V. Find the exponential Fourier transform g(a) of the given function f(x) and write it as a Fourier integral (find g(a) in equation (12.2) and substitute your result into the first integral in equation (12.2)). f(x) [1, 0
V. Find the exponential Fourier transform g(a) of the given function f(x) and write it as a Fourier integral (find g(a) in equation (12.2) and substitute your result into the first integral in equation (12.2)). f(x) [1, 0
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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Transcribed Image Text:V.
Find the exponential Fourier transform g(a) of the given function f(x) and
write it as a Fourier integral (find g(a) in equation (12.2) and substitute your
result into the first integral in equation (12.2)).
[1, 0<x< 1
otherwise
0,
Use the result to show that
(12.2)
f(x) =
f(x) =
g(a) =
sin(a/2)
α/2
-da = 2π
g(a)e¹az da,
f(x)e-iaz da.
Transcribed Image Text:III. Sketch each of the following functions on the interval (-1,1) and expand it in
a sine-cosine series.
-{
f(x)=
-1 < x < 0,
0 < x < 1.
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