Unformatted text preview: Electrical Engineering 431 Problem Set III Due: February 6, 2004
Reading: OSB: 5.15.6 3.1 Properties of Allpass Filters . This signal Let ܴҵ be a causal signal that equals zero outside the domain serves as the input to a system having an input-output relationship determined by the difference equation ҵ ܴ ܴҵ (a) Find the poles and zeros of the transfer function. (b) Find the magnitude and phase of this system's frequency response. (c) Find the unit-sample response of this filter. (d) You are given that 3.2 ҵ . What does Ƚ ҵ equal? Equalizers A common problem in wireless communications is multipath: the arrival at the receiver not only of the transmitted signal, but also its delayed version. Letting ִҵ being the sampled received signal and ܴҵ the sampled transmitted signal, an example of multipath reception would be ִҵ ܴҵ ܴ (a) Find the the transfer function between the transmitted and received signals. Plot the polezero pattern and indicate the region of convergence. and , plot the resulting frequency responses (magnitude and (b) Letting phase) of this transfer function. You will find the freqz function in Matlab helpful. Be sure to force the same vertical scales on the magnitude plots as well as the scales on the phase plots. (c) To eliminate multipath, a clever ELEC 431 student suggests filtering the received signal. Systems that remove multipath are known as equalizers. Find a stable, causal equalizer (if any exist) that, when ִҵ serves as its input, yields ܴҵ as its output. 3.3 2-D -Transforms Find the -transforms of the following two-dimensional signals. Note the region of convergence for each. (a) ܴ ҵ (b) ܴ ҵ (c) ܴ ҵ otherwise ״ ҵ ״ ҵ״ ҵ ELEC 431
3.4 2-D Systems A 2D filter is governed by the following difference equation. Problem Set III ҵ (a) Find the transfer function of this filter. ܴ ҵ (b) Is this filter recursively computable? If so, what direction in the ҵ-plane can the filter be computed? If not, why not? (c) Determine the region of support for the filter's unit-sample response. 2 ...
View Full Document