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a) Compute the Fourier transform for the following function. f(x) = 0, for 0 < x < 1/2 1, for 1/2 < x < 1 b) Compute the Fourier transform for the following function. g(x) = -1, for 0 < x < 1/2 1, for 1/2 < x < 1 c) Note that g(x) = 2f(x) - 1 and check that the result of b) can be obtained from the result of a) without explicit computation.

a) Compute the Fourier transform for the following function. f(x) = 0, for 0 < x < 1/2 1, for 1/2 < x < 1 b) Compute the Fourier transform for the following function. g(x) = -1, for 0 < x < 1/2 1, for 1/2 < x < 1 c) Note that g(x) = 2f(x) - 1 and check that the result of b) can be obtained from the result of a) without explicit computation.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 22E
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a) Compute the Fourier transform for the following function. f(x) = 0, for 0 < x < 1/2 1, for 1/2 < x < 1 b) Compute the Fourier transform for the following function. g(x) = -1, for 0 < x < 1/2 1, for 1/2 < x < 1 c) Note that g(x) = 2f(x) - 1 and check that the result of b) can be obtained from the result of a) without explicit computation.
Transcribed Image Text:a) Compute the Fourier transform for the following function. f(x) = 0, for 0 < x < 1/2 1, for 1/2 < x < 1 b) Compute the Fourier transform for the following function. g(x) = -1, for 0 < x < 1/2 1, for 1/2 < x < 1 c) Note that g(x) = 2f(x) - 1 and check that the result of b) can be obtained from the result of a) without explicit computation.
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