(c) Let x1(t) = sinrt and x2(t) = sint. Determine whether the signal y(t) = x1(t)+x2(t) is periodic.

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Author:Robert L. Boylestad
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(a) (a) Consider the causal LTI system that is characterized by the difference
equation, y[n] - ay [n -1] = x[n], a < 1.
(i) What is the frequency response of this system?
(ii) What is the impulse response of this system?
(EV 8marks)
(b) Suppose that we are given a LTI system with input x(t), output y(t), and
impulse response h(t) where h(t) = u(t).
Show that this system is the integrator characterized by the equation
y(t) = s* -- x(t)dt.
(c) Let x1(t) = sintt and x2(t) = sint.
Determine whether the signal y(t) = x1(t)+x2(t) is periodic.
Transcribed Image Text:(a) (a) Consider the causal LTI system that is characterized by the difference equation, y[n] - ay [n -1] = x[n], a < 1. (i) What is the frequency response of this system? (ii) What is the impulse response of this system? (EV 8marks) (b) Suppose that we are given a LTI system with input x(t), output y(t), and impulse response h(t) where h(t) = u(t). Show that this system is the integrator characterized by the equation y(t) = s* -- x(t)dt. (c) Let x1(t) = sintt and x2(t) = sint. Determine whether the signal y(t) = x1(t)+x2(t) is periodic.
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