ProblemSet1

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

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Electrical Engineering 430 Problem Set I Due: January 23, 2004 Reading : OSB: 2.1-2.9 1.1 Approximating Continuous-Time Filters We want to approximate the continuous-time operation of differentiation with a discrete-time counterpart. (a) Show that differentiation indeed corresponds to a linear, time-invariant operation. Find the transfer function. (b) Can differentation of a band-limited signal be performed exactly by a discrete-time sys- tem? Why or why not? (c) The de fi nition of the derivative is Once we have sampled (sampling interval ), we can approximate the derivative as Show that this operation corresponds to a linear, shift-invariant system. Find the transfer function and the unit-sample response. (d) Another approximation to the derivative is Find its transfer function and frequency response. (e) Which approximates the derivative better? Justify your answer. 1.2 Blurring an image The fi le camera.mat contains a black-and white image of a camera man. Blurring amounts to low-pass fi ltering.

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