A warm welcome to the 28th lecture on the subject of wavelets and multirate digital signal processing. Let us spend a minute or two in recalling what we did in the previous lecture. We had in the previous lecture briefly introduced the need for thinking out of the box in the context of multi resolution analysis. Specifically, we had introduced some variants of the idea of multi resolution analysis and these variants that we had talked about where one where we do not insist on the synthesis and the analysis filter banks to be the same or for that matter we do not insist on an orthogonal filter bank. The second where we do not insist on iterating only on the low pass branch and third where we do not insist on FIR filters. Today we shall explore in greater depth the possibility of allowing different analysis and synthesis filter banks and in fact related to that is the idea of having different length low pass and high pass filters. After we complete our discussion on one such filter bank which has been accepted in the standards we shall also make it clear why such filter banks are attractive. So, with that then let us proceed to the main theme of the lecture today. You will recall that in the previous lecture we had briefly introduced the one the recent standard for data compression called JPEG 2000 joint photographic experts group standards introduced around the calendar year 2000 and we were going to talk about what is called the 5 3 filter bank and associated with it what is called the spline multi resolution analysis. Well just to put back a few points that we had talked about towards the end of the previous lecture we had seen that we could extend the dilation equation constituted for the R MRA namely phi 0 t is phi 0 2 t plus phi 0 2 t minus 1 by convolution with itself to get phi 1 t is half phi 1 2 t plus phi 1 2 t minus 1 plus half phi 1 2 t minus 2 and we had noted that if we look at the coefficients of this dilation equation diadic dilation equation. The coefficients essentially represent the filter half 1 plus z inverse the whole squared and in fact, phi 1 t is piecewise linearly. Now, an important observation is that as we convolve phi 0 t with itself repeatedly we seem to get piecewise polynomials of higher and higher degree and this notion of piecewise polynomial of higher and higher degree is what is captured in the word spline. So, let me put down a not so formal, but a reasonably clear definition of the word splines. Spline are polynomial pieces or piecewise polynomial functions. In fact, to be more precise they are piecewise polynomial interpolants functions that interpolate that join that complete in between samples using piecewise polynomials and as you can see there is a generalization here from the idea of piecewise constant approximation with which we began the discussion on the higher multi resolution analysis. Now, we also noted the shortcoming of phi 1 t. The shortcoming of phi 1 t is that it is not orthogonal to all integer translates. I must make one thing clear here phi 1 t is of course orthogonal to integer translates where the integers are multiples of 2. Let me sketch phi 1 t for you once again phi 1 t looks like this and it is of course orthogonal to phi 1 t minus m for m greater than 2, but it is not orthogonal to phi 1 t minus 1 and that is the catch point or that is the shortcoming here. When we say orthogonal to all integer translates we mean all integer translates we cannot excuse one, but then you know we will see after a while that although we cannot excuse that one integer translate where it is not orthogonal we can indirectly incorporate it to build a different paradigm of orthogonal multi resolution analysis, but that is a more difficult exercise. We agreed towards the end of the previous lecture first to take a slightly out of the box approach not to insist anymore on orthogonal multi resolution analysis and we shall take that approach first. In other words let us put down one of the low pass filters either on the synthesis or the analysis side to be exactly the filter that constitutes the coefficients of this dilation equation. Let us consider a filter bank a two band filter bank just to recapitulate some of our ideas what we are saying is we have this two band filter bank where the low pass filters are H 0 z and G 0 z on the analysis and synthesis sides respectively and the high pass filters are H 1 z and G 1 z again on the analysis and the synthesis sides respectively in here out there. So, what we are saying is let without loss of generality G 0 z equal to 1 plus z inverse the whole square. Now, I must before I proceed make an important remark about perfect reconstruction filter banks you know the question is we have chosen G 0 z to be 1 plus z inverse the whole square we could have as well chosen H 0 z to be 1 plus z inverse the whole square. An important question that we must answer is if I interchange the analysis and the synthesis side what difference does it make? Now, to answer that question let us look at the requirements of aliasing cancellation and perfect reconstruction. The aliasing cancellation requirement essentially says G 0 z H 0 minus z plus G 1 z H 1 minus z is 0. Now, if we replace it by minus z we would get H 0 z G 0 minus z plus H 1 z G 1 minus z is equal to 0. Now, let us keep this as one of our observations and take the second observation now namely that of the perfect reconstruction condition. The perfect reconstruction condition says G 0 z H 0 z plus G 1 z H 1 z is essentially of the form a constant and then a delay. Now, here we can interchange G and H as you notice in other words we could say H 0 z G 0 z plus H 1 z G 1 z is the same thing trivially true and now if I combine these two observations that I have made you will notice that this equation is an aliasing cancellation equation for the case when you have interchanged the analysis in the synthesis side. So, here the synthesis low pass filter has become the analysis low pass filter and the synthesis high pass filter has become the analysis high pass filter and this then becomes the aliasing cancellation condition for this interchanged filter bank. As far as the perfect reconstruction condition goes we do not need to do anything at all it is already an interchanged condition. So, if H 0 where the synthesis low pass and G 0 the analysis low pass and correspondingly if H 1 where the synthesis high pass and G 1 the analysis high pass we would still have this perfect reconstruction for this rearranged or exchanged two band filter bank as the case is and therefore, we have a very important conclusion that we draw here. Once the perfect reconstruction conditions are satisfied in a two band filter bank analysis and synthesis filters can be exchanged to give another perfect R P R stands for perfect reconstruction perfect reconstruction two band filter bank. A very important observation because it tells us that it is not so critical it is not so important which pair of filters we put on the analysis side and which pair of filters we put on the synthesis side as far as perfect reconstruction goes. But there is a subtle point here and that subtle point is if you look at the low if the low pass filters happen to be different on the two sides and if you use the low pass filters to construct a dilation equation a dyadic dilation equation I mean the coefficients of the low pass filter could be thought of as representative of the coefficients of a dilation equation that operates on the scaling function. So, if you visualize the two different scaling functions that come out of the analysis and the synthesis side it is quite possible that one of them is quote unquote