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For each of the given functions Define the Fourier transform of each function analytically (use the integral for the first one, then tables of Fourier transforms for the rest.) Discuss the representations and the value of ƒ(0) for the given functions. -1, if – 1 < x < 0, if 0 < x < 1, (a) f(x) = 1, 0, otherwise 1 (b) f(x) 1+ x2 sin(2.x) (c) f(x) = S sin(x), ifla| < T, (0, otherwise (d) f(x)= (e) f(x) = e-x²/4

For each of the given functions Define the Fourier transform of each function analytically (use the integral for the first one, then tables of Fourier transforms for the rest.) Discuss the representations and the value of ƒ(0) for the given functions. -1, if – 1 < x < 0, if 0 < x < 1, (a) f(x) = 1, 0, otherwise 1 (b) f(x) 1+ x2 sin(2.x) (c) f(x) = S sin(x), ifla| < T, (0, otherwise (d) f(x)= (e) f(x) = e-x²/4

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.5: Applications
Problem 27EQ
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For each of the given functions Define the Fourier transform of each function analytically (use the integral for the first one, then tables of Fourier transforms for the rest.) Discuss the representations and the value of f(0) for the given functions. -1, if – 1< x < 0, (a) f(x) = 1, if 0 < x < 1, 0, otherwise (b) f(x) = 1+ x2 sin(2x) (c) f(x) = Ssin(x), iflæ| < T, 10, otherwise (d) f(x) = (e) f(x) = e¬æ²/4
Transcribed Image Text:For each of the given functions Define the Fourier transform of each function analytically (use the integral for the first one, then tables of Fourier transforms for the rest.) Discuss the representations and the value of f(0) for the given functions. -1, if – 1< x < 0, (a) f(x) = 1, if 0 < x < 1, 0, otherwise (b) f(x) = 1+ x2 sin(2x) (c) f(x) = Ssin(x), iflæ| < T, 10, otherwise (d) f(x) = (e) f(x) = e¬æ²/4
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