Okay, so what I would like to do is I would like to introduce our department, introduce what we do, and then obviously focus on the main program that hopefully you came for, and that's our BA languages and cultures with a focus on Asia, Africa and the Middle East. I hope that some of you already know something about us, but for us is a very unique institution, it's the only university in the UK that actually specializes in the study of Asia, Africa and the Middle East and our department, the School of Languages, Cultures and Linguistics is the only department which actually has comprehensive coverage of the languages and cultures. So, of course, you know, we are teaching, but also researching some of the most dynamic and also diverse regions in the world, you know, Asia, Africa, the Middle East are regions which are fascinating, you know, mix of cultures, languages, religions, traditions, but at the same time it's a very modern upcoming sort of area, you know, it's very dynamic, a very fast changing part of the world, and it's these regions are playing increasingly a very sort of important and strategic role in global affairs and in a global society. So, the basic philosophy behind what we do is based on the fact that we approach these regions from their own perspective, and we base our teaching and research on the knowledge of language. So, really, we believe that obviously knowing the language is the best way, the deepest way how you can engage with different cultures. So, all of our programs incorporate a study of language. I will talk to the next slide and I have also noticed that another colleague has joined us and that's our colleague Naresh Sharma, who is our South Asianist, so if you are interested in the South Asian part of this degree then obviously please ask questions and we will be able to give you a little bit more insight. So, through the speaking, we focus on the study of languages, cultures, film or screen studies, we engage with issues of gender, equalization, all these issues form a very important part of our curriculum. But as I have said at the heart of our program is the study of languages. We have a very broad range of languages we teach, I think I can find a slightly more detailed list. This is, you know, an example of the languages which we currently teach that we actually have an expertise in many other languages. So, some of the languages are taught every year, some languages are sort of taught maybe first for one year and then, you know, taught the following year. So, again, depending on which language you are interested in, that would be the sort of focus of your degree. What we also feel very, very passionately about is the fact that we provide our students with an experience in the country. So they can actually study in the region that can improve their linguistics skills, but also it's the fact that they are able to immerse themselves in your culture, that particular region, etc. Typically we send our students for a year abroad. I will explain the proper structure of the program later on. And during that year abroad you obviously study the language, but also you usually work on some sort of independent study project.  So it's a great opportunity and this is obviously the main part within the degree when you are testing your language skills and you are really improving your language skills and hopefully very fast. So, everything we do in our department or aspects and disciplines and things we teach are obviously based on our academic research. We have very experienced academic researchers, scholars, who cover in the research programs, topics and themes, and this research then informs our teaching, the modules, the proposals and the modules that you can attend. And as a basic main, very important resource, we have a very well-stocked library, which is one of the national research libraries. And so, if you have a chance to actually come to campus, you still need to visit the library. We have very unique collections, especially in the regional languages, we have archives and special manuscripts collections, so very many rare resources that obviously are available to our students. Okay, so that's just simply by way of introduction, but then maybe slightly more specifically about our main degree, so it's called the languages and cultures. And it's a degree which is now structured as part of our guided curriculum, which essentially means that in year one, the program is structured in a guided way, so you have a limited choice in what you can do. You know, the curriculum is slightly more fixed, even though there are some options. In year two, then your options are freedom to choose the modules that you are interested in is slightly increasing. And then obviously in year three, you have a little bit more option yet. In year three is obviously the sort of culmination of the degree, and in most cases the students are working on the undergraduate dissertation or independent study project, which usually means that you can select a topic that interests you, and you sort of draw on all everything that you have learned in the previous years. And you work independently during a really in-depth research of that topic, and you present that in a very, you know, scholarly, academic project. All our, or this particular degree, but all our degrees in the department have a three-year option without the year at all, or a four-year option, which includes the year at all. Although you may have to enroll on a three-year option, which is relatively easy to transfer later on if you decide that you want to go to the year abroad and transfer to a four-year option. And by several self, if for any reason you don't want to go on the year abroad, then you can transfer to a three-year degree program. Please, I'm going to ask my colleagues perhaps, you know, that they can come in and, you know, just, and what I have forgotten or just expand on some of the issues. Yeah, I don't, I don't have anything to add at the minute. I just to say that I've been looking at the chat and quite a few people interested in Korean, Japanese, and, or Korean, Japanese and other languages. So I wonder if, Dana, you can say something about the options for combining languages. Yes, obviously we are in this department. We have a separate department, which is called the Department of East Asian languages and cultures, which we are specializing in the study of Japanese, Korean, and Chinese. Obviously, within the programs we offer here, you can also study some of the East Asian languages, but that's not essentially the whole department. We have a postgraduate program such as the Incorporate East Asian languages on the undergraduate level. It's mainly, you know, languages of Southeast Asia, South Asia, Africa, and the Middle East. So our main language is Arabic. We also have the Middle Eastern side, and we also teach Persian. On the South Asian side we teach Hindi, Urdu, Bengali, but we also have expertise in some of the other languages, and on the African side we teach Swahili, which is our biggest