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Consider the train pulse signal defined as x(t) = Σ -∞ x1(t + Tk), with T = 4, where 10

Consider the train pulse signal defined as x(t) = Σ -∞ x1(t + Tk), with T = 4, where 10

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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Consider the train pulse signal defined as x(t) = Σ -∞ x1(t + Tk), with T = 4, where 10<t<2 x1(t) = 0 2<t<4 (1) (i) What is the fundamental frequency of this signal? Obtain the Fourier series coefficients ak for this signal. (ii) Assume that this (periodic) signal x(t) is the input to an LTI system with impulse response h(t) = e−2tu(t). a) What is the Fourier series coefficients bk of the system output y(t)? b) Using the Fourier series coefficients bk you obtained, plot the output signal y(t). Note: to plot y(t), use the synthesis equation with the 2N-term approximation: ŷ(t) = Σ__ be³kwot, with a large enough N. N
Transcribed Image Text:Consider the train pulse signal defined as x(t) = Σ -∞ x1(t + Tk), with T = 4, where 10<t<2 x1(t) = 0 2<t<4 (1) (i) What is the fundamental frequency of this signal? Obtain the Fourier series coefficients ak for this signal. (ii) Assume that this (periodic) signal x(t) is the input to an LTI system with impulse response h(t) = e−2tu(t). a) What is the Fourier series coefficients bk of the system output y(t)? b) Using the Fourier series coefficients bk you obtained, plot the output signal y(t). Note: to plot y(t), use the synthesis equation with the 2N-term approximation: ŷ(t) = Σ__ be³kwot, with a large enough N. N
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