smoother than the other and in that case one might want to decide which scaling function to put on the analysis side and which one to put on the synthesis side. A broad guideline is that it is desirable normally to put the smoother function on the synthesis side because if one uses smoother functions to synthesize one would get more appealing reconstruction after quantization that is an aside, but an important observation. But coming back to this spline filter bank that we are now going to build let us consider a two band filter bank as we have here with g 0 z as it were equal to 1 plus z inverse the whole square. Now, we shall take the alias cancellation equation first and we shall insist initially only unsatisfying the alias cancellation equation which tells us that g 0 z h 0 minus z plus g 1 z h 1 minus z is equal to 0. Now, we can rearrange this as you know to the following equation g 0 z by g 1 z is minus h 1 minus h 1 minus h 1 minus h 1 minus h 1 minus h 1 minus z by h 0 minus z and one simple choice to ensure alias cancellation is to choose numerator equal to numerator here and denominator equal to denominator and that is exactly what we shall do. We shall choose g 0 z equal to minus h 1 minus z and g 1 z is equal to minus h 0 minus z and therefore, the equations that we would get now we want to write all the equations in terms of g 0 and h 1 because once we know g 0 we know h 1. So, therefore, in our discussion here we would have minus h 1 minus z is 1 plus z inverse the whole square from here and therefore, we would have h 1 of z is minus of course, take the minus sign on the other side and replace z by minus z. So, 1 minus z inverse the whole square this is what we have. Now, we write down the perfect reconstruction condition as well. The perfect reconstruction condition says g 0 z h 0 z plus g 1 z h 1 z is a constant and a delay and we know h 1 and we know g 0. We are required to find h 0 h 1 minus and g 1. Here again we know that g 1 can be expressed in terms of h 0 in fact, we have the expression here. So, let us make a substitution of g 1 in terms of h 0 we essentially wish to obtain h 0. So, making this substitution we would have g 0 z h 0 z plus h 0 minus z well h 1 z, but h 1 z can again be expressed in terms of g 0 z. So, we leave it like that we know it is c 0 z raise the power minus t. In fact, let us write down h 1 in terms of g 0 notionally first. So, you know if you recall g 0 z is minus h 1 of minus z. Now, of course, we have an explicit expression for h 1, but what I wish to do is to bring out a property of this product here g 0 h 0 by making an explicit substitution. So, let me take h 1 z and rewrite it in terms of g 0 z. So, h 1 z would clearly be minus g 0 minus z and we can make that substitution here. So, we will substitute h 1 by minus g 0 minus z and all in all we then have something very interesting in terms of the samples of this product. So, now again we have a situation where we have a product of z transforms and then the same product of z transforms with z replaced by minus z. Let us see what we have here. So, you notice we have g 0 z h 0 z minus g 0 minus z h 0 minus z is essentially a constant and a delay. And if we choose to denote g 0 z h 0 z by another kappa 0 z, what we are saying in effect is kappa 0 z minus kappa 0 minus z is essentially a constant and a delay. And recall that this operation kappa 0 z minus kappa 0 minus z essentially brings up the odd samples and destroys the even samples. So, kappa 0 z minus kappa 0 minus z is c 0 z raise the power of minus t means that if we kill the even samples in the inverse z transform of kappa 0 z.  And out of the remaining odd samples only one is non-zero and that is captured in this c 0 z raise the power of d. The c 0 z raise the power of d is the z transform of essentially the inverse z transform of kappa 0 with all the even samples killed and the odd samples left. That means among the odd samples the d th sample is equal to c 0. In fact, we can say something specific here we can say the d th sample is equal to c 0. And now our whole exercise is to impose this condition on the product kappa 0 z raise the power of minus h 0 z g 0 z amounting to kappa 0 z. Now to do that let us of course, recognize that we have too much of freedom here. In imposing Elias cancellation we have put down only two conditions we have constrained one of the filters. The other low pass filter is free for us to choose, but we must choose it strategically. Now you will recall the importance of the factors 1 plus z inverse or their higher powers. A factor of the form 1 plus z inverse ensures a 0 at z equal to minus 1 or e raise the power j omega equal to minus 1 or omega equal to pi. So, on the unit circle we are putting a 0 a null at pi pi or minus pi that is not an issue. Now this as you recall is one of the sufficient conditions to ensure that when we iterate such a low pass filter to produce a scaling function that iteration converges to a quote unquote smooth scaling function. So, it is one of the conditions that ensures what is called regularity of the iterated scaling function. In our choice of g 0 z we already have two factors 1 plus z inverse the whole squared. If we wish to bring at least some degree of symmetry on the analysis and synthesis side although we do not intentionally wish to bring complete symmetry only a little bit of symmetry. At least we can ensure that they have the same degree of regularity the same degree of smoothness in iteration. And therefore, we shall choose h 0 z also to have 2 0s at z equal to minus 1. In other words we shall choose h 0 z to have a factor 1 plus z inverse the whole squared. Now what we wish to do next is to look for the minimum possible solution which we can get to satisfy perfect reconstruction. So, as is always the case we start very parsimoniously very stingily we want to construct kappa 0 z. Now we already know that we have a 1 plus z inverse squared corresponding to g 0. We have a factor of 1 plus z inverse the whole squared in h 0 and we wish to introduce just as many additional 0s in h 0 as are required to satisfy the perfect reconstruction condition. And by the by one of the shortcomings of an orthogonal filter bank. In fact, if you look at the Dabash series of orthogonal filter banks of that matter if you look at the very conditions on perfect reconstruction and iris cancellation when we look at the filters in orthogonal filter bank. One can with a little effort it is a slightly difficult exercise, but with a little effort one can show that one cannot possibly get what is called linear phase. In other words the impulse response cannot possibly be symmetric I will give you a hint why that is so. For a symmetric impulse response in a finite impulse response filters the 0s must occur in reciprocal pairs. So, for every 0 inside the unit circle there must be a 0 outside the unit circle. Now this kind of a choice of reciprocal pair of 0s is just not possible when we construct the low pass filter in an orthogonal filter bank. I shall not dwell any further on the proof of why this is not possible or why this is true, but this is the central reason why one cannot get linear phase in an orthogonal filter bank beyond the very trivial and simple case of h r where the 0 lies on the unit circle. So, it is 1 plus z inverse there and 1 minus z inverse for the high pass filter 0 lies on the unit circle, but for any higher order multi resolution orthogonal analysis one just cannot get linear phase. And this is one of the reasons why as I said we wish to think out of the box we do not wish to confine ourselves to orthogonal multi resolution analysis. We would like to explore