African language, but we also offer Yoruba. So to some extent in the past definitely we had Swahili, which we hope that we will be able to reintroduce. So, perhaps, Naresh, could you say something about the South Asia part of this program. Yes, I've put up my contact details in the chat and also I've mentioned the South Asia languages that we offer. So the languages that run every year are Hindi, Urdu, and Sanskrit, and then sometimes we offer Prakrit, Punjabi, and Bengali as well. If you're interested in doing the year abroad, which would be the third year of your degree, then it's usually to do Hindi, Urdu, or Sanskrit. And that can be a really significant part of the study experience going and spending the academic year in India, learning the language, being immersed in the environment, but also participating in other culture-related activities whilst you're out there. So I would strongly recommend considering the four-year option. Having said that, if you think it's too much to commit to a four-year degree, then I believe, Dana, you could correct me if I'm wrong, that for some languages we have a summer abroad option as well, where you can spend sort of eight to 12 weeks in an emotionally-emotional environment and really building on the language that you've learnt whilst you've been in classes in London. What else can I tell you? I think that's about it. Yeah, you know, my email address is in there. If you have any specific questions, drop me an email. I'd be happy to reply or set up an online meeting to talk about options. Yes, just to add, as you can see, hopefully you can see I have shared with you a list of some of the destinations that our students travel to when they are going for their year abroad. Sometimes we are now exploring the possibilities and we are increasingly allowing students to perhaps, you know, split the abroad between two destinations. For example, for the Southeast Asia year abroad, it is now possible to spend, you know, one time, say in Vietnam and another one in Indonesia, because we do have students who obviously actually are real linguists who don't have a very fashionable language and study more than one language. So what normally happens in year one, you have to study one language and then in year two, should you find it too difficult and you can't cope, then we allow you to drop the language. On the other hand, there are actually students who really want to study language in depth and therefore they take on two intermediate level and then they go abroad for an advanced study of the language. So, you know, there is a certain flexibility within the program allowing you to explore the cultures you are studying. This is the last two years because of COVID and the pandemic, you know, our year abroad program has been somewhat disrupted but some students are now already again abroad, some students did sort of online distance learning version but we obviously hope that we will be able to reinstate all of our year abroad programs for the following session, which is obviously when you would be reasonably applied. Talking about the language, I also just wanted to emphasize that we have really huge expertise in the teaching and research into Asian-African and Middle Eastern languages. Many of our colleagues wrote, you know, language textbooks or grammars, scripting grammars and linguistic studies, and I have just, you know, picked up some of the commercial books that came out of these expertise. But we also have a principle that all students have access to a native speaker, so normally our classes would be taught by a non-native speaker but an expert in the particular language. But in that case, we will always also have a native speaker so that we can practice the language, the conversation classes are always done by the native speaker. So we will get a lot of opportunities to just learn and practice the language. I think, oh yeah, this is the main part which I have not yet emphasized. So via languages and cultures, you can study as a single subject degree, or you can obviously study it as a joint degree program, which means that you would combine the languages and cultures part with a discipline. You can essentially combine it with all the various disciplines taught around us. You have some examples that development studies, economics, history, history of law, linguistics, music, politics, anthropology, art philosophies, etc. We also allow a combination of the languages and cultures with our Arabic program. We have a separate Arabic studies program, but if you want just a little bit of Arabic language, then you can combine it with via languages and cultures. Normally what would happen is that really the program, if you do the joint program, your credits would be sort of split evenly between the two subjects of languages and cultures and then the discipline. Obviously there are certain synergies because in your perhaps independent study projects or in some of your essays, you can actually combine these two sort of parts of your degree together and produce a very, very, very interdisciplinary research or study of a particular subject. I will perhaps later on talk about, you know, some of the career destinations our students end up with, but I think perhaps now I would hand over to my colleague like I just so that you can just give you some sort of insights into some of the modules or themes and issues that we actually address in our program. Nareesh, do you want to say something? Sorry, I just wanted to say that I have to head off. So good to meet you all. Please do get in touch if you have any queries, any questions about South Asia related languages or studies. Good. Thanks. And see you later, Dana. Thank you. Thank you for joining us. Thank you. So, Dana, I wonder, can you make me a co-host so I can change the slides or can you change the slides for me? This is your first slide or do you want to start? I will. You do it for me? Okay. I am trying to make you co-host, but you know, my screen is slightly obscured at the moment so I can't see everything unfortunately. Oh yeah. You might not be able to. So I'll just ask you to change the slide when I do it. I'm sorry, I don't seem to be able to do that now. That's fine. Yeah. So yeah, so as Dana said, I'm just going to be talking for 10, 15 minutes or so about to just give you an idea of what sort of things we do in the classes on the BA languages and cultures and to try to connect to some of the big questions that SOAS is really invested in and that you will be trying to answer while you are here if you come here. So one of the, as I'm sure you know, one of the big strands of inquiry at SOAS is this question of decolonizing the curriculum, the university, knowledge as a whole. And this is something that's really threaded through a lot of things that we do. So you probably know the history of SOAS, but it was set up very much as a colonial institution for training those officials who went on to administer the British Empire. So obviously that's a very problematic history. And what we have done