Use the general definition and properties of Fourier transforms to show the following (a) If f(x) is periodic with period a then f(k)- 0, unless ka (b) The Fourier transform of tf(t) is idf(co)/do. (c) The Fourier transform of f(mt +c) is 2πη for integer n.
Use the general definition and properties of Fourier transforms to show the following (a) If f(x) is periodic with period a then f(k)- 0, unless ka (b) The Fourier transform of tf(t) is idf(co)/do. (c) The Fourier transform of f(mt +c) is 2πη for integer n.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please label answer clearly. Use the ~ symbol for the transformed function above the function label. For example:
~ f(w)
write the ~ symbol above the function f letter. Also label each section as a, b and c. Thank you.

Transcribed Image Text:Use the general definition and properties of Fourier transforms to show the
following
(a) If f(x) is periodic with period a then f(k)- 0, unless ka
(b) The Fourier transform of tf(t) is idf(co)/do.
(c) The Fourier transform of f(mt +c) is
2πη for integer n.
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