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The output of a causal LTI system is related to the input x(t) by the differential equation dy(t) + 2y(t) = x(t) dt Y(@) (a) Determine the frequency response H(w) and sketch the phase and magnitude of H(@) X(w) (b) If x(t) = e-tu(t), determine Y(@), the Fourier transform of the output. (c) Find y(t) for the input given in part (b).

The output of a causal LTI system is related to the input x(t) by the differential equation dy(t) + 2y(t) = x(t) dt Y(@) (a) Determine the frequency response H(w) and sketch the phase and magnitude of H(@) X(w) (b) If x(t) = e-tu(t), determine Y(@), 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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The output of a causal LTI system is related to the input x(t) by the differential equation dy(t) + 2y(t) = x(t) dt (a) Determine the frequency response H(@) = and sketch the phase and magnitude of H(w) (b) If x(t) = e tu(t), determine Y(@), the Fourier transform of the output. (c) Find y(t) for the input given in part (b). X(@)
Transcribed Image Text:The output of a causal LTI system is related to the input x(t) by the differential equation dy(t) + 2y(t) = x(t) dt (a) Determine the frequency response H(@) = and sketch the phase and magnitude of H(w) (b) If x(t) = e tu(t), determine Y(@), the Fourier transform of the output. (c) Find y(t) for the input given in part (b). X(@)
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