at SOAS is that we do recognize that and lots of people at the institution have been thinking about it and clearly times are very different now and things are done extremely differently. But what we do then and now is this as Astana said a real emphasis on language acquisition that was really at the core of what SOAS was founded, when SOAS was founded in 1917, if I got that right. And so that was, you know, language acquisition and really understanding other cultures, other peoples was essential to SOAS and it's essential to SOAS now. So now our questions and the reasons that we want to do that are different. You know, who are we now? Well, if you come to SOAS, you'll see it's extremely diverse in all kinds of ways. And that's really one of its great strengths as an institution. But the question of how do we understand the rest of the world on its own terms from their own perspective as Astana mentioned earlier. So this is a key question and one that I think we can get to. One of the ways that we can try to answer it is by looking at literature produced in the rest of the world and really engaging in a detailed, informed way with it. And I think I wanted to put up a picture of Abdul Raza Gourna because as many of you may know, he was awarded the Nobel Prize for Literature just last week, I think. And he is a, he writes in English and he's been in the UK for a long time, but he is of Tanzanian origin and from specifically from from Zanzibar. And lots of his work engages with these questions. You know, the big questions about time decolonization in broad terms, but refugee experience, migration, alienation and things like that. I'm really, I was really happy to discover that one of our lecturers and SOCL and languages, cultures and linguistics that's Dr. Ida Haji Bayanes who teaches Swahili. Of course the language of East Africa. He is, you know, long before the Nobel Prize she has been working on a translation of one of Abdul Raza Gourna's novels from English into Swahili. So, you know, that's such a nice. So as SLCL project, we have always been interested in this stuff, you know, before the Nobel Prize, before everyone started talking about decolonization, we were interested in it and we're still interested in it. And we and if you come here, we will give you that linguistic cultural grounding to really engage in a meaningful way with with with what's like like Gournas, but lots and lots of others as well. Okay, so, Donna, could you change the slide next brilliant thank you. So I wanted to talk to you about a module that I'm teaching and this is running for the first time this year so I'm co teaching it with a colleague Dr. Anjaria, who works on Turkish. And so this is a core module for the BA languages and cultures and it happens in the second year. And then it's called understanding texts. And the, the idea of this module is really to give students of a grounding in textual interpretation. And this could be texts of all kinds, it could be literary texts which is the focus of the first part of the module. You know, criticism, analytical texts, and how do you make meaning out of it, how do you understand what is going on in it. And so some, some students have have done something like this, maybe I've done English literature a level but we find that a lot of students haven't. So it is, you know, partly to develop the kind of analytical skills that you need throughout the degree, and also which are really useful in professional life afterwards, you know, you will always need to know how to read something carefully, understand it, figure out what's going on in it, and express your opinion, your reasoned opinion in writing and orally. So these are skills that will serve you throughout your degree at SOAS and throughout your life. So partly the module is designed to inculcate that. And it's also to think about texts, literary production in a non-eurocentric frame. So, you know, and in a way that most people probably haven't had the opportunity to do before they come to university. So if you did literature at school, depending on where you studied, what country studied in, you know, it's going to be English literature or it's going to be the national literature of your country of origin. So what we try to do is open it up a bit more, read literature in a bigger frame. And of course, you know, strategies of interpretation, ways of reading are going to be very, very different from one context to another. And another I think key sort of SOAS or LCL principle is that rather than just flattening it all out and say, well, we read all these things in the same way, you know, we assess literary value in the same way. What we really want to stress is you need to understand the values of the culture, their aesthetic values say what a poem is good in the language that I studied in Malay for these reasons. Those aren't the same as the reasons a poem is good in English. And so you need to know both of those things and to sort of put them in dialogue with each other. We also look in this module a little bit at oral literature. So that's not produced in writing. And this is something that, you know, exists in lots and lots of cultures around the world, but we tend not to study very much, you know, or come across very much in our daily life in the modern west. But it's really useful and it's a good challenge to our normal conceptions of literature and textual interpretation to look at that material as well. We look at questions of translation. So how do you, if you read something in translation, can you interpret it in the same way as if you had access to the original. We would love you all to learn a language and to learn it to an advanced level. And then you won't have the barrier of translation, but none of us can learn every language. So one of the things we, and there is great value still in reading things in translation, of course, but thinking about the issues around that. So one of the things that's quite interesting for me teaching this course, and seeing what's the kind of questions that my students are asking. And, of course, it's, we're very much trying, you know, in all of our courses, I think to have the lectures and the tutorials to be interactive people, you know, I want to hear from my students and not just them hearing from me, and I want them to talk to each other, because a lot of learning takes place between students. So one of my students is slightly skeptical, I think, about what's the point of reading literature what, you know, it's just a novel, it's just a story. Well, and good, but what's the point of that so I'm going to try and suggest one, or one reason why literature is good now I'm going to use an example of why, why we can learn something worthwhile from it. I'm going to show you. So Dan, could we go to the next slide, please. Thank you. Yeah, that's great. So this is the novel that we are reading it in this module understanding texts. And it's a really interesting one by Zimbabwe an author published, sorry originally came out 1988. And this is the opening