other options that is what we are doing here. So, if we do wish to bring in that additional degree of freedom we wish to explore the possibility of bringing in in such a way that linear phase can be ensured. So, what we shall do now is to introduce just one more degree of freedom in constructing h 0 in such a way that linear phase is maintained. In other words that the impulse response continues to be symmetric. So, parsimoniously in informal language stingily extending h 0 z to retain symmetry we shall therefore introduce as I said just one parameter. So, we will introduce a factor 1 plus h 0 small h 0 z inverse plus z raise the power minus 2. So, what I am saying is retain symmetry this is a symmetric factor and the only degree of freedom is this. And therefore, we have h 0 z is essentially 1 plus z inverse the whole squared times 1 plus h 0 z inverse plus z raise the power minus 2. Now, I am a couple of remarks you know in retaining symmetry I could have used the same constant let us say h 1 here and here and kept a constant h 0 here. So, apparently I would have had two degrees of freedom, but this factor h 1 here essentially scales the whole filter by a constant. Now, I am not really interested in scaling you know I could scale all the impulse responses by appropriate constants and thus change the constant c 0 that is not going to materially affect the nature of my filter bank. So, I am introducing only so many degrees of freedom as give me something novel in terms of nature of frequency response not in terms of the scaling constant c 0 which I can always adjust in the end. So, therefore, keeping only this degree of freedom here let us now impose the condition on g 0 h 0. Let us now consider the product g 0 h 0 and that product is going to be g 0 z h 0 z given by 1 plus z inverse the whole squared times 1 plus z inverse the whole squared times 1 plus h 0 z inverse plus z raise the power minus 2 and let me expand this 1 plus z inverse the whole squared times this is 1 plus z inverse the power 4. So, let me first expand 1 plus z inverse the power 4 essentially 1 plus 4 z inverse plus 6 z raise the minus 2 plus 4 z raise the power minus 3 plus z raise the power minus 4 and now I shall use the convenient notation of coefficients only. So, when I multiply this factor by the factor 1 h 0 1 you know. So, let us use this representation. So, I have 1 4 6 4 1 convolved with essentially you are multiplying 2 by 2. Z transforms amounting to convolving the sequences it would give me essentially 1 4 6 4 1 h 0 4 h 0 6 h 0 4 h 0 and h 0 and back again 1 4 6 4 1 and when I add them I have 1 minus 4 plus h 0 1 plus 4 h 0 plus 6 and you have 8 plus 6 h 0 1 plus 4 h 0 plus 6 4 plus h 0 and 1. This is the 0 h sum and therefore, you have the even samples here the second sample here fourth sample here the sixth sample here. We are not worried about the even samples we are going to kill them anyway in kappa 0 z minus kappa 0 minus z. What worries us is the odd sample let us mark them and we are required to retain only one odd sample. How can we do that? Notice that these are essentially the same sample. So, if I anal this sample I have achieved my objective essentially if we make 4 plus h 0 equal to 0 in other words h 0 equal to minus 4 we have retained only one odd sample. And therefore, let us make precisely that choice h 0 equal to minus 4 and therefore, h 0 z is essentially 1 plus z inverse the whole squared times 1 minus 4 z inverse plus z raise the power minus 2. Now, let us look at the degree of h 0 here h 0 z can be of course, expanded now you know we will use the same strategy we will convolve 1 to 1 convolved with 1 minus 4 1. So, we have 1 to 1 minus 4 minus 8 minus 4 and 1 to 1 1 minus 2 minus 6 minus 2 n 1. This is the impulse response of the other low pass filter as you notice again symmetric. And therefore, h 0 z would turn out to be 1 minus 2 z inverse minus 6 z raise to the minus 2 minus 2 z raise to the power minus 3 plus z raise to the power minus 4. Now, what we have just arrived in this discussion is a very important bi orthogonal filter bank. Let us look at the length of the impulse response of h 0. Obviously, the length is 5 and let us look at the length of the impulse response of g 0. Let me put down g 0 for completeness here. Obviously, the length of the impulse response is 3. So, let us write that explicitly length 5 and length 3 and that is precisely the reason why this filter bank that we have just arrived this perfect reconstruction filter bank that we have just brought out in this discussion is called a 5 3 filter bank. This is the celebrated 5 3 filter bank in JPEG 2000. Now, you know JPEG 2000 admits two kinds of filter banks a 5 3 filter bank and a 9 7 filter bank and now we know what 5 3 and 9 7 mean. They essentially refer to the lengths of the impulse responses. 5 3 means the impulse responses are of lengths 3 and 5. Now, which impulse responses as you can see you could think of them as the impulse responses of the two low pass filters or you could think of them as the impulse responses of the two high pass filters. It does not matter. You could also think of them as the lengths of the impulse responses of the analysis filters or the lengths of the impulse responses of the synthesis filters. In fact, let us put it down explicitly what the lengths are in this 5 3 filter bank. So, in the 5 3 filter bank as you recall h 0 has a length 5, g 0 has a length 3. Now, if this has a length 5 then the high pass filter on the synthesis side would also have a length 5 and if this has a length 3 the high pass filter on the analysis side would also have a length 3, analysis synthesis. So, this is the length distribution in a JPEG 2005 3 filter bank. Now, you know let us put down explicitly all the filters in the JPEG 2005 3 filter bank and for that let us just recall the relationships. We had g 0 z is minus h 1 of minus z. In other words h 1 z is minus g 0 minus z and therefore, h 1 z is going to turn out to be minus 1 minus z inverse the whole squared. Further g 1 z is h 0 of minus z and that would turn out to be 1 you know. So, wherever you have odd powers of z inverse the signs are going to get reversed.  This is the high pass filter. You know in fact if you care to look at the impulse response and if you add up the impulse response coefficients 1 2 minus 6 2 and 1 you can see their sum is 0 and that is to be expected. After all the impulse response of a high pass filter which has a null at 0 frequency as many good high pass filters have must sum up to 0. It is very often the case that a high pass filter has its impulse response summing to 0 indicating that it has a null at 0 frequency and that is true in this case as well. In fact here the high pass filter has a double null at 0 frequency because it has a factor of 1 minus z inverse the whole squared. Anyway that a part we have now put down very clearly what the impulse responses are on the entire 5 3 jpeg 2000 filter bank. The aim of this exercise was to show you how one builds what is called a bi orthogonal filter bank and I wish to spend some time on discussing this notion of bi orthogonality. You know in the axioms of a multi resolution analysis we had put one of the axioms to be the scaling function must be orthogonal to its integer translates. Now if you construct the axioms with a scaling function from g 0 here namely phi 1 t that piecewise linear triangular function that we started with in this lecture it is obviously not true for that scaling function. So this g 0 by itself is not going to give us an orthogonal multi resolution analysis. What is the slight generalization that we need to make here then? Well the generalization is in terms of dealing with a pair of scaling functions. So you have one scaling function emerging from the synthesis side and one scaling function emerging from the analysis side from g 0 and from h 0. The orthogonality is actually when you take them together and so as to explain the idea little better let me start from a two dimensional space. You know in a two dimensional space if you have two orthogonal unit vectors let us say u 1 cap and u 2 cap then this forms an orthogonal system by itself.  