Fourier Series

[mathsuser314159]

I have seen some fourier examples using the equation for a0 as 1/L x the integral of f(x) and other times the equation has been for a0 1/2L x the integral of f(x). Please can someone explain why this is? I know when you have an even function you multiply the integral by 2 and halve the limits but I'm unsure about this. Any help would be greatly appreciated.

 

[tkhunny]

Given limited RANGE for which you wish to extend to your full-range Periodic Fourier Series, you must DECIDE how to do that. A common decision point is between the Odd Function or Even Function extension. Depends on what you are doing. If your application demands an Even Function, then don't pick the Odd Function extension.