paragraph. This is one of my best conditions by Tzidzi Dungaremga. I'm reading because I think it's a good, it's a really good opening paragraph so I was not sorry when my brother died, nor am I apologizing for my callousness as you may define it, my lack of feeling, for it's not that at all. I feel many things these days, much more than I was able to feel in the days when I was young and my brother died. And there are reasons for this more than the mere consequences of age. Therefore I shall not apologize but begin by recalling the facts as I remember them that led up to my brother's death, the events that put me in a position to write this account. Though the events of my brother's passing and the events of my story cannot be separated. My story is not after all about death, but about my escape and the cheers about my mother's and my guru's entrapment, and about Nyasha's rebellion. Nyasha far minded and isolated my uncle's daughter, whose rebellion may not in the end have been successful. So we spent a whole tutorial hour, looking at this opening paragraph, and just this opening paragraph. Because what I'm trying to get students to do is close reading. So a lot of the time you know you've a lot of you come to university have a lot to read and people skim. You have to do that to some extent for some purposes but sometimes we really need to focus. And one of the things that I want to emphasize is, you get a lot. You have to concentrate on this one paragraph so here we have a very arresting first sentence a very challenging first sentence I was, I was not sorry when my brother died. And so critics have pointed out is very obvious right this is a, a sentence a defiant sentence, and not the kind of one that you would expect stereotypically from a woman from the global SAP. So he and we, we are already told from that very first sentence the very opening paragraph that we are in the presence of a particular consciousness, someone who is able to articulate for herself, someone who is. Yes, who is so secure in that sense of identity that she says, I know what you might think of me, my callousness as you may define it, my lack of feeling, but this isn't the story when you hear my story which is the whole novel. You will understand differently. So very self possessed voice, but already and again just in this opening paragraph we are told, you know there's a lot at stake. And we had an emerges that the brother's death, put me in a position to write this account so it is the because the brother was sent to school. So the because the brother was a boy he was sent to school because the narrator was a girl she was not sent to school. When the brother died it became possible for her to go to school, therefore becoming literate, and I am in a position to write this account. So is, you know, how is it that this book is in your hands, because my brother died and this kind of recognition of the not guilt exactly but she has she knows she has profited from her brother's death. So I won't want to sort of replicate what we did in the class but I hope that this gives you a sort of sense of how reading literature and really reading it with attention and focus. And as literature, you know, can really be rewarding and help us to answer these big questions these big sort of global questions, because the first step is not to read it as anthropology or to read it as data about the lives of others but when you treat it as a work of literature a work of art like, like any other novel, then we can get. We can speak on the same level right we can and then we can really learn about this other consciousness is other way of living this other cultural context. So that's what I think you know literature can help us to do. And that's one of the ways that we can maybe start to build a sort of different world if that's not too much of a big claim. So let me go to the next slide, please. Yeah, so that this is a picture from one of my. So my area is a Southeast Asia this is a girl illustration from the early 30s of an engineer Japanese woman going to the library and and reading books so. And it's just to, you know, think about the, it's just as an illustration of the kind of cultural different cultural contexts, different historical contexts, which we can all we all of which we can access in some way through reading works of literature if we are willing to do the, you know, certain amount of learning about the history about the context and ideally also about the language, then lots of things will open up to us just like to the to the narrator of the novel I just, we just talked about, and just like to the reader pictured here. I think that's the end of my slides. Yeah, so I will hand it over back to Donna to talk about the careers aspect. Thank you very much that was really fascinating and I hope that you have all feel now so motivated that you will go and look up this book and read it, because I will definitely do it. Thank you very much over the time. We have, you know, probably around 1215 minutes, and I obviously want to read some time for your questions. So, really, the most of this question we get asked by students is, you know, what do our students actually end up doing, why are there be languages and cultures like to embrace, you know, the study of Asia Africa and the Middle East, what sort of practical purpose these degrees actually have. It would be very difficult for me to give you image of a typical student, we have really a very, very different students who draw on different aspects of this degree program so obviously there are students whose main interest is the language, and their careers would actually then rely on the knowledge of the language so obviously, such as, you know, restaurants writers, perhaps editors, but also teachers. But then there are students who obviously perhaps throw more on some of the cultural aspects of the degree. So, quite a few of our students in the past ended up working either in the foreign office or the home office, civil service, diplomats, etc. Journalism, publishing, and in modern times we have actually several students who are independent advisors. So they have their sort of small agencies working as advisors to Westerners, positioned in the region, but, you know, advising. Quite a lot of our students end up working for various NGOs or charity organizations. And that's actually also often. Those students who come to our department because they might have actually, during their gap year, gone to the region and they would have been involved that they then want to have changed formalized knowledge of the region by having a proper university education and grounding, in the region. But obviously, you know, just any of the jobs that requires that you know, understanding of the culture, you know, working in museums, museum curators, we had few of our alumni who actually worked in the British Museum, in charge of the regional collections, librarians, etc. But obviously some students actually end up in the slightly non-academic part of their careers market and they actually go to business, even though we don't really focus predominantly on some sort of, you know, economic, political issues. Obviously, within the study of culture, etc., we cannot not to touch on sort of political reality, historical reality, etc.  