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1. The signal x(t) is shown as following figure. Please sketch the signals of (a) x(2t) (b) x(t/3) (c) 2x(-t/2) (d) x(2t+2) X(*)

1. The signal x(t) is shown as following figure. Please sketch the signals of (a) x(2t) (b) x(t/3) (c) 2x(-t/2) (d) x(2t+2) X(*)

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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1. The signal x(t) is shown as following figure. Please sketch the signals of (a) x(2t) (b) x(t/3) (c) 2x(-t/2) (d)x(2t+2) > 2. Find the even and odd parts of the signal_x(t)=3t³-t²+4t+2e²t. 3. Determine if each of the following signals is periodic. If the signal is periodic, find its period. (a) x(t)=2cos(√Zπt) (b)x(t)=3e³t (ei³t-cos(t) + j sin(t) : A complex number) 4. Evaluate the following signals. (a) cos(5t) 6 (t+2) dt 5. Evaluate y(t)=x(t)*h(t). Where, x(t)=u(t+1)+2u(t), h(t)=exp(-2t)u(t). 00 (b) exp(at) 6 (2t-2) dt 6. Discuss whether or not each of the following equations is memoryless, linear, time-invariant, and causal: (a) y(t) = −2+3u(t), (b) y(t)= tu(t), (c) y(t)=u²(t) 7. Find the response y(t) of the LTI system with impulse response_h(t) = (t+1)e-²¹u(t) to the input x(t)=e¹u(t).
Transcribed Image Text:1. The signal x(t) is shown as following figure. Please sketch the signals of (a) x(2t) (b) x(t/3) (c) 2x(-t/2) (d)x(2t+2) > 2. Find the even and odd parts of the signal_x(t)=3t³-t²+4t+2e²t. 3. Determine if each of the following signals is periodic. If the signal is periodic, find its period. (a) x(t)=2cos(√Zπt) (b)x(t)=3e³t (ei³t-cos(t) + j sin(t) : A complex number) 4. Evaluate the following signals. (a) cos(5t) 6 (t+2) dt 5. Evaluate y(t)=x(t)*h(t). Where, x(t)=u(t+1)+2u(t), h(t)=exp(-2t)u(t). 00 (b) exp(at) 6 (2t-2) dt 6. Discuss whether or not each of the following equations is memoryless, linear, time-invariant, and causal: (a) y(t) = −2+3u(t), (b) y(t)= tu(t), (c) y(t)=u²(t) 7. Find the response y(t) of the LTI system with impulse response_h(t) = (t+1)e-²¹u(t) to the input x(t)=e¹u(t).
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