Digital Signal Processing: A Modern Introduction by Ashok Ambardar

By Ashok Ambardar

Overview

This ebook offers a latest and self-contained creation to electronic sign processing (DSP). it's supplemented by way of an unlimited variety of end-of-chapter difficulties similar to labored examples, drill routines, and alertness orientated difficulties that require using computational assets akin to MATLAB.

Also, many figures were incorporated to assist clutch and visualize severe thoughts. effects are tabulated and summarized for simple reference and entry. The textual content additionally offers a broader standpoint to the content material via introducing invaluable functions and extra designated themes in every one bankruptcy. those shape the history for extra complicated graduate classes.

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27 (Periodic Extension) The sum of an absolutely summable signal x[n] and its shifted (by multiples of N ) replicas is called the periodic extension of x[n] with period N . (a) Show that one period of the periodic extension of the signal x[n] = αn u[n] with period N is y[n] = αn , 1 − αN 0≤n≤N −1 (b) How does the sum of one period of the periodic extension y[n] compare with the sum of x[n]? 5 and N = 3, compute the signal energy in x[n] and the signal power in y[n]. [Hints and Suggestions: For one period (n = 0 to n = N − 1), only x[n] and the tails of the replicas to its left contribute.

27 (Periodic Extension) The sum of an absolutely summable signal x[n] and its shifted (by multiples of N ) replicas is called the periodic extension of x[n] with period N . (a) Show that one period of the periodic extension of the signal x[n] = αn u[n] with period N is y[n] = αn , 1 − αN 0≤n≤N −1 (b) How does the sum of one period of the periodic extension y[n] compare with the sum of x[n]? 5 and N = 3, compute the signal energy in x[n] and the signal power in y[n]. [Hints and Suggestions: For one period (n = 0 to n = N − 1), only x[n] and the tails of the replicas to its left contribute.

What is the frequency (in Hz) of the analog signal reconstructed from the samples? (b) A 160-Hz sinusoid x(t) is sampled at 200 Hz. What is the period N of the sampled signal? How many full periods of x(t) are required to obtain these N samples? What is the frequency (in Hz) of the analog signal reconstructed from the samples? (c) The signal x(t) = cos(60πt + 30◦ ) is sampled at 50 Hz. What is the expression for the analog signal y(t) reconstructed from the samples? (d) A 150-Hz sinusoid is to be sampled.

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