I just want to give you an example. For example, I have a student who did Vietnamese and he did a full degree, so he very much focused on this culture literature, and he then went and he was recruited by a very famous global corporate company. He was a very difficult, very sought after difficult to get into. And he was telling me how most of his interview, the final interview before he was offered a job. He actually spent the interview discussing a Vietnamese novel. And I just want to sort of show you that, you know, obviously you learn a set of skills.  All these skills are very practical and very transferable and that could be used in essentially any type of job beyond the obvious. So actually to have a degree such as this, which to some extent is slightly more specialized, that's something which usually makes you stand out in the job market. There are many agencies and companies are actually impressed when they see that you went beyond the obvious and that you went for something which is rightly or wrongly perhaps perceived as more complicated, etc. And I mustn't forget those who are students who obviously are much more interested in an academic career, perhaps so there are students who obviously then go for a postgraduate study. And either continue again within the sort of regional area studies, but very often they can go to a completely different, you know, study, so they sort of create an extra level of knowledge to complement the undergraduate degree. So obviously they continue to do the research degrees or entire PhD. So it's actually a really great mixture and sometimes we are really fascinated by hearing back from our students and learning what they do. So because of the time, I think I will sort of stop, I will stop sharing the screen because at the moment I can't actually read your questions in the chat. And please if anybody wants to ask why simply then you can obviously raise your hand and just ask the question and we will try to answer. Otherwise I will, you know, need to look through the questions and see if we have answered or not. Anybody wants to ask please just. There's a question here from Fion. If I pronounce that right. Are there any opportunities to learn languages outside of your degree extracurricular so extracurricular and I'm not quite sure what the language center or what the policy is. Well, first of all, we all all students as far as can take a language as their open option so even those students who would not be registered on a language degree. They could study a language and quite a few of our students obviously do that. We used to have something called language entitlement program which actually allowed students to attend some of the language courses that are taught in the language center. Aside from our sort of academic departments we also have a language center which is basically really a language tuition provider to general public and most of the courses that obviously are taught in the evening as evening courses. So I think that's one opportunity, but at the moment I'm not sure whether students can actually attend these modules full of charge. I think you would be definitely given a discount but I think that that would be fine. Having said that. If you already have some basic knowledge and you want to perhaps improve that a lot of students societies and exchanges and you can find you know somebody sources of various sort of international institution. We have students from all over the world, speaking so many different languages so many of our students perhaps you know, pair up this with a fellow student and maybe they help them with improving their English while the student from Vietnam helps them with their Vietnamese, etc. I'm sorry, I really can't read the questions. I can read it I don't know there was a lot of discussion about the Japanese side of things which Penny has very kindly answered. I don't think. I guess I would add to to what I just said that you know if you are thinking of doing a language and I really encourage you to have it be part of your degree, because although you know there's so many things to study and the temptation is all audit or I'll take it on. When you do you're going to be so busy. And it. So if you really want to, you know, progress in a language and then I really encourage you to put it into your degree so that you're going to get the most possible out of it. The question about is there a Japanese society, Penny do you want to answer. I think there is a Japan society where you can pop in. And there will be people who are actually from Japan that you can talk to in Japanese.  This is a question from my colleague who's now doing a PhD in Japanese studies. She said that some people from like Honda, the car company came over into the Japan society just to talk because they were like hi I'm lonely. No one speaks Japanese at the office so I thought I'd stop by. So you can meet all kinds of people there. And I think this would be similar for any of the regions you know in Africa the Middle East because we have regional centers that organize seminars so you can attend. We have a wide range of activities if you are interested in particular country or language, etc. Of course, so as is positioned at the heart of London, you know, in the Bloomsbury behind the British Museum very close to the British Library, Royal Asiatic Society, and any of these sort of famous institutions So, you know, there's a lot of activities that you can actually outside source, you know, expand your knowledge and get involved. So any more questions. So Fiona again, I'm interested in studying Japanese Korean or Arabic, any tips on how to choose which one. Very quick question isn't it. Obviously that depends on your personal interests. You are spending you know different different areas, different cultures. I can speak about the Arabic, our Arabic program is obviously quite, quite broad. We have a number of Arabic modules at all levels, and we have also a very intensive Arabic studies program, but also we have a slightly less intensive for those who want to learn just the basics of the Arabic language without obviously becoming a completely sort of fluent. A full in depth Arabic studies program obviously you study, you spend many hours a week, dedicated to study of Arabic language while for the non intensive version, you would probably have four hours as is the case for most of our languages usually have four hours per week of language tuition. I really don't feel sufficiently I don't know you are to advise you on your choice. So, anything. So before before perhaps we close this session. Just to say that. Obviously, you have all this information on our website. So if you go to the school so our school of languages and cultures and linguistics. More specifically, if you find the languages