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Trignometric Polynomial complex form

by phillyj
Tags: complex, fourier transform
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phillyj
#1
Sep7-11, 05:09 PM
P: 30
Hi,
I'm trying to learn Fourier transforms by myself. I'm a bit confused about how the trignometric polynomial complex form was derived. I'm refering to this:

http://en.wikipedia.org/wiki/Trigonometric_polynomial

Now, I haven't taken complex analysis so I only know the basics. I used Euler's formula and got that far but I'm not sure what to do next.

Thanks
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micromass
#2
Sep7-11, 05:13 PM
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micromass's Avatar
P: 18,345
Substitute

[tex]\cos(nx)=\frac{e^{inx}+e^{-inx}}{2}, ~\sin(nx)=\frac{e^{inx}-e^{-inx}}{2i}[/tex]

in the series and rearrange everything. This should give you the required form.


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