They are unit vectors but not orthogonal. However of course they are linearly independent. Obviously these two unit vectors u 1 cap let us call them u 1 till day cap and u 2 till day cap. u 1 till day cap u 2 till day cap do form a basis in two dimensional space because they are linearly independent. But if I wish to obtain the coordinates so suppose I wish to take any vector let us say x in two dimensional space and I have this pair of unit vectors here u 1 till day cap and u 2 till day cap and I wish to express x as c 1 times u 1 till day cap plus c 2 times u 2 till day cap. How would I obtain the constants c 1 and c 2? I cannot do them by taking the dot product with respect to u 1 till day u 2 till day cap because they are not orthogonal that is the convenience of an orthogonal basis. What I can do however is to construct what is called a bi orthogonal basis. So, I could instead start from this basis u 1 till day cap and u 2 till day cap. Now I could take a vector which is perpendicular to u 2 but not to u 1 and let me show that one. Let me call this v 2 cap. So, v 2 cap is perpendicular to u 2 but not to u 1. Similarly I could have a vector perpendicular to u 1 but not to u 2 maybe this vector let me call it v 1 cap. Now if I were to take the dot product here if I come back to this if I take the dot product of x with v 1 cap here they would be u 1 would go away because of the dot product because of v 1 being perpendicular to u 1 cap but this c 2 would remain and similarly when I take the dot product with respect to v 2 cap here. So, if I take the dot product of x with respect to v 2 cap it would destroy the term of u 2 till day but retain the term of u 1 till day namely I would be able to obtain c 1 by taking the dot product of both sides of this equation with v 2 cap and I would be able to obtain c 2 by taking the dot product of both sides of this equation with v 1 cap and therefore, we say v 1 cap v 2 cap is a bi orthogonal basis a bi orthogonal basis to this basis. In fact, they are mutually bi orthogonal each of them is bi orthogonal to the other and in fact this is the idea that is generalized when one builds a bi orthogonal filter bank. This is one generalization one variant that we have introduced in two band filter banks. In the next lecture we shall introduce another variant. Thank you.


A very good evening friends, I welcome you all to the Hindu Newspaper Analysis brought to you by the Shankara AIS Academy. Today's date is 13th December 2023. Before entering our discussion, I have an important announcement to make. See, batch 4 of the pre-storming test series of the Shankara AIS Academy is going to start on 16th December 2023. Even though the orientation got completed on 10th December, you can still enroll on the program and watch the orientation appear for the first test which is going to be held on 16th December. So, you can enroll in the program and boost your propellant score. Now back to our business, let's look at the list of articles which we are going to discuss today. So, without wasting time, let's get into discussion. The news here is that the public sector banks have transferred non-performing assets or NPA of more than 11,617 crores to the NARCL between January to November of this year. See, this is the crux of the article. So, in our discussion today, we will see what is NPA and we will also discuss about NARCL from a print perspective. First of all, what is non-performing assets or NPA? See, NPA refers to the loans and advances that are in default or in arrears, that is principal and interest payments are late or missed. You may note that for a bank, the loans given by it are considered to be the assets of the bank. So, as per RBI, an asset becomes a non-performing when it stops to generate income for the bank. So, if the principal or the interest or both the components is not being paid back to the lender, then it would be considered as a non-performing asset. Put it simply, NPA is any asset of a bank which is not producing any income and these NPAs are declared by the concerned banks. As per the RBI, a non-performing asset is a loan where interest or installment of principal remains an overdue for a period of more than 90 days in respect of term loans. The bills which is remaining overdue for a period of more than 90 days in case of a bills being purchased or discounted. See, any amount is said to be overdue if it is not paid on the date of due as fixed by the bank. See, the installment of principal or interest remain overdue for two crop seasons for the short duration crops. Moreover, the installment of principal or interest remain overdue for one crop season for long duration crops. See, the last two parameters which we have discussed with respect to the agricultural loans. See, this is all about the basics of NPA. Now, let us move on to National Assert Reconstruction Company Limited or NARCL. See, NARCL is a bad bank created by the government. The NARCL has been incorporated under the Companies Act. Note that the state owned banks will have a 51% stake and the debt management companies will hold 49% stake in the NARCL. See it is registered within Reserve Bank of India Assert Reconstruction Company or ARCs. See, this is under the surface Act 2002. Here let us see a little brief about the bad bank. See bad bank is a financial institution that primarily deals with distressed or non-performing assets. The primary purpose of a bad bank is to separate the non-performing assets from the performing or healthy assets of the bank. The separation helps the main bank to focus on the core functions without being weighed down by the troubled assets. Okay, now coming back to our discussion. As a bad bank, NARCL will pick up the bad loans from the commercial banks. It would then sell them to the prospective buyers of the distressed assets. The NARCL will also be responsible for valuing the bad loans to determine at what price they should be sold. Okay, to resolve the NPA crisis in our country, the government along with the NARCL has also set up Indian Depth Resolution Company Limited or IDRCL. See IDRCL is an asset management company just like our NARCL. This entity will provide management and resolution of asset support to the NARCL. This company will evolve strategies to ensure the best possible recovery and the resolution process of the bad loan. The public sector banks will hold a maximum of 49% stake in this IDRCL. The remaining 51% will be with the private sector lenders. Okay, having covered all the basics of these two separate entities, we will now look at its working with an help of a practical example. Now let us assume Ms Devi borrowed 200 crores from this State Bank of India to set up a business. But due to COVID-induced lockdown, the business failed and Ms Devi failed to repay the entire loan of Rs 200 crores. So for SBA, the loan given to Ms Devi has become a stressed asset. So SBA is looking to sell off this asset. This is where NARCL will come in. NARCL will negotiate with SBA and buy the 200 crore asset for Rs 100 crores. The NARCL will pay 15% of the agreed price that is 15 crore in cash and it will pay the remaining 85% that