and cultures program, you will find a more detailed structure, you will see actually the modules that you can take the options that are available to you throughout the degree program. And most importantly, you have the name of the convener which is Dr. Ben Mehta who couldn't be here today, but you have this email address as well. So, you can email him, but you know you can email anybody, me, but any of our colleagues, because if you are interested in a specific language specific region then it's very easy on our website we have all members of staff listed with the email addresses. And so if you want to know more about Arabic classes or Swahili classes, then you know you can email directly and all colleagues are very happy to, you know, engage in conversation and give you more. Yeah, and just to add to, I think if you look at the so as YouTube channel I know last year during lockdown most of the language teachers did like a language taster thing. So if you have a look on there. And so if you really are choosing completely blind between Arabic Korean, you know, have a look and see how you feel about the different language tasters. Yes, all our email addresses are obviously on the website but if you want more specifically mine is the VH4 usually use the initials for email addresses. It's VH4s at soas.ac.uk and more like is MH and that's the number. 86. 86, yeah. And then again so as.ac.uk. But yeah, please feel free to email us. Yeah, and our next session is about Arabic. So student who mentioned about Arabic you can attend for our Arabic session later at 2pm, because we need to finish now to start next session. So thank you everyone. Okay, thank you everybody. Thank you. Take care. Bye.


Welcome to the 27th lecture on the subject of digital signal processing in its applications. We have in the previous lecture completed the design of infinite impulse response filters using the bilinear transformation approach and frequency transformations. There are of course other ways to design infinite impulse response filters that is not the only way. Just to mention a couple there is what is called the impulse invariant method. In the impulse invariant method what one does is to keep the impulse response the same at chosen points of sampling that is why it is called impulse invariant and build the impulse response of the discrete time filter around that principle. In another approach one can use optimization methods. One can use methods to optimize the coefficients with respect to a desired frequency response. We are not going to discuss those approaches in this course for want of time. Instead we would now proceed to the design of finite impulse response filters and that shall be the theme of the lecture today. We are going to talk about finite impulse response filter design and specifically we are going to talk about designing finite impulse response filters with what is called the windowing approach. There are various approaches. We shall look at a few of them based on the time that we have. But this is one of the most commonly used approaches and therefore we shall look at this approach in some depth. Now as the name suggests a finite impulse response filter is one whose impulse response is finite in length and obviously the whole aim of that impulse response is again to approximate the desired frequency response with as close an approximation to the ideal as one can get. Now the design of finite impulse response filters can be likened in many ways to approximating numbers except that this is one level higher. This is an approximation of a function and there we are trying to approximate just one number. For example suppose you wish to approximate the number square root of 2. Now you know the approximation of numbers and the approximation of functions in many ways have parallels. In fact one can take inspiration from the way one approximates irrational numbers. Now remember it is irrational numbers that really require approximation. What I mean by approximation is approximation with a rational representative. When one carries out calculations on a calculator which involves irrational numbers one does not really use the irrational number at all in the calculation. One uses a representative which stands in for that irrational number and the representative has to be rational. It has no choice. That is because you have only a finite number of bits in which you can represent any number. Forget about irrational any number in the computer and if your representation in the binary form exceeds that length you are of course going to incur some error. But what you are looking for is the best approximate the best representative. It is like saying that you know I have a function to perform I have a task to do and since I cannot myself go and perform the task I send somebody else who can do the task almost as well as I can if not as well. That is what I mean by a representative. And something similar happens in the context of a finite impulse response filter. Anyway let us look at how we would approximate numbers. The irrational numbers because we already seen that the ideal impulse response that we are going to deal with is irrational. By rational I mean you can never realize it using a rational system function we have shown why. So what we are trying to realize is irrational but what we are going to use is rational. So we have this conflict right in the beginning. Now in the IR case we resolve the conflict by allowing both zeros and poles. Now we will not allow a denominator at all the denominator would be trivial. And it is only the numerator polynomial which will play a role. And therefore in a way the design of FIR filters or approximating an irrational response by using FIR filters is a polynomial approximation problem. It is a problem in which you are trying to approximate an irrational response by a polynomial. A polynomial in Z or Z inverse as you like it to be thought. Anyway coming back how would you write the number square root of 2 if you were asked to do it in decimal. Well of course many of us are familiar with what we call the square rooting algorithm but let us assume that the first few digits have been calculated. So maybe you know you would have something like 1.4142 and something beyond that. Approximate square root of 2. And of course you can convert this to binary. So you see what we do when we write this number on a computer is to truncate. That is one way to do it. You can truncate the representation up to a certain number of digits. Not at all difficult to understand. Something better that we can do is to round. By rounding we mean we look at the next digit and then we decide whether we should add one or not add one to the last digit that we have. Rounding is in some sense better than truncation because in rounding you are incurring only say potentially half the error that you might in truncation. In rounding you would not incur you know you are at most 0.5 away. You cannot really do much better than that. And the spirit behind rounding is that even after you