Let x(t) = sin^2(2pit), a periodic signal of fundamental period T0 = 1, and y(t) = |sin(2pit)| also periodic of the same fundamental period (a) A trigonometric identity gives that x(t) = 0.5[1-cos(4pit)]. Use this result to find its complex exponential Fourier series (b) Use the Laplace transform to find the Fourier series of y(t) (c) Are x(t) and y(t) identical? Explain. (d) Indicate how you would use an ideal low-pass filter to get a dc source from x(t) and y(t). Indicate the bandwidth and magnitude of the filters. Which of these two signals is used for generating full-waved rectified dc source?
Let x(t) = sin^2(2pit), a periodic signal of fundamental period T0 = 1, and y(t) = |sin(2pit)| also periodic of the same fundamental period (a) A trigonometric identity gives that x(t) = 0.5[1-cos(4pit)]. Use this result to find its complex exponential Fourier series (b) Use the Laplace transform to find the Fourier series of y(t) (c) Are x(t) and y(t) identical? Explain. (d) Indicate how you would use an ideal low-pass filter to get a dc source from x(t) and y(t). Indicate the bandwidth and magnitude of the filters. Which of these two signals is used for generating full-waved rectified dc source?
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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Let x(t) = sin^2(2pit), a periodic signal of fundamental period T0 = 1, and y(t) = |sin(2pit)| also periodic of the same fundamental period
(a) A trigonometric identity gives that x(t) = 0.5[1-cos(4pit)]. Use this result to find its complex exponential Fourier series
(b) Use the Laplace transform to find the Fourier series of y(t)
(c) Are x(t) and y(t) identical? Explain.
(d) Indicate how you would use an ideal low-pass filter to get a dc source from x(t) and y(t). Indicate the bandwidth and magnitude of the filters. Which of these two signals is used for generating full-waved rectified dc source?
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