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THREEFILTERDES - two points(pinv does not give a straight...

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THREE FILTER DESIGN PROJECTS THAT COME IMEDIATELY TO MIND MORE LATER FREQUENCY SAMPLING Ordinary frequency sampling is an inverse DFT, and we know we can do better if we allow ourselves to use more general frequency sampling and solve N equations in N unknowns. We also know that we can have many more frequency samples (knowns) than tap weights (unknowns) and still solve for a good approximation by least squares. This latter we do using (E’E) -1 E’ or through Matlab’s pinv. Does it make any sense, in filter design, to have fewer frequency samples than we do taps? Can we solve such a problem? For example, we might have 21 taps available but only have five frequencies where we care about the response. In such a case, pinv should give us some answer. (In this case, it uses svd.) Where this might come in useful is if it gives a set of tap weights that are particularly simple. In any case, it would be interesting to see what happens. Perhaps you could start by looking for a parabola that first
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Unformatted text preview: two points. (pinv does not give a straight line, which would have been my guess.) MODIFIED HAMMING WINDOW In lecture, we discussed what was wrong with the standard Hamming window. We found that the continuous time Hamming window had to be sampled in a different way to get rid of “lazy zeros.” That is not the only thing we can change – we can use mixes other than the 92%-8% of the original window, which allows us to further manipulate the no longer lazy zeros. In some initial test, this seemed to give a significantly better filter. EQUIVALENT WINDOWS Windowing is often used to reduce Gibbs phenomenon. It is not the only method. If we find that a filter design method gives a filter with reduced Gibbs, is it not true that the same tap weight modification could have been achieved with a particular “equivalent” window which we can calculate? Are any of these windows relatives of the Hamming modifications discussed above....
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