is 85 crores in the form of security receipts. Then NARCL will take the help of IDRCL. See as we have discussed already, IDRCL will provide management support now. So IDRCL will use its expertise and manage the asset. It will try and maximize the value of the asset. Once this is done, NARCL will try to sell it to other prospective buyers for the profit. Say it finds a new buyer Ms Rani and sells that assets of Devi to 120 crores. In such a scenario, NARCL will pay the balance 85 crores to the State Bank of India. It will also pay some money as a consulting fee to IDRCL and it will also make a profit as the asset is sold at Rs 120 crores. See this is what happens if NARCL is able to sell the asset for profit. Now let us see the other side of the coin. Now if NARCL is not able to sell the asset as a profit even after seeking the help of IDRCL. Let us see this scenario also. Let us assume Ms Rani is a better negotiator and is not offering anything above 80 crores. In such a situation, the government provides guarantee to the NARCL. This difference between what the commercial banks were supposed to get and what NARCL was able to raise will be paid by the government. So as per our example, the government will pay 20 crores to the NARCL. See this is how NARCL and IDRCL will function and helps to dispose the stressed assets. In simple ways, NARCL offers the same service as provided by Murli Prashat Sharma in Munabhai MBBS or Rajaram in Vasul Raja. Finally, before concluding, let us see how NARCL is different from the already existing ARCs. See, in NARCL, the PSB's public sector banks are the majority stakeholders. So it will have a public sector character. At present, ARC is trying to take a steep discount on the loans. But since NARCL is a governmently-backed one, it will have deep pockets. That is, it will have a substantial financial resources or a significant amount of money at their disposal. See, this is used to buy out the big accounts and thereby freeing up the balance sheets of the bank. See, this is all regarding this discussion. In this discussion, we saw about the basics of non-performing assets and we also saw the working principles of the NARCL and IDRCL. Okay, with all these learned points, let us conclude this discussion and take up the next news article for our analysis. Lugthi's editorial article. This article is written in the backdrop of a recent Supreme Court judgment on the abrogation of special powers to Jammu and Kashmir. In 2019, the President of India issued Constitution Application to Jammu and Kashmir Order 2019. This order removed the special status that was earlier granted to Jammu and Kashmir under Article 370. This presidential order was challenged before the Supreme Court. In this case, recently, the Supreme Court pronounced the judgment. The Supreme Court stated that the decision to abrogate the special status of J&K Article 370 was valid. The SC highlighted that the Article 370 was a temporary provision and Article 370 itself granted authority to the President to abrogate the same article. So citing these provisions, the SC validated the abrogation of this article. The Supreme Court further directed the Election Commission to conduct the elections to the Legislative Assembly of the J&K within September 30, 2024. But note that the SC did not mention about the restoration of statehood to the bifurcated U.T. So, the author of the article says that the Supreme Court should have given a deadline for the restoration of statehood along with the deadline for the elections. See, this author points out that the restoration of statehood is important to guarantee a degree of federal autonomy to J&K. It will help the elected government to better address the concerns of the electorate. See, this is the crux of the editorial article which was written in Hindu today. Now in our discussion, let us understand the advantages and disadvantages of the abrogation of Article 370. We will approach this topic using our usual main censor writing approach. Now let us see the question. The question is, recently the Supreme Court upheld the decision of the central government to abrogate the special status of J&K under 370. In the light of this above statement, discuss the impact of abrogation of Article 370 in India. See, this is the question which is asked for 15 marker and 250 words. See, this type of question can be asked in the G.S. paper 2 under the syllabus of Indian constitution, historical underpinnings, evolution, futures, amendments, significant provisions and basic structure. And this also can be asked under functions and responsibility of the union and states, issues and challenges pertaining to federal structures. Okay, this is all about the syllabus. Now come back to the question. Here the keywords discuss. If the keywords discuss, then we have to write a written debate about the given question. We have to provide prose and cons of the issue with some valid evidences. So for this question, we have to write prose and cons for Article 370. Now let us get into introduction. Since the question is about Article 370, we can write about the background of 370 in our intro part. See, before India's independence, the JNK was a princely state. During partition, the state decided to remain a princely state rather than joining India or Pakistan. But later on, Pakistan launched the war in order to annex Kashmir. So the then Maharaja of Kashmir, Hari Singh sought the help of Indian forces. As a result, Maharaja signed the instrument of accession with India. India also provided assurance to provide some special status to JNK. Later, Article 370 was enacted by the Indian government to secure Kashmir relationship with India. This article granted a special status, certain special rights to Kashmir. Article 370 allowed Kashmir to keep its own separate constitution, which is somewhat independent from Indian constitution. This article also limits the legislative power of the central government vis-à-vis Kashmir. This provisions hindered the complete integration of JNK with India. So in 2019, the President of India issued a constitution application to JNK order 2019. This order states that all the provisions of the constitution of India will be applied to the state of JNK. So this order ultimately abrogated the special power which was granted to JNK under 370. Later this order was challenged before the Supreme Court. The Supreme Court recently upholded the presidential order. So as of now, JNK no longer enjoys the special power which was granted under Article 370. See in this way, you can give an introduction. Here I have provided a background information from the creation to abolition of 370. You can write some important points from the intro part for the background of Article 370. See, this is a model intro which was given by me. If you have a better intro, write it and post it in the comments section. Ok, now let us come back to our discussion. Now let us see the body part of our answer. As I said earlier, in the body part we have to write the pros and cons of the 370 abrogation. First let us see the pros of the abrogation of Article 370. Firstly, the abrogation strengthened the unity and integrity of India. Due to the abrogation of Article 370, that separate constitution that existed to the JNK got abolished. As a result, JNK residents can now truly enjoy the status of Indian citizens. This allows them to integrate with the rest of India and it also strengthened the unity of India as a whole. Secondly, the abrogation of 370 results in the equal access to rights. See, before abrogation, only the permanent residents of JNK were able to get employment under the JNK government. Apart