Discrete-Time Signal Processing (2nd Edition) (Prentice-Hall Signal Processing Series)

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Unformatted text preview: Electrical Engineering 431 Problem Set II Due: January 30, 2004 Reading: OSB: Chapter 3 2.1 -Transforms Find the causal inverse z-transforms of the following. (a) (b) (c) (d) 2.2 ޿ Causal and Noncausal Filtering A system is described by the transfer function ޷ (a) Find the causal and purely noncausal unit-sample responses corresponding to this transfer function. (b) What is the difference equation in each case? (c) Which of these filters is stable? Why? 2.3 Making filters work An ELEC 431 student found a filter (by trial-and-error) that has the frequency response he wants. (a) Is his proposed filter be causal and stable? (b) Find a better filter that has the same magnitude as his, but with nicer properties? 2.4 Autocorrelation The correlation function of the signal ܴҵ is defined to be е ܴҵܴ е The index is known as the lag. (a) Show that correlation functions are even functions. ELEC 431 (b) Show that the -transform of the correlation function equals Problem Set II ٴҵ, find its correlation function. Sketch the pole-zero plot of the correlation (c) If ܴҵ function and indicate the region of convergence. (d) Find a signal not equal to the signal in the previous part but which has the same correlation function. (e) Define the causal part of an even signal to be that signal having an even part equal to the given signal. In other words, if ״ҵ is an even signal, its causal part, ҵ, satisfies ״ҵ ҵ ҵ ҵ Show that the -transform of ҵ has poles located where the -transform of ״ҵ has poles, but that the zeros don't necessarily agree. Which poles are shared? 2 ...
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This homework help was uploaded on 02/11/2008 for the course ELEC 431 taught by Professor Abercrombie during the Spring '07 term at Rice.

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