The Fourier expansion of an odd function F(1) must use sines instead of cosines: 2nnI 2nRI dr Ffr)-Σ Β, sin F(r) sin with %3D %3D n=0 ere, the B are the Fourier coefficients. Consider the square wave shown below as an example ol E periodic odd function F(r). (a) Write down an expression for F(r) valid for the range 0
The Fourier expansion of an odd function F(1) must use sines instead of cosines: 2nnI 2nRI dr Ffr)-Σ Β, sin F(r) sin with %3D %3D n=0 ere, the B are the Fourier coefficients. Consider the square wave shown below as an example ol E periodic odd function F(r). (a) Write down an expression for F(r) valid for the range 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:The Fourier expansion of an odd function F(1) must use sines instead of cosines:
2.
2nRI
de
F(r) = Bn sin
with
Bn =
F(x) sin
%3D
%3D
nere, the B are the Fourier coefficients. Consider the square wave shown below as an example of a
periodic odd function F(r). (a) Write down an expression for F(r) valid for the range 0<r< A. (b) by
evaluating the integral in the equation above, show that the Fourier coefficients B, for this square wave
are given by
f(r)
a = X/2
0.
for even n
Bn =
%3D
A
4A
for odd n
nR
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