from this, the outsiders did not be able to buy property in the state. With this abrogation, every eligible citizens of India can get employment under the JNK government. Then, the members from the outside states will also be able to buy property in the state. As I said earlier, this abrogation guarantees the equal access to rights in the JNK. Thirdly, this abrogation aid in the economic growth of the state. As a result of this abrogation, the private investors can now be able to invest in purchasing the lands and establishing companies in the state. This will result in increasing the job opportunity and it eventually will boost the economy of the state. Fourthly, it will help the JNK people to get better health facilities. As I said earlier, due to the abrogation of 370, the members from the outside states will now be able to buy property in the state. So more private hospitals will be built in this region. This will in turn increase the availability of the better healthcare centres in JNK and people will get better treatment. And finally, this abrogation will strengthen the fundamental principles of equality before law. As I said earlier, before the abrogation, JNK have a separate constitution. So the residents had their own separate laws and rights. This defeated the principle of equality before law. Now due to abrogation, the rights of the JNK citizens will be equal to the rest of Indians. This removes the special privilege to the citizens and ensures a greater national integration. See this is all about the pros of the Article 370 abrogation. Now moving on to see the cons of the abrogation. The first disadvantage is that there is a possibility of violent breakdowns. As significant JNK residents are against the abrogation of the special status, there is every possibility of a violent protest in JNK. This will seriously hinder the or seriously affect the internal security of India. Apart from this, some radical elements also use this chance to propagate their separatist and radicalist ideas. This will also increase the threat of terror attacks and it will eventually affect the security of India. The second disadvantage is that there is an increased control of central government in the JNK region. See after the abrogation, JNK has been proclaimed as a union territory with the legislature. As we all know, the power of the union territory government is substantially lower than that of the state government. So the central government will now have more power over JNK. As a result, the degree of federal autonomy to JNK will be diminished. See this is the second disadvantage. Let us see the third one. There is a possibility of environmental pollution in JNK. See as we all know, JNK is one of the main attractions for the tourist. So due to the abrogation of 370, more private business will engage in building the tourist infrastructure in the state. Availability of better tourist facilities will lead to increased inflow of tourists. So if the government won't employ proper management plans, this will increase the waste system in JNK. This will eventually pollute the environment of the state. See these are all some of the cons of the abrogation of 370. Guys, I have given you a schema of the body part or if you have alternative viewpoints, you can write and feel free to post in the comment section. See this is all about the body part of the answer. Now let us see the conclusion. In the conclusion, we can give a balanced view of the abrogation. The conclusion can be like, there is no doubt that abrogation of article 370 will strengthen the unity and integrity of India. Abrogation of this article brought the people of JNK very closer to the other state people. This will foster a better relationship among the people and will further the socioeconomic development of both Kashmir and India. But soon, the central government should restore the statehood to JNK in order to guarantee a degree of federal autonomy. This will help the JNK government to better address the concerns of the electorate. See in this way, you can give a conclusion for this answer. As I said already, I have given you my schema of conclusion. So if you have your own conclusion, feel free to write and post it in the comment section. See this is all about this discussion. In this discussion, we saw about article 370, its abrogation and the pros and cons associated with the abrogation of article 370. So with this learned points, let us conclude this discussion and let us take up the next news article for our analysis. Look at this news article. The annual global partnership for artificial intelligence summit was started in New Delhi yesterday. The previous summit was held in Osaka, Japan. Know that in 2024, India will be the lead chair of the grouping. Our Prime Minister, while addressing the summit, made some suggestions to make the use of AI safer. He also mentioned that by only ensuring the transparency and safety, the use of AI can be expanded. This is about the crux of the article. In this context, let us see some points about the global partnership for artificial intelligence or GPAI. The GPAI is a multi sector initiative. This initiative brings together experts from science, industry, civil society, government and international organizations to boost the international cooperation in artificial intelligence technology. This initiative was framed as per the OECD recommendation on artificial intelligence. Let us see the basics of this initiative. See, its establishment was announced during the 2018 G7 summit by Canada and France. Know that it is often described as the fruitation of an idea developed within the G7 nations. After the process, finally the initiative was launched in 2020. In 2020, there were only 15 members and note that India was one of the founding members of the summit. Currently, the GPAI membership has expanded to 28 member countries and European Union. Let us see the organizational structure of the organization. In terms of organization structure, the GPAI has a council, steering committee and two center of expertise. Actually, the two centers are in Montreal and in Paris. This is about the basics of this global partnership. Now, let us see the objectives of it. Its objectives include, firstly, facilitating the international cooperation. Secondly, reducing the duplications. Thirdly, acting as a global reference point for specific AI related issues. Fourthly, promoting the trust in the artificial intelligence arena. And finally, ensuring the adoption of a trust toward the AI. And as a part of this mission, GPAI will mainly focus on certain thematic areas of cooperation. Let us see the thematic areas. They are responsible AI, data governance, future of work, innovation and commercialization. See, by adopting the objectives, GPAI aims to aid in the responsible development of AI, which is also called as trust toward the AI. See, this is all about the objectives and missions. See, I mentioned that GPAI aid in the development of trust toward the AI, right? The GPAI has a set of principles that must be adopted by developing an AI to make it a trust toward their one. Let us see the principles of it. These principles are inclusive growth and sustainable development, human-centered values, transparency and explainability, robustness, security and safety, and finally, accountability. By adopting these principles, AI can be made a trust toward their one. See, this is all regarding this discussion. In this discussion, we saw about an important organization called Global Partnership for Artificial Intelligence. In the second part, we saw about the principle which should be incorporated to make the AI a trust