have truncated you are trying to see if you can to some extent put some band aid on the wounds that you have created. You see by truncating you have actually cut off some vital part of that number. The number is not the truncated number. The number is much more than that. So you have cut off something vital in that number. And that cut off or that process of severing those digits from the number is going to leave scars on the value of the number. What you are doing in rounding in a certain sense is to try and apply ointment on those scars in the best possible way and you cannot do much better in the context of number than rounding. So in the case of FIR filters one is doing something similar but at a slightly higher level. Let us take the example of a low pass filter. So if you have an ideal low pass filter with the following frequency response, we know what its ideal impulse response would be. The ideal impulse response would be sin omega Cn by pi n for n not equal to 0 and omega C by pi for n equal to 0. We have seen this more than once before. Of course we are familiar with the fact that this is an irrational filter. So it is also infinite in length in both directions. We have seen what precludes this from ever being realized. Let us just repeat. For one it is infinitely non-causal, secondly it is unstable, thirdly it is irrational. And if you want a finite length filter or finite length impulse response to go as close to this as possible, one obvious thing to do is to simply truncate this response. So for example if you desire that you want an impulse response of not more than 11 samples in length. For the moment I am taking an odd number of samples and I will explain why. You see if you look at this impulse response, the ideal impulse response here let us call it H ideal of n. So if you look at H ideal of n, one very obvious thing about H ideal of n is that H ideal of minus n is equal to H ideal of n. Now you see if you look at the way you represent square root of 2, so here it is very clear that whatever you say on the positive side of n is mirrored on the negative side. Now if you look at the way you represent square root of 2 on a computer, you retain the most significant places. So suppose you want to calculate square root of 2 up to 20 decimal places and you are asked which of these decimal places should I retain. It does not require almost a no-brainer. You would obviously say keep the most important ones. Keep the integer part and keep the next few places as many as you can accommodate. It does not require too much of thinking to come to that conclusion. Now in the case of the impulse response here that is not so obvious. If I have the option of keeping 11 samples, which of them should I keep? It is not so obvious. Of course intuition tells me that I should keep the most important of them. I mean a certain sense that indeed serves the same purpose as keeping the most important digits does. And what do you mean by the most important samples? One way to identify the most important samples is to think of the samples with maximum magnitude. But then you see you cannot decide to keep some samples and throw away others in between. You know you are forced if you do wish to truncate an impulse response, you cannot keep the first and third sample and throw away the second. That would lead to something very very peculiar. So you are restricted to of course retaining or throwing away contiguous samples. And then the most obvious thing to do is to look for that part of the impulse response which has the most important samples. And in this case we can sketch how that impulse response looks. We know that this impulse response is a sampled version of the following envelope. So you can visualize this envelope. In fact you also know what this envelope means. Sine omega ct by pi t and of course at this point it is 0. And so what we have is sine omega ct by pi t sampled with rate 1 including t equal to 0. That is what you are doing. You have this ideal response, this ideal continuous function sine omega ct by pi t. You are sampling this at integer spacing and you are including t equal to 0. Now remember you might also have decided not to include t equal to 0 and we shall do that later. We also want to give an interpretation to this continuous function that we have drawn. This continuous function is the band limited function which you would get. If you restricted the discrete time Fourier transform to the range minus pi to pi. Now remember quite some time ago we had talked about the underlying band limited function corresponding to a certain discrete time Fourier transform. We said that the discrete time Fourier transform is periodic with period 2 pi. And if we choose we can always restrict that discrete time Fourier transform to minus pi to pi. What I mean by restricting is keep what is between minus pi and pi and throw out the rest. If you did that you automatically have a band limited function with a band width of pi and of course obviously pi on the normalized angular frequency axis. So of course Nyquist theorem tells us that we should sample at least an angular frequency of 2 pi and that is all that is really about the discrete time Fourier transform. So when you sample that then that means you know sampling in an angular frequency of 2 pi means a frequency of 1 and that means taking samples with an integer spacing. And of course then if you choose to sample it starting from t equal to 0 you get back the original sequence H ideal of n. And of course the Fourier transform that sample sequence is essentially the discrete time Fourier transform may be to within some constant. So we do not need this idea of the underlying band limited function here. In fact the underlying band limited function as we see it is symmetric in nature here as you see it is an even function of t and that is also reflected. Now you know it does depend on whether you have included t equal to 0 or not. If you have included t equal to 0 then if you sample at the integers the evenness is preserved. But if you choose to sample say starting from t equal to 1 by 3 onwards and that evenness is not preserved although the original underlying function is even. So one must be careful to see that evenness needs some effort to be preserved. There is another way to preserve evenness. Instead of sampling at t equal to 0 you could have also sampled beginning at t equal to minus half. You would get minus half plus half 3 by 2 5 by 2 and so on on the positive side and minus half minus 3 by 2 minus 5 by 2 and so on so forth on the negative side. Even then you would have symmetric preserved evenness preserved and you can see with some effort that these are the only 2 ways in which you can preserve the evenness. Any other process of sampling of this with integer rate will not preserve evenness. Either take 0 and then take samples symmetric around and then you know if you do wish to retain that evenness after you have truncated. So remember you have H ideal n which lasts forever on both sides. But if you wish to keep