Fourier Series - Introduction

Fourier series are used in the analysis of periodic functions.

math expression
A periodic function

Many of the phenomena studied in engineering and science are periodic in nature eg. the current and voltage in an alternating current circuit. These periodic functions can be analysed into their constituent components (fundamentals and harmonics) by a process called Fourier analysis.

We are aiming to find an approximation using trigonometric functions for various square, saw tooth, etc waveforms that occur in electronics. We do this by adding more and more trigonometric functions together. The sum of these special trigonometric functions is called the Fourier Series.

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Jean Fourier

Jean Baptiste Joseph
Fourier (1768 - 1830).

Fourier was a French mathematician, who was taught by Lagrange and Laplace.

He almost died on the guillotine in the French Revolution. Fourier was a buddy of Napoleon and worked as scientific adviser for Napoleon's army.

He worked on theories of heat and expansions of functions as trigonometric series... but these were controversial at the time. Like many scientists, he had to battle to get his ideas accepted.