I have been trying to follow how the complex Fourier coefficients are obtained; the reference I am using is at www.thefouriertransform.com. However I am unable to follow the author's working exactly and wondered if anyone could help me see where I am going wrong.(adsbygoogle = window.adsbygoogle || []).push({});

First, I understand that the coefficient [itex]c_n=\frac{1}{T}\int^T_0 f(t) e^{\frac{-i2\pi nt}{T}}dt[/itex]

Given a square wave, of period 2T, and amplitude :

http://s90.photobucket.com/user/jonnburton/media/SqareWave_zpsbdf193c1.jpg.html

It can be seen directly from the graph that [itex]c_0=\frac{1}{2}[/itex] (I also managed to calculate this, too.)

But I can't follow how the author obtained expressions for [itex]c_n[/itex].

This is what I have done in attempt to obtain [itex]c_n[/itex]:

[itex]c_n=\frac{1}{T}\int^{\frac{T}{2}}_0 1 \cdot e^{\frac{-i2\pi nt}{T}}dt[/itex]

[tex]\frac{1}{T}\left[\frac{T e^{\frac{-i2\pi nt}{T}}}{i2\pi n}\right]^{\frac{T}{2}}_0[/tex]

[tex]\frac{1}{T}\left[\left(\frac{T e^{-in\pi}}{in2\pi}\right)-\left(\frac{T}{in2\pi}\right)\right][/tex]

[tex]\left(\frac{e^{-in\pi}}{in2\pi}-\frac{1}{in2\pi}\right)[/tex]

However, the expression the author finds is:

[tex]\frac{1}{i\pi n}[/tex] for odd n, and zero for even n.

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# Fourier Series complex coefficients

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