# Lecture – 1 Introduction to Adaptive Filters

to the source part of it comes back to this side So, what basically comes out here is you can say d of n, which is this fellow signal y n plus a part of this incoming signal, which you call echo; because that will go back to the speaker on this side, who spoke those because this is coming from hybrid here also and here is another source. So, this echo part of the leakage that the leakage to the hybrid that is; what that is say part of the signal coming from speaker at this end; that will go back to that speaker only after a delay. So, that will be an echo along with that echo the actual signal y n transmitted by this source generated by this source that also will go So, what will go is d n equal to y n plus e n? Now, if it is purely telephonic conversation the e n of course, is a disturbance is an irritant; it will create some problem, but still you know human beings are intelligent using their brain and all they can find they can somehow ignore that and listen to only y n But it becomes a more acute problem; if you are dealing with data modem where there is no human being and computers are processing, receiving, transmitting. That time the data that is transmitted through this line is not only is never the one that should have been transmitted; this extra component which occurs noise or disturbance which as interference that comes up; as a result we need to remove it So, what we do there you module this hybrid as an FIR filter. Model as FIR filter a very large order large order and suppose you know the filter, you then connect that filter here Filter, by this FIR filter what you are modeling actually not the hybrid, but the leakage generation echo generation mechanism. That mechanism you are modeling by an FIR filter. In fact, if that mechanism is a linear system; you can always approximate to a by a very high order FIR filter. Any linear size linear time invariance system can be approximate it Why a by a very large order FIR filter? Because even if it is IIR if it is a stable system it will die out after a time, so naturally if the order is large you will take almost all the samples of the impulse. Once you if you put at large order FIR filter that will approximate or that it will model the echo generation process. Suppose, I construct that here and then that will generate the same echo e n and I simply subtract it. So, what will go here is again y n? Echo is gone. Now, how do you do that? You do it adaptively it is because you the hybrid characteristics may change from to I mean that echo generation process can differ. Can change from time to time and you change the hybrid again it changes So, you cannot design the filter once for all. So, you use an adaptive mechanism this is your desired response. You try to match that desired response you know then it can be shown the best you can go is when this is equal to e n; this is that is theory. So, this is that error and that error the filter output and its desired response or target sequence that the difference is the error that error will be put in that adaptive algorithm; AA adaptive filter algorithm. This will go here and this will adjust the weights. This is called adaptive echo canceller On this again plenty of work has taken place and this is only a very basic concept basic scheme. But actually there are many you know detail issues involved in echo cancellation; you can read books on echo cancellation They are coming courses purely on echo cancellation; I am just giving a basic theory to you to generate motivation for this course. Then we take another example, suppose we have got some antenna dipoles and then arrays like you know your TV antennas; we have seen them now that here you the antenna some dipoles array of dipoles Normally, if you give some signals to them this array and there is some phase difference You adjust between the signal given here and there distance is I think lambda by two lambda is lower length or lambda by four; some specified distance and phase difference given to the signal here and here. I mean phase difference between the signal same signal is given to all the dipoles, but with a phase difference; then what you can happens is you can have some kind of beam forming. That is most of the energy if it is transmitted antenna it might go in one direction; in few directions; or in this directions nothing So, those in these are these directions I have null and in this directions we have got