Schaum's Outline of Digital Signal Processing by Monson Hayes

By Monson Hayes

Reflecting the quick advances in microelectronics and laptop know-how, this strong learn advisor is perfect as a complement to any direction in this topic or for self reliant learn by way of electric engineering majors and practising engineers. Readers will learn the way electronic sign processing options come into play in a variety of fields and should have fun with this thorough, but concise assurance. the numerous illustrative issues of designated ideas and the supplementary self-tests pace comprehension and reduction remembering.

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Example text

C) Yes. + N), by shift-invariance, y(n) = y(n + N). Therefore, y(n) is periodic with period N. CHAP. 45 Even. 46 (a) is true. 49 (a) Linear, shift-varying, stable, noncausal, noninvertible. (6) Linear, shift-varying, unstable, noncausal, invertible. ( c ) Linear, shift-invariant, stable. noncausal, invertible. (d) Nonlinear, shift-invariant, stable, causal, invertible. ( 0 ) Nonlinear, shift-invariant, stable, noncausal, noninvertible. 51 No. Consider the system y(n) = x(n)cos(nr/2). 53 (a) Yes.

A sketch of yn(n) is shown in Fig. I-8(d). (c) The third sequence, y3(n) = x(8 - 3n), is formed through a combination of tirne-shifting, down-sampling, and time-reversal. To sketch y3(n) we begin by plotting x(8 - n), which is formed by shifting x(n) to the left by eight (advance) and reversing in time as shown in Fig. 1 -8(e). Then, y3(n) is found by extracting every third sample of x(8 - n), as indicated by the solid circles, which is plotted in Fig. 1-8(f ) . (4 Finally, y4(n) = x(n2 - 2n + 1) is formed by a nonlinear transformation of the time variable n.

U(n) = y ( n ) - y ( n - I) To show that this is the inverse system, note that n-l (e) Invertibility must hold for complex as well as real-valued signals. Therefore, this system is noninvertible because it discards the imaginary part real-valued signals. 23 01' x ( n ) . One could state, however, that this system is invertible over the set of Consider the cascade of two systems. S I and S2. (a) If both SI and S2 are linear, shift-invariant, stable, and causal, will the cascade also be linear, shift-invariant, stable, and causal?

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