Lecture 25 Blog, ECE438 Fall 2011, Prof. Boutin
Friday October 21, 2011 (Week 9) - See Course Outline.
Today we discussed the relevance of "filter design" in today's world, including some open problems for which research is needed. We also discussed the relationship between the location of the poles of the transfer function of a causal LTI system and the existence of the frequency response of that system. We also covered several different ways to make sure that the response of an LTI system to real input signals is always a real signal. We finished the lecture with an example of implicitly defined system, for which we obtained the transfer function. It was observed that it is more convenient to this of H(z) as a function of $ \xi=z^{-1} $: the values of $ \xi $ that correspond to poles of the transfer function (including poles at infinity) can then be transformed into the corresponding values for z. (Note that when $ \xi=\infty $ is a pole, then $ z=0 $ is a pole.
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