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Problem 12 The output of a causal LTI system is related to the input x(t) by the differential equation dy(t) dt + 2y(t) = x(t) (a) Determine the frequency response H(w) Y(w)/X(w) and sketch the phase and magnitude of H(w). (b) If x(t) = e 'u(t), determine Y(w), the Fourier transform of the output. (c) Find y(t) for the input given in part (b).

Problem 12 The output of a causal LTI system is related to the input x(t) by the differential equation dy(t) dt + 2y(t) = x(t) (a) Determine the frequency response H(w) Y(w)/X(w) and sketch the phase and magnitude of H(w). (b) If x(t) = e 'u(t), determine Y(w), the Fourier transform of the output. (c) Find y(t) for the input given in part (b).

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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Problem 12 The output of a causal LTI system is related to the input x(t) by the differential equation dy(t) dt + 2y(t) = x(t) (a) Determine the frequency response H(w) magnitude of H(w). (b) If x(t) = e 'u(t), determine Y(w), the Fourier transform of the output. (c) Find y(t) for the input given in part (b). = Y(w)/X(w) and sketch the phase and
Transcribed Image Text:Problem 12 The output of a causal LTI system is related to the input x(t) by the differential equation dy(t) dt + 2y(t) = x(t) (a) Determine the frequency response H(w) magnitude of H(w). (b) If x(t) = e 'u(t), determine Y(w), the Fourier transform of the output. (c) Find y(t) for the input given in part (b). = Y(w)/X(w) and sketch the phase and
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