# 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 $\frac{1}{P}$
• An infinite sum = series

## Definition

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 $\frac{1}{T}$ (the inverse of the fundamental period).

## Documentation / Reference

• Fourier Series by Jim.belk - Own work. Licensed under Public Domain via Wikimedia Commons

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