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 f 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 f le camera.mat contains a black-and white image of a camera man. Blurring amounts to low-pass
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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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ProblemSet1 - Electrical Engineering 430 Problem Set I Due:...

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