toward their one. So, with this learned points, let us conclude this discussion and take up the next news article for our analysis. The article here is about the impact of global warming on Indian monsoon. See, Indian monsoon is already a complex phenomenon. Global warming has made this even more complex. See, this is about the article. In our discussion today, let us cover some various terms related to Indian monsoon that are often asked in the preliminary examination. See, first of all, what is monsoon? Know that the term monsoon refers to the seasonal reversal in the windy direction during a year, that is between summer and winter seasons. In India, there is a double system of seasonal winds which cause two different monsoon patterns. See, these two different monsoon patterns are southwest monsoon and northeastern monsoon. Let us see southwest monsoon. The southwest monsoon season falls between June to September. During this season, the wind will flow from the sea to land during the summer. This is due to the differential heating of land and sea. We know that during summer, the northwestern part of India become very hot due to high temperature. This is mainly due to the apparent shift of sun in the northern hemisphere. Now, due to high temperature over the land in summer, a kind of low pressure develops over the land. So, the winds blow from the neighboring ocean towards the land. Since these winds are of maritime origin and blowing over the warm water bodies before they reach onto the land, they are often containing moisture, that is, they are moisture land. This in turn cause ample rainfall in the summer season. The sudden onset of rain is called break-off monsoon or burst-off monsoon. See, this is why southwest monsoon period is the chief rainy season for whole of India. Know that about 75% of India's annual rainfall is being due to southwest monsoon. And then secondly, the northeast monsoon. In winter, the sun's parent position is vertically over the tropic of Capricorn. So, the land develops high pressure while the ocean develops low pressure. So, naturally, there is a flow of monsoon is reversed to form the northeast end monsoons. Know that this is also called as re-creating monsoon. See, this type of monsoon occurs in India from October to December. See, this is about the basics of monsoon. Now, let us look at the other basic terms which are related to this monsoon phenomena. First of all, let us see El Nino. Actually, what is El Nino? To understand about the El Nino, we must first acclimatize ourselves with a condition which is prevailing along the Peruvian coast, that is, in the eastern Pacific region. See, look at this map. This is the ocean current pattern during the normal years. In this map, the cold currents are highlighted by blue colored lines and the warm currents are highlighted in red colored lines. If you notice closely, you can find a cold current near the Peruvian coast, that is Peru coast. This is called Peru current. So, in a normal year, the sea surface temperature in the eastern Pacific is cold. Before moving further, let us take a small detail and understand why there is a cold current along the Peruvian coast. Actually, cold currents are associated with the areas of upwelling. Okay, now look at this image. When there is an offshore wind, that is, when wind blowing from land towards the ocean or any water body, the wind pushes the water on the surface away from the coast. So, there will be a gap created along the coast. To fill this gap, cold water from the bottom rises up, as you can see in this image. This water from the deep ocean is colder than the surrounding areas and the water is also rich in nutrients. Since water here is colder than the surrounding area, it is called cold ocean current. So, basically, when there is an offshore wind, then there will be a occurrence of cold water current. Now, look at this map, which is highlighting the trade winds. If you can notice, you can find that the southeast early trade winds are along the western coast of South America. These southeast early trade winds are called offshore winds, which we have discussed to know now. So, in the normal years, there will be upwelling along the coast of Peru and resulting in the cold Peru current. During the normal conditions, there will be less rainfall along the coast of Peru and there will be normal rainfall along the coast of Australia and Indonesia. See, this is because, as we all know, it's a warm air there which rises up and causes the rainfall. But, as we saw along the coast of Peru, we have a cold current. So, due to this, the air will be also cold. See, we know the basic climatological phenomenon that the cold air does not rise up the atmosphere and there will not be any rainfall along the coast of Peru. See, the world's driest place, the Atacama Desert is in Chile, is due to the presence of Peruvian cold current. See, this lack of rainfall is actually a boon for Peru because, as we saw, the upwelling brings a lot of nutrients onto the surface. The paito plankton feeds on these nutrients and the fishes intend to feed on the paito plankton. So, although Peru does not bring any rainfall to the Peruvian coast, it makes Peru a rich breeding ground for fish. We have comprehensively covered the normal conditions during the normal years. Okay, now let us see what happens during the El Nino years. We know that we have a cold current due to the presence of offshore winds along the Peruvian coast. This offshore wind is due to the southeasterly trade winds. During the El Nino years, this trade wind will weaken and in turn weaken the offshore winds. So, in turn, the upwelling that usually happens, no, this will not happen. This result in making the sea surface temperature in the central and eastern tropical ocean substantially higher than the normal conditions. In other words, I am putting it simply, guys. The warm ocean current temporarily replaces the cold Peruvian current. And this warm current starts flowing during the Christmas time. Therefore, baby Christ was the name given to this event. El Nino is a Spanish word, meaning the child and refers to baby Christ. Okay, now look at this map. So, during the El Nino year, the water along the coast of Peru becomes warmer and the water along the coast of Australia becomes colder. So, due to this, during the El Nino year, there will be increased rainfall along the Peru and drought conditions along the Australian coast. Actually, El Nino affects the fishing economy along the coast of Peru and it also cause forest fires in Australia by creating a drought-like conditions. Now, we have to see a correlation between El Nino and Indian monsoon. Whenever it is a El Nino year, it affects the Indian summer monsoon in June to September. This is because El Nino is associated with the weakening of trade winds, which are primarily driving the Indian monsoon. That is abruptly, warm equatorial Pacific water will pull the moisture laden clouds away from the Indian subcontinent. In the sense, we should know that El Nino is associated with the drought-like conditions in India. See, this is about the El Nino phenomena and we also know the correlation between the El Nino and Indian monsoon. See, in this news analysis discussion, I have comprehensively covered the El Nino phenomenon. You can also cover La Nina, El Nino, Madoki, et cetera on your own for comprehensive coverage of these climatological terms because this is very important from our preliminary perspective. So, with this learned points, let us conclude this discussion and take up the next news article for our analysis. Look at this news article. Recently, the Food and Agricultural