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By Ashok Ambardar
Overview
This booklet presents a contemporary and self-contained advent to electronic sign processing (DSP). it truly is supplemented via an enormous variety of end-of-chapter difficulties reminiscent of labored examples, drill workouts, and alertness orientated difficulties that require using computational assets akin to MATLAB.
Also, many figures were incorporated to assist snatch and visualize serious suggestions. effects are tabulated and summarized for simple reference and entry. The textual content additionally presents a broader standpoint to the content material by means of introducing worthwhile functions and extra certain issues in each one bankruptcy. those shape the history for extra complex graduate classes.
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Additional resources for Digital Signal Processing: A Modern Introduction
Sample text
6 The Sampling Theorem The central concept in the digital processing of analog signals is that the sampled signal must be a unique representation of the underlying analog signal. When the sinusoid x(t) = cos(2πf0 t + θ) is sampled at the sampling rate S, the digital frequency of the sampled signal is F0 = f0 /S. 5. This implies S > 2|f0 | and suggests that we must choose a sampling rate S that exceeds |2f0 |. More generally, the sampling theorem says that for a unique correspondence between an analog signal and the version reconstructed from its samples (using the same sampling rate), the sampling rate must exceed twice the highest signal frequency fmax .
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. Pick the range of sampling rates (in Hz) closest to 150 Hz that will cause aliasing but prevent phase reversal of the analog signal reconstructed from the samples.
Their periods are N1 = 15 and N2 = 5. 1 2 The common period is thus N = LCM(N1 , N2 ) = LCM(15, 5) = 15. The fundamental frequency of x(t) is f0 = GCD(20, 30) = 10 Hz. 1 s. 2 s, it takes two full periods of x(t) to obtain one period of x[n]. We also get the same result by computing GCD(k1 , k2 ) = GCD(4, 2) = 2. 25nπ+30 ) ? Is x[n] periodic? 5n + 30◦ )? Is y[n] periodic? 5nπ + 30◦ )? 2 21 Discrete-Time Harmonics Are Always Periodic in Frequency Unlike analog sinusoids, discrete-time sinusoids and harmonics are always periodic in frequency.