the evenness of H ideal n after truncation then you need to take an equal number of samples on the positive side of t equal to 0 as on the negative side and therefore we shall first begin with odd length finite impulse response filter design. So for example as I said suppose you wish to preserve exactly at not more than not say exactly not more than 11 samples in the impulse response then the most sensible thing to do as you can see from here is to retain 5 samples on the positive side 5 samples on the negative side and the sample in the middle at t equal to 0. Now on the other hand if you are asked to retain only 10 samples not more than 10 samples and you still want evenness to be preserved then you have to work a little harder. Clearly you need 5 samples on the positive side and 5 samples on the negative side. So then you have to resample this continuous function. You need to resample it starting from t equal to half. So let us look at this function. You know if you want an even number of samples then you have samples starting from t equal to half and then of course you would include half 3 by 2 5 by 2 and so on and half minus 3 by 2 minus 5 by 2 and so on. And then you can take 5 samples on this side 5 samples on this side and you would still have symmetry. So now it also tells us how to deal with the situation when you want an odd length FIR filter and when you want an even length FIR filter while preserving symmetry while preserving evenness. For the odd length there is no problem. Just retain as many samples. For example if you want an odd length filter of length not more than 11 just retain 11 samples keeping the center intact 5 on either side. If you want the length 21 keep the middle t equal to 0 and then take 10 on either side and so on. But if you want an even length then you have to work a little harder you must shift the point of sampling by half and then take an equal number of samples on the positive and negative side. So this should be observed right in the beginning right odd length or even length. So you see now we will keep on talking odd length even length every time. We will discuss the odd length case and for the even length case you need to make that little change and what is the effect of making that little change when you sample starting from half onwards all that you are doing is introducing a delay of half a sample an effective delay of half a sample. It does not affect the magnitude of the frequency response it only affects the phase response that too it introduces a constant time delay at all frequencies so it can be condoned. So even length FIR filter incurs even length FIR filter design by truncation incurs the additional penalty of introducing that delay which we can anyway we will see in a minute that you cannot do without a delay you know but you have to bring in that delay right in the beginning when you resample. We will discuss odd length FIR filter design and from for the even length you just have to make this little change you can keep that in mind right from the beginning. Anyway now the point is that the simplest thing to do as I said if you wish to retain a certain number of odd samples to n plus 1 so let us assume that you wish to design.


I've always been a radical, I've always challenged the state's quo. Do you feel that you're part of a libertarian movement? No, I don't. No, so what are you then? Well, I'm not a part of a movement. I've never been a part of a movement. I just I just do my own thing. Walter Williams, the free market scholar and iconoclast, died last week at the age of 84. He was the author of 13 books and was best known for his work demonstrating that government interference in the free market has been especially harmful to black Americans. Born in 1936, Williams grew up in the Richard Allen homes, one of Philadelphia's first housing projects. I broke out of the North Philadelphia ghetto nearly 30 years ago and so did most of my friends. When he was a small child, his father deserted his family. He was brought up by his mother, a high school dropout, and the family spent time on welfare. But Williams would later draw a distinction between material poverty and what he called poverty of the spirit. Even though we grew up poor, we didn't we didn't consider ourselves poor. That is a matter of fact, during those days to call somebody poor was an insult. When I was a kid, my mother used to always say to us, she says, you know, we have a beer pocketbook, but we have champagne taste. Williams worked as a taxi driver in the city of brotherly love and was once ordered out of his cab by a white police officer beaten up and then charged with disorderly conduct. He was drafted into the army and while stationed in Georgia kept getting in trouble, occasionally with his fists for standing up to the racism of white officers. But he came to believe that discrimination should be legal just as long as it didn't involve government resources. One of my strong values is freedom of association. If you believe in freedom of association, you have to accept that people will associate in ways that you find offensive. And I believe people have the right to discriminate on any basis they want so long as they're not using a government. For me, discrimination is just simply an act of choice. After the army, Williams studied economics at California State College and then went to UCLA for graduate school where he was exposed to titans of free market economics, including Milton Friedman, James Buchanan and UCLA's department chair, Armin Alcheon. Flunking economic theory the first time around he wrote in his memoir, I later realized did have a benefit. It convinced me that UCLA professors didn't care anything about my race. They'd flunk me just as they'd flunk anyone else who didn't make the grade. I don't judge people by colors.  And that's what my stepfather used to say.  In 1977, Williams started writing a weekly column which was eventually syndicated in 140 newspapers. He was also a contributor to Reason Magazine and served as a trustee on the Board of Reason Foundation, the non-profit that publishes Reason TV. For all his individual accomplishments, Williams was especially proud of his role in making George Mason University's economics department a home for free market radicals. There was considerable hostility towards our department and I had a lot of difficulty and so I just said well the only way I'm going to improve the department is to try to privatize the department and actually go out and raise money. Last week, his former colleagues at George Mason paid tribute to their mentor and friend. GMU Econ has lost an iconic and heroic figure, wrote Pete Betke. He taught with wit and passion the logic of economic reasoning. He's one of my few heroes, wrote Don Boudreau. Liberty is the rare state of affairs in mankind's history. Arbitrary abuse and control by others is the standard dish even now and all the tendencies are it's for us to have greater and greater amounts of our liberty usurped by government. Rest in peace, Walter Wuggins.