Fourier transform math

This page describes some of the math you need for the Fourier transform, as well as deriving some of the formulas you might see thrown around. I'm not a math person, so this is not meant to be as accurate or precise as you will probably see elsewhere. I am including many links to tutorials I found useful in this process.

Fourier Series

Any repeating waveform can be written as an infinite sum of sine and cosine waves at frequencies from 0 toinfinity. Each sine and cosine wave at each frequency will have a coefficient, or amplitude, that shows how much that sine and cosine wave contributes to describing the repeating waveform. For example, suppose we have a waveform that has a lot of "sine wave at f = 3" character. The coefficient of the sine wave at f = 3 will thus have a large coefficient.