Organization, FAO of the UN released a report. This report provides an overview about the food security and nutritional security across the world regions. So, this is the crux of the article. In our discussion today, let us understand the important findings of the report with the specific city towards India. Why this is important means you can use this in your main sensor for increasing the credibility of it. First, let us see the title of the FAO report. See, this report is titled Regional Overview of the Food Security and Nutritional Security 2023 Statistics and Trends. Firstly, the report says that more than 74% of Indians could not afford a healthy diet in 2021. See, this is a slight improvement vis-a-vis that 2020. Because in 2020, the percentage was 76.2%. So, it was improved around 2.2%. Okay, now if we compare this data with our neighbours, in 2021, around 82.2% of Pakistan faced a difficulty in finding a healthy diet. So obviously, Pakistan performing worse than India. But if we take another neighbour, Bangladesh, it's around 66.1% of the population facing difficulties. So obviously, Bangladesh is performing way better than India. The report says that if the rising food costs are not matched by the rising income, then it would often lead to a poor healthy diet. This is the first finding. Secondly, the report says that around 31.7% of the children in India under the age of five years showed stunted growth in 2021. See, here, stunting refers to the condition where a child under age five has a low height for their The stunted growth of children in India was due to various reasons. They include poor maternal health and nutrition, inadequate child-feeding practices and repeated infections. See, this is the second finding of the report. Thirdly, the report found out that India record the highest rate of child fasting in South Asian region in 2021. Here, fasting refers to the condition where a child under age five has a low weight for their height. The FAO report says that 18.7% of the Indian children facing this problem. The report further highlighted that India had the highest prevalence of low birth to weight in the South Asian region. See, in India, around 27% of children born with a low birth weight in 2021. India is followed by Bangladesh and Nepal. The fourth finding of the report is that around 2.8% of the Indian children below the age of five were overweight in 2021. The report pointed out that this is a huge health risk that affects the overall development of the children. The report also highlighted that around 1.6% of the adult were obese in 2021. Fifthly, the report pointed out that around 53% of the women who are aged between 15 to 49 in India had anemia in 2021. See, anemia is a condition where the number of RBC or the hemoglobin concentration within RBC will be lower than the normal. The FAO report says that anemia significantly affects the health and well-being of the woman. Also, it has increased the risk for adverse maternal and neonatal outcomes. See, this is all about the findings of FAO report. Kindly note that and revise it often because all the statistics and data are very relevant for your main examination. Okay, finally, let us see in a brief about FAO organization with respect to our preliminary examination. See, FAO is a specialized agency of the United Nations. It was established in 1949. Note that it is headquartered in Rome, Italy. The FAO complieses of over 195 member states, including the European Union. See, the main objective of FAO is to achieve food security for all. It also aims to make sure that people have regular access to enough high-quality food in order to live a healthy and active lives. To put simply, FAO leads the international efforts to defeat hunger. See, this is all about this new discussion. In our discussion, firstly, we saw about the various findings of the recent FAO report and lastly, we saw about the organization itself. This is all regarding the new discussion. Now, let us move on to the next part of our video that is to discuss the preliminary practice questions. Now, I'm having four questions. Let us solve them one by one. See the first question. Which of the following statements with reference to the non-performing asset or NPA is incorrect? Let us see the statements and we can examine whether it is correct or not. First statement, NPA is any asset of the bank which is not producing any income. See, as we have already discussed that NPA is an asset of the bank which is not producing any income. Generally, if the interest or the installment of principal which remained overdue for a period of 90 days will be considered as an NPA. So the option A is correct. Option B, an asset can be considered as an NPA if the installment remains overdue for one crop season for crops of any duration. See, in our analysis, we saw that the installment of principal or interest will be different for different crops. That is for one crop season generally for long duration crops and for two crop season for short duration crops. So it's different for different crop seasons. So this option B is incorrect. See the third one. Generally, loans given by the bank are considered as the liability of the bank. See, in our discussion, we saw that the loans given by the bank are the asset of the bank. So option C is also wrong. Here incorrect statements are asked. So the correct option is option D. See the second question of the day. Consider the following statements about the global partnership for artificial intelligence. See the first statement. It was framed as per the OECD recommendation on artificial intelligence. See it is correct as we have already discussed in our analysis. See the second statement. India was one of the founding members of the GPI. Yes, it is also correct. See the third one. The main aim of the GPI is to aid in the creation of a trustworthy AI. See this is also correct as we have seen in our analysis. So all the given statements are correct. So the correct option is option C. See the third question. Consider the following statements in regard to the Ilaal Nina event. See, during Laanina event there will be a blow pressure conditions along the Peruvian coast. See, even though we have not covered it in our analysis, we should also be aware of the Ilaal Nina phenomenon because it is often asked in our preliminary examination. See here, the statement one is incorrect because during Laanina event there will be amplified appalling along the Peruvian coast. Due to this, the Peru current will be colder than the normal. Due to the presence of cold current, air starts sinking in producing the high pressure conditions. So the first statement is incorrect. See the second statement. Laanina event has no effect on the Indian ones. See this is also wrong because India will receive more rainfall during the Laanina years. So it is definitely impacting the monsoon of India. Let us see the third statement. It is characterized by unusually cold temperature along the coast of Australia. This is also incorrect because Laanina event is characterized by usually warm current along the Australian coast. So this statement is also incorrect. Here the correct option will be option D. See the final question of the day. Which one of the following organization involves in the publication of Food Security and Nutrition in the World SOFI report? See out of the four options. The correct option is the Food and Agricultural Organization FAO releases this report. So the correct option is option B. If you like today's video, like, comment and share it with your friends. For more updates regarding the UPC preparation, subscribe to Shankar IIS Academy. Thank you.