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Additional info for Schaum's Outline of Digital Signal Processing
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?