Fourier series summary

# Fourier series summary - Fourier series a summary by Dr...

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Fourier series: a summary by Dr Colton Physics 123 Section 2, Fall 2010 I found the summary contained in Table 6.1 of Physics phor Phynatics to be hard to follow. Here’s my version. Colton’s short Fourier series summary : Any periodic function (period = L ) can be written as a sum of sines and cosines, as: 0 1 1 2 2 ( ) cos sin n n n n nx nx f x a a b L L π = =     = + +  ÷  ÷     ∑ ∑ The a n and b n numbers are called the “Fourier coefficients”. a 0 represents the average value of the function, and is calculated by: 0 0 1 ( ) L a f x dx L = The a n coefficients can be calculated by the formula: 0 2 2 ( )cos L n nx a f x dx L L   =  ÷   The b n coefficients can be calculated by the formula: 0 2 2 ( )sin L n nx b f x dx L L   =  ÷   If the function f ( x ) is even, only the cosine terms will be present. I.e., the b n coefficients will all be zero.

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Fourier series summary - Fourier series a summary by Dr...

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