Page 65 - Schaum's Outline of Theory and Problems of Signals and Systems

54 SIGNALS AND SYSTEMS [CHAP. 1

1.52. Show that if x[n] is periodic with period N, then

Hint: See Prob. 1.17.

1.53. (a) What is S(2t)?
(b) What is S[2n]?
Am. (a) S(2t)=$(t)
(b) S[2nl= S[n]

1.54. Show that

sy -I) = -S1(t)
Hint: Use Eqs. (1.101) and (1.99).

1.55. Evaluate the following integrals:

Ans. (a) sin t
(b) 1 for t > 0 and 0 for t < 0; not defined for t = 0
(c) 0
(d) .sr

1.56. Consider a continuous-time system with the input-output relation

Determine whether this system is (a) linear, (b) time-invariant, (c) causal.

1.57. Consider a continuous-time system with the input-output relation

Determine whether this system is (a) linear, (b) time-invariant.
Am. (a) Linear; (b) Time-varying

1.58. Consider a discrete-time system with the input-output relation
y[n] = T{x[n]) =x2[n]

Determine whether this system is (a) linear, (b) time-invariant.
Ans. (a) Nonlinear; (b) Time-invariant