Trigonometry - Fourier Series (Fourier Transform for periodic functions)


The Fourier Series breaks down a periodic function into the sum of sinusoidal functions.

A Fourier series is a way to represent a wave-like function (like a square wave) as the sum of simple sine waves.

The Fourier Series decomposes any periodic function or periodic signal into the sum of a (possibly infinite) set of simple oscillating functions, namely sines and cosines (or, equivalently, complex exponentials).

The Fourier Series is the Fourier Transform for periodic functions.

  • period P
  • frequency <math>\frac{1}{P}</math>
  • An infinite sum = series


A Fourier Series, with period T, is an infinite sum of sinusoidal functions (cosine and sine), each with a frequency that is an integer multiple of <math>\frac{1}{T}</math> (the inverse of the fundamental period).

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