a method of expressing an arbitrary periodic function as a sum of cosine terms

Fourier Series Applet demonstrates Fourier series, which is a method of expressing an arbitrary periodic function as a sum of cosine terms.

a method of expressing a periodic function in terms of sinusoidal basis functions

The Fourier series is a method of expressing a periodic function in terms of sinusoidal basis functions.

periodic functions

In signal processing you encounter the problem, that Fourier series represent periodic functions and that Fourier series satisfy convolution theorems (i.e. convolution of Fourier series corresponds to multiplication of represented periodic function and vice versa), but periodic functions cannot be convolved with the usual definition, since the involved integrals diverge.

a way to represent a function as the sum of sine waves

If you remember your schooling on Fourier series, you recall that Fourier series is a way to represent a function as the sum of sine waves.

a mathematical tool

For better understanding of better understanding , read Fourier series' Fourier series is a mathematical tool.

a summation of harmonically related sinusoidal functions, also known as components or harmonics

A Fourier series () is a summation of harmonically related sinusoidal functions, also known as components or harmonics.

a sum

Such a sum is known as a Fourier series, after the French mathematician Joseph Fourier (1768–1830), and the determination of the coefficients of these terms is called harmonic analysis.

a series whose terms are composed of trigonometric functions

A Fourier series is a series whose terms are composed of trigonometric functions.

Such a decomposition of periodic signals

Such a decomposition of periodic signals is called a Fourier series.

an expansion of a periodic function

A Fourier series is an expansion of a periodic function.

infinite series of sine waves

This infinite series of sine waves may be referred to as a Fourier series.

a sum of this form

A Fourier series is a sum of this form: where each of the squares () is a different number, and one is adding infinitely many terms.

The inverse transform

The inverse transform, known as Fourier series, is a representation of in terms of a summation of a potentially infinite number of harmonically related sinusoids or complex exponential functions, each with an amplitude and phase specified by one of the coefficients:

this method of decomposing periodic functions into sines

Depending on how the original signal is expressed, this method of decomposing periodic functions into sines is known as Fourier series or Fourier transform.

a kind of representation for periodic functions

Fourier series are a kind of representation for periodic functions.

a series of origonometric terms

The Fourier Series is a series of origonometric terms which converges to a periodic function over one period.

a way of expressing periodic functions they aren't random

Fourier series are a way of expressing periodic functions they aren't random, they repeat.

a series ) based on preiodic fucntions: \(\sin\) and \(\cos\

The Fourier Series, is a series based on preiodic fucntions: \(\sin\) and \(\cos\).

a series that decomposes any periodic curves into a sum of sines and cosines

The Fourier Series is a series that decomposes any periodic curves into a sum of sines and cosines.

a series

In mathematics, a trigonometric series is a series of the form: a series is called a Fourier series if the terms and have the form: