being under what are they called? Record levels and stuff like that. What would that look like for an artist as you who's worked solo on a whole album by yourself? What would that transition feel like in your opinion? I think it would be easier in such a way that given that now I've learnt most of these things by myself if I do get a manager that say hata kwa na kazi mingi saana ita kwa sati ananzakuni funza these are things happening. I already know so it should be more of a partnership kind of thing. What are some of your dream collabs? Right here and probably just international? Dream collabs. Sayama to all of them. Someone could be listening somewhere. Let me start with Huku. Huku I dream to collab with Kenoti. Kenoti is Ethan. Jerai. Yes. Tuna tuki panda. Bien. Tuna tuki panda. Plafika Bana Boy. Yes. So inanda tuki panda. Shiran. Kenya to make it. And Shiran. Oh my gosh that would be so lovely. But yeah it's a journey. Yeah I'm getting there. For sure and wish you the very best of luck. All right. I'm so glad you came in studio because now at least we'll get to hear some of your music first hand acoustic music. And also you have a live show coming up as well. Yes. That's the vibe. Yes it will be happening on 31st of March and I hope you've gotten your tickets. I'll actually be performing, I'll be opening the stage for great artists such as Kenoti. When you mentioned to say yeah and there's Wanjine, there's African Vic and there's Modest Jabba. Looking forward to it. I'll plug you onto something. So next Sunday you could come to a show that Gadutu is performing at alongside other people as well. And then two weekends after that you get to go to his album launch to support the creative arts as well. Okay. Your socials. Please also first before your socials your music where can we get what's your on Spotify, YouTube where is it? Yes my music is on all streaming platforms just such the name Gadutu G-A-T-H-U-T-O. I like how you emphasize the people because I personally know for fucks I said Gadutu the first time I met you. It's right there. That's all I did so many people will mispronounce that name I have to spell it out G-A-T-T Actually I know what it is So in this video you can see what it is Actually I have merchandise in my album launch So yeah I was saying it's G-A-T-H-U-T-O Anywhere all social media platforms Facebook, Instagram, TikTok just such the name Gadutu and you'll find my music there Details on my upcoming events Okay that's love it here Thank you so much now without further do Let's hear a little bit of something Reminder it's Gadutu on all social media platforms and for Spotify and YouTube as well I think I'll start with I'll do one song This song is called Esther It's the first song I released after I started working as an independent artist So it's a love song about a lady named Esther Bum Bum Bum Bum Bum Yeah First time that I saw you smile Made me feel like I'm gonna die Made me feel like I could get high Yuka ni changanya na your waistline I made my move Nika songa karibu Nika g-introduce Hoping that town Hoping that town And I made my move Nika songa karibu Nika g-introduce Hoping that town The news say your name was Esther And that you wanted to get down So you gave me your number Illiniku vuti ewa The news say your name was Esther And that you wanted to get down To get down To get down I made my move Nika songa karibu Nika songa karibu Nika songa karibu Nika songa karibu Nika songa karibu Nika songa karibu Nika songa karibu Nika songa karibu Nika songa karibu Nika songa karibu Nika songa karibu


A warm welcome to the 44th session on the subject of wavelets and multirate digital signal processing. In this session, we continue what we have been doing over the past few sessions namely looking at student efforts and presenting tutorials or expositions on the topics already taught or discussed. This is with the aim of understanding those topics better by actually working out some examples and in that spirit we take today the two band filter bank in depth. So, the session today would be devoted to a tutorial on the two band filter bank that we have studied in such depth. Now, let me recall for you the basic structure of the two band filter bank and let us also recall what it is that we ask for from the different components in the two band filter bank. What we shall be doing in this session is to study it in the time domain and the frequency domain, but with examples. So, our aim is to present a tutorial today. We are going to work out together some examples where we given sequences and we see what comes out at different points in the filter bank. You will recall that somewhere earlier on in this series of lectures we had of course analyzed the two band filter bank in depth. We had also presented examples cursorily in some sense we had said we had in brief at a superficial level we had exposed the student to how the two band filter bank works and we had also put forth some exercises to be done, but then that is not the same thing as working out a tutorial example in total and that is what we intend to do today to work out a couple of tutorial examples on the two band filter bank in total. So, with that background let us recall the main structure or the prototype structure