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For a sine function, the maximum value sin(x) returns will always be 1 (and -1) correct? Is this the same for a Fourier function?

I'm writing a program that simulatates oscillators, and my fourier functions are returning slightly more than one at the tips of the saw wave, and it's a bit unsettling. If it is normal, then I can move on with things, but if it's not - then I'll have to investigate whatever programming issue it is.

If you're interested, here's a paste of the code pseudo code and original c .

If it is normal - any interesting implications for it? For me - this program is a step towards generating sound with it - a value of more than 1 would cause clipping (ie you'd simply be chopping those tips off), so perhaps some gain reduction is required.

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up vote 2 down vote accepted

It's normal. The Fourier series of discontinuous functions always show a similar pattern. It's called Gibbs' phenomenon (see for example Wikipedia: Gibbs phenomenon)

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