Fourier Series

A Fourier series is an expansion of a periodic function by a series in terms of sines and cosines i.e you can represent any function as a summation of sine and cosine waves. This methodology is used to analyse and work on periodic signals in various fields such as Control systems, Telecommunication systems etc.

Why only sine and cosine for representing a periodic signal? sine and cosine are so special function his amplitude value are the border between (1,-1)! and give you any value from - infinity to +infinity in an easy way!; a lot of identities, integrable, differentiable that help engineer and mathematician to solve any problems.

Mathematical Expression:

Exponential expression:

Where Xk is complex coefficient.

Visualizing fourier series using P5.js in Angular

Here is an example for visualizing square wave as a sum of f(x) = sin x + 1/3 sin 3x + 1/5 sin 5x + 1/7 sin 7x etc + 1/9 sin 9x + .... 1/n sin nx.

For n=1

For n=3

For n=5

For n=10

For n=50

For n=100

For n=500