of a two band filter bank once again recall that we have an analysis section and a synthesis section. We shall denote the analysis section filters by h 0 z and h 1 z these are followed by down samples this is the analysis section. Now we shall intentionally break the filter bank into two parts the analysis and the synthesis section. So, this is the point x the point of input we shall call this point y 1 we shall call this point y 2 this point y 3 and this point y 4 and you will recall that this is essentially intended to be a low pass filter with a cutoff of pi by 2 and this is intended to be a high pass filter again with a cutoff of pi by 2. So, let us now go to the synthesis section in the synthesis section we take over from the points y 3 and y 4 up sample by 2 and subject it to the action of two filters followed by a summation and we shall show the output coming here. We call this point y 5 this point y 6 this point y 7 this point y 8 and the output y o or y out and you will recall that g 0 intends to be an ideal low pass filter again with a cutoff of pi by 2 g 1 intends to be an ideal high pass filter again with a cutoff of pi by 2. Now, this is the synthesis section and the names are suggestive the synthesis section re-synthesizes the output from the inputs. So, we have had two branches two outputs come here and there is a re-synthesis at the point y 0 here. In contrast the analysis section analyzes or breaks down the word analysis means to break down. So, the analysis section analyzes or breaks down the input into two branches or two components which we ultimately call y 3 and y 4. Now, it is very important to understand that there is of course, an impossible situation here we are never able to reach the ideal low pass or the ideal high pass filter there are some fundamental things which prevent us from doing that. Even so we recall it is possible to build perfect reconstruction structures. For example, if we take the hard two band perfect reconstruction filter bank what we have there is a set of filters h 0 h 1 g 0 g 1. In fact, all of them essentially with an impulse response of length 2 which can create a perfect reconstruction situation that means the output y 0 is essentially the same as the input except possibly for a constant multiplier and a shift. So, what we shall do is to review again the hard filter bank by applying a finite length sequence at the input. So, let us study the output at every point to understand this better. Now, what we shall do is first to look at a finite length input sequence and then we shall periodize that same sequence that means we shall extend that sequence repeated periodically to get a periodic sequence that is called periodization. And we shall study what happens when the periodic sequence is applied at the input of the hard two band filter bank. So, let us come down to the hard two band filter bank in particular you will recall that h 0 z in the hard two band filter bank is essentially 1 plus z inverse h 1 z can be taken to be minus 1 plus z inverse of course, there are variants possible, but we shall choose this for the moment g 0 z is again taken to be 1 plus z inverse and g 1 z can be taken to be 1 minus z inverse. And of course, we may also include a factor of half the factor of half can either be on the analysis or the synthesis side. Now, let us take as an example the sequence x n equal to 7 plus x n equal to 7 plus x n 5 minus 4 6 3 and 8 located from 0 onwards as the input to this hard two band filter bank. And what we intend to do is to study the output at every point. And we do this with the intent of understanding fully how each point works, what happens at every point and we are doing this in the time domain at the moment we are doing it in the time domain. Why are we doing this exercise? We must understand why we are doing this exercise in a tutorial. You see we keep saying perfect reconstruction, but it is very important that we understand how perfect reconstruction actually works with sequences as examples. How do the intermediate sequences add and combine to get back the original to within of course, a constant and a delay. This must be fixed in our minds with a couple of examples. So, let us take the sequence as the input and look at what happens at every point on the analysis side and on the synthesis side. So, on the analysis side we have the point y 1. Now, we have x. So, we shall of course, follow the same convention small letter denotes time domain and the corresponding capital letter whether written with or without the argument. So, when we write x z we mean the same thing as when we simply write x capital x and similarly here when we write x in we mean the same thing as when we simply write small x. So, this denotes the frequency domain. So, of course, this really and very accurately denotes the complex frequency domain and by now we are very familiar with what we mean by all these domains. So, we can always replace z by e raised to the power j omega and that would give us the sinusoidal frequency domain. So, this is a little bit about notation. Now, let us look at the outputs at every point first as I said in time. So, you will recall that if h 0 z is 1 plus z inverse as we have taken it to be and the corresponding impulse response is essentially 1 and 1 located at 0. So, you will recall this notation in fact let me explain this notation for the input as well. When we use this notation what we mean is that at n equal to 0 the sequence takes the value 7 and therefore, at 1 it has the value 5 at 2 minus 4 at 3 6 at 4 3 and at 5 8 and the sequence is 0 outside. So, this is a convenient way of writing down finite length sequences and we shall use this notation in the sequel as well. Of course, together with this we must take the impulse response here and then if we wish to find the output at y 1 we need to convolve the input with the impulse response. So, there we go y 1 is essentially x convolved with this impulse response which we shall call h 0. So, I do not need to explicitly write down. So, you know h small h 0 is the impulse response of h the filter whose system function is capital H 0 z. This is small h 0 n and a similar form of notation will be used elsewhere. So, when we convolve x with h 0 which you will see is essentially 7 5 minus 4 6 3 8 convolved with 1 and 1 and then we get well at 0 we would have 7 plus 0 there is a 0 behind at 1 we would have 5 plus 7 at 2 we would have minus 4 plus 5 and this can be continued. So, let me write down the results right away 7 plus 0 is 7 5 plus 7 is 12 minus 4 plus 5 is 1 6 plus minus 4 is 2 3 plus 6 is 9 and 8 plus 3 is 11 followed by 0 plus 8 is 8 and after that we get we continue to get a sequence of zeros. So, as expected the original sequence was of length 6 the impulse response is of length 2 and therefore, the output after this convolution is of length 6 plus 2 minus 1 which is 7 that is what we get here. So, as this is x convolved with h 0 that is the output at the point y 1 as expected of length 7. Now let us take the output at y 2. So, at y 2 of course, we have x convolved with h 1 and we know what h 1 is h capital H 1 z is of course, minus 1 plus z inverse and therefore, small h 1 n is going to be minus 1 at 0 and 1 at 1 and here again when we convolve x with h 1 let me put back x for you for a minute. So, when we convolve x with h 1 at this point we want to take well this and the past. So, minus 1 minus 1 times 7 plus 1 times 0 and that would give us essentially minus 7 at this point it would be minus 5 plus 7 at this point it would be minus 4 into minus 1 which is 4 plus 5 and so on. So, we can construct the whole output accordingly. So, x convolved with h 1 is going to give us minus 7 plus 0 at the point 0 minus 5 plus 7 that is 2 at the point 1 minus of minus 4 which is 4 plus 5 and that is 9 at the point 2 minus 6 minus 4 that is 10 minus 10 minus 3 plus 6 and that is 3 minus 8 plus 3 and that is minus 5 and finally, 0 and then plus 8 that is 8. So, this is the output at y 2 again as expected of length 7. So, this is straight forward now we need to do the next step that is down sampling by 2. So, on down sampling by 2. So, we have y 1 being down sampled by 2 to give us y 3 and I know what y 1 was let me put it flash it back for you for a minute this is how y 1 looked and when you down sample what is at 0 remains at 0 what is at 2 comes to 1 what is at 4 comes to 2 and so on. So, let us put it down. So, y 3 would look like this to essentially be 7 at the point 0 1 at the point 1 9 at the point 2 and 8 at the point 3 and 0 else and similarly, we can put down the output when we down sample by 2 on the lower branch. So, when we down sample y 2 by 2 we get y 4 and y 4 looks like this at y 4 now let me put down y 2 once again to show you. So, when we down sample this point comes to 0 this point would come to 1 this point to 2 and this point to 3. So, we have minus 7 at 0 9 at 1 3 at 2 and 8 at 3 and as expected the result after down sampling here is of length 4 and the result after down sampling here the second one with y 4 is of length 4 2. So, that is quite clear and as expected now let us keep these down sampling outputs before us because now we need to up sample them and then filter them once again. So, we have here the outputs y 3 and y 4 as outputs of the analysis section here. So, we now need to work on the synthesis side. So, the first thing to do is to up sample. So, we first need to up sample y 3 to obtain y 5 and that is easy this is how y 3 looks and therefore, y 5 will look like this 7 and then a 0 1 and then a 0 9 and then a 0 and finally, 8. So, we are back to a length of 7 as before and on a similar note we know what y 6 will look like 2 y 6 is essentially obtained by up sampling y 4. So, we have y 4 here when we up sample this by a factor of 2 we get y 6. So, let us draw y 6 2. So, y 6 would appear like this minus 7 and then a 0 9 and then a 0 3 and then a 0 and finally, 8 as expected again of length 7. Now, we need to subject these to the action of the synthesis low pass and high pass filters. So, of course, we have the upper one that is y 5 which we have here being subjected to the action of the synthesis low pass filter and y 6 here being subjected to the action of the synthesis high pass filter. So, let us do these 2 operations. So, y 5 when subjected to the action of g 0 z would give us y 7 and that is easy to do we know what g 0 z does it is essentially 1 plus z inverse by 2. So, for example, when we subject y 5 to the action of g 0 z at this point we shall get 7 plus 0 by 2 which is 7 by 2 at this point we shall get 0 plus 7 by 2 which is again 7 by 2 at this point we get 1 plus 0 by 2 at this point we get 0 plus 1 by 2. So, that is an interesting situation we what we have essentially is the number repeated with a factor of half. So, y 7 would look like this 7 plus 0 by 2 here 0 plus 7 by 2 there 1 plus 0 by 2 there and 0 plus 1 by 2 there 9 plus 0 by 2 and 0 plus 9 by 2 finally, 8 plus 0 by 2 that is 4 if you like and again 0 plus 8 by 2 which is 4 after which of course, we keep getting a sequence of 0's and similarly of course, we need to evaluate y 8. So, we have y 6 being subjected to the action of g 1 z to obtain y 8 and g 1 z you will recall is 1 minus z inverse divided by 2. So, essentially what it does is to take each sample and subtract the past sample from it in fact, let me write this down in the time domain y 8 n is y 6 n minus y 6 n minus 1 divided by 2 and therefore, I have here this sequence y 6 at this point I shall get minus 7 minus 0 by 2 which is minus 7 by 2 at this point I would get 0 minus minus 7 by 2 minus minus which is 7 by 2 and so on let me complete the working here. So, I have y 8 n is as follows minus 7 minus 0 by 2 followed by 0 minus minus 7 by 2 again 9 minus 0 by 2 and 0 minus 9 by 2 this is 9 3 minus 0 by 2 and 0 minus 3 by 2 8 minus 0 by 2 and 0 minus 8 by 2 simple enough and now let me put them together. So, you will recall this was y 7 this is now y 8 and we can add them point by point to do that let me write them down on the same sheet for convenience.  Let me for your reference put down before you the sequence x n as we started with once again here we started with the sequence 7 5 minus 4 6 3 8 starting from n equal to 0 and what we have here is 7 5 minus 4 6 3 8 but starting at n equal to 1 and this is exactly what we mean by perfectly construction. We had the original sequence what has been obtained after addition that means at the output y 0. So, what we have here remember is y 0 essentially what we have at the point y 0 is essentially the original sequence shifted by one step shifted by one sample and with no other change. So, let us make a note of that that is a very important observation. We notice that y 0 n is essentially x of n minus 1. So, you know the division by 2 the factor of half and so on has taken care of the constant relationship. So, you know the output is essentially the same as the input as far as scaling goes a scaling has been taken care of, but the delay could not be taken care of the delay is required and the delay has occurred on account of the requirement of causality. We want the filters to be causal in fact now I would like you to study as an example this particular sequence at different points as we obtain it. How did the requirement of causality create a delay? You are doing some processing at different points in the two band filter bands. Now, if you are not willing to allow some time for the processing by time I mean a delay then it would not be possible to do this processing in real time. So, causality is a requirement when we want to do real time processing when we want to process samples as they come not store all the samples and then process them. Of course, the way we have done it here on paper is as if we have stored the samples and processed. So, we could have done without a delay if we do non causal filtering somewhere either on the analysis side or on the synthesis side or perhaps even both, but if we cannot do non causal processing a delay is inevitable. Anyway, so much so for the case of a periodic sequences I said our next step would be to periodize. So, what we are going to do now is to periodize the input. So, essentially we construct a new input which we shall call x tilde n and that is essentially you know remember x n was of length 6 here. So, what we shall do is to periodically repeat this sequence with the period of at least 6. So, it could be summation k going from minus to plus infinity x n to minus plus k times capital N where capital N is greater than or equal to 6. Now, in fact for simplicity what we shall do is to take capital N equal to 6 and work out what happens at different points and what we shall do then is to write down how this sequence will look for some range. So, we have 7, 5, minus 4, 6, 3, 8, at 0 this is the point 0. Of course, here I cannot think of this is a finite length sequence. Now, it is a periodic sequence. So, at this point you will have 7 back again and then 5 and this would continue here and on this side you would have 8 coming here, 3 coming there and this would continue backwards. Now, what we shall do is to analyze the output only in the range from 0 to 5 only in this range and we are justified in doing that because after all you can see as far as the linear shift invariant part of the processing in the 2 band filter bank is concerned namely with the filters. A periodic sequence of period 6 would result in a periodic sequence of period 6 after filtering. As far as down sampling goes we have intentionally taken a period of 6 and the reason for that is when we down sample a sequence of length 6 we get a sequence of length 3. So, that is convenient. So, let us focus on this range of times and see what happens at different steps. Now, you know really speaking we will have to probably include one more sample because you will recall that there is a delay of one sample in the overall processing. So, we will have to allow for one more sample. So, let us focus with one more sample there and let us straight away write down the outputs at different points. So, the output at y 1 is of course, obtained in this region. So, as I said please do not forget this is an infinite length sequence, but I am only focusing between 7 and 7 here on the output. So, I would get y 1 essentially 7 plus 8 that is 15 5 plus 7 that is 12 minus 4 plus 5 and that is 1 6 minus 4 which is 2 3 plus 6 which is 9 8 plus 3 which is 11 and 7 plus 8 which is 15 back again. So, I am talking about what has happened to this after being subjected to the action of the analysis low pass filter and similarly y 2 y 2 of course, would give me minus 7 plus 8 which is 1 minus 5 plus 7 which is 2 minus of minus 4 which is 4 plus 5 and that is 9 minus 6 minus 4 which is minus 10 minus 3 plus 6 and that is 3 minus 8 plus 3 and that is minus 5 and once again minus 7 plus 8 which gives me back a 1 and there I am and of course, now I can subjected to the action of down sampling. So, I have there. So, you see remember down sampling will bring me to a period of half the original period and that half is meaningful if my original period is a multiple of 2 and here it is there is no problem. So, y 3 is going to bring me to y 1 down sample by 2. So, I have 15 coming here 1 9 and then back to 15. So, now this becomes periodic with period 3 and similarly I have y 4 y 4 gives me 1 9 3 and then back to 1 again with the period of 3. So, much so for y 3 and y 4 now let me look at y 5 and y 6 which is obtained by upsample that is easy. So, y 5 which is essentially y 3 upsample by a factor of 2. So, I put back y 3 for your site and y 4 for your site. So, when I upsample y 3 by 2 I would get 15 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 and then 15 and I am back to a period of 6. So, I expected when I upsample I would have a periodicity of period 6 and so much so for y 6 2 I have 1 0 9 0 3 0 and then 1 back again. Now, I need to look at y 7 you see when I construct y 7 and y 8 I must now be a little careful. I need to realize that there is a repetitive behavior here. So, you know you have 15 0 1 0 9 0 15 and then the 0 1 continues here and this way too. So, if I wish to focus my attention only in this part then I must of course, look only at the outputs here because you know if I wish to find out what is going to happen here then I have to take into account the sample there. So, may be it is better that I focus my attention only on the outputs here. So, to obtain y 7 I would essentially take y 5 and subject it to the action of the filter. Now, what was the filter? The filter was essentially this plus this by 2 and it would be this minus this by 2. So, let us write that down. Now, you know as I said let us write it down only for the clear part of the interval. So, here I would not write the output here I will just leave it blank I will write it from here onwards. So, I will just leave it blank and then I have 0 plus 15 by 2. So, I have 15 by 2 there then I have a 1 plus 0 by 2 and then a 0 plus 1 by 2 and so on. So, 1 plus 0 by 2 and a 0 plus 1 by 2 9 plus 0 by 2 and then a 0 plus 9 by 2 15 plus 0 by 2 and then back again similarly y 8 y 8 of course, would begin once again from here. So, I would have 0 minus 1 by 2 which is minus 1 by 2 here 9 minus 0 by 2 and so on. So, I have well I would not write it at this point, but I will write 0 minus 1 by 2 and 9 minus 0 by 2 0 minus 9 by 2 3 minus 0 by 2 0 minus 3 by 2 and finally 1 minus 0 by 2 and now it is easy to add. So, when I add I get very simply well unknown here, but here we have 15 minus 1 that is 14 by 2 and that gives me a 7 9 and 1 10 by 2 which gives me a 5 1 minus 9 that is minus 8 by 2 and that is a minus 4 9 and 3 12 by 2 which is a 6 9 minus 3 and that is 6 by 2 which is a 3 and finally 15 and 1 16 by 2 which is 8 and back we are again to the sequence as expected delayed by one position. So, here I focused my attention on those 7 samples and we notice that we did get back the input we had started with this input periodically repeated with a period of 6 we do get back the same input periodically repeated. So, if you really did the calculations carefully you would see 8 appears here and of course this sequence would essentially be placed behind repeated periodically with every period of 6 and also repeated in the forward direction with a period of 6. So, what we have done here is to illustrate how this two band filter bank works with the sequence when it is initially taken to be a periodic and then when it is taken to be periodized and the intent behind this tutorial example was to show you how to implement the wavelet transform. So, there are two ways of doing it if you have a finite length sequence you could either implement the wavelet transform by keeping the sequence as it is a periodic in nature and therefore, obtaining the finite length outputs at each point in time at each point on the filter bank in time and then of course, processing it as it is or one could periodize it and one would obtain the same sequence in the interval of interest. Of course, you know you may want to look at this from a slightly different point of view when you realize that this is periodic with the same period of 6 you could think of this being circularly shifted. So, you know the 8 would also appear here. So, it is as if the sequence has got shifted forward by one place and what is spilling out has been brought back here this is called a circular shift. So, when we periodize the sequence and when we subjected to the action of this two band filter bank what we are going to get is an output which is of course, periodic with the same period, but in each period there is a circular shift by the delay that is incurred. Now, we must keep this in mind when we implement the Haar filter bank on a computer. It is very important that we understand this circular shift which is a consequence of the delay in the filter bank carefully during implementation. So, much so then for the time domain interpretation or time domain tutorial. Now, let us look at the frequency domain behavior of the Haar filter bank as an example. So, to make a frequency domain study nothing works as well as to take a sinusoidally sampled I mean essentially a sampled sinusoid as an input. So, the input now would be a sampled sinusoid. So, let us take that sampled sinusoid to be x n is cos pi by 4 n to begin with you know cos pi by 4 n lies only in the lower band. So, this is rather simple let us take cos pi by 4 n plus cos 3 pi by 4 n to begin with and let us study what happens at every point. Now, of course, what we are going to do now is to look at the output after each filter. So, what I intend to do now is to put before you the steps as to how we should go about analyzing this in frequency and as has been the practice in previous tutorials to leave it to you to complete the rest of the calculations. So, rather than do the whole example for you I would like to guide you through the steps and then leave it to you to complete the steps and the steps are as follows. You see what happens when we subject a sinusoid to a filter when we subject a sinusoid to a filter of course, it undergoes a change of magnitude and a change of phase. So, sinusoid of course, this is a sampled sinusoid when it is subjected to the action of a discrete filter there is a change of magnitude same frequency of sinusoid, but magnitude and phase changes. So, in this example if we take this sinusoid as the input what we would have to do is to look at the analysis filters which if you recall are essentially 1 plus z inverse and 1 minus or minus 1 plus z inverse whose frequency responses are respectively 1 plus e raised to the power minus j omega and minus 1 plus e raised to the power minus j omega. I shall straight away write down the magnitude and phase change. So, the magnitude change here is essentially of the form 2 cos omega and you can similarly work out the phase change by rewriting this as e raised to the power minus j omega by 2 times e raised to the power j omega by 2 plus e raised to the power minus j omega by 2 which gives you a phase change of minus omega by 2. So, phase change in the analysis low pass filter is essentially minus omega by 2 I would similarly expect that you work out the phase change for the high pass side of the analysis filter bank and the magnitude change we have done that before. So, remember when we take a sinusoid as the input we keep getting sinusoids after filtering, but what happens after down sampling now recall the frequency domain behavior of that. Now what we shall do is to again put before you just the expression for the down sampling. So, in down sampling if we have x e raised to the power j omega here what we get here is half x e raised to the power j omega by 2 plus x e raised to the power j omega by 2 plus minus pi. So, essentially an aliases created. So, two things happen the sinusoidal frequency is changed by a factor of half and there is another frequency added an alias frequency obtained by shifting the original frequency by pi either forward or behind it does not matter there is a periodicity of period 2 pi. And similarly, if we look at the up sampler we have x e raised to the power j omega being given here up sampled to produce x e raised to the power j 2 omega. Now remember in up sampling two things happen this is deceptive it looks as if there is just one frequency created no there are two frequencies created you know when you contract the frequency axis by a factor of 2 as this expression suggests. The periodic repetitions around 2 pi now repeat around pi. So, each frequency brings an image frequency into the region 0 to pi. So, what I have done is to give you the basic steps in doing a frequency domain analysis this is an exercise a tutorial exercise for U S students you know what happens when you subjected to the action of the synthesis filters and then one could add it. So, it would be very desirable that the student actually works out this example in total to understand the frequency domain perspective too. If we get an opportunity we might actually illustrate this in more detail in one of the subsequent sessions with that then we shall close the tutorial session today. Thank you very much.