Thursday, February 18, 2010

Exponential Fourier series

Recall that, from the Euler’s identity,

Then the Fourier series representation becomes

Then, the coefficient Cn can be derived from

· In fact, in many cases, the complex Fourier series is easier to obtain rather than the trigonometrical Fourier series

· In summary, the relationship between the complex and trigonometrical Fourier series are: