Fourier Analysis

A mathematical analysis of waves, discovered by the French mathematician Fourier (1768-1830). Fourier proved that any periodic sound, or any non-periodic sound of limited duration, could be represented (Fourier analysis) or created out of (Fourier synthesis) the sum of a set of pure tones with different frequencies, amplitudes and phases.

For the function f(x) defined over the interval c ≤ x ≤ c+2L

Where

Special Fourier Series

Square wave given by the function

This can be expressed as the fourier series:

As the number of terms, n in the series is increased so the accuracy of the approximation improves.

Sawtooth given by the function

This can be expressed as the fourier series:

Triangular wave given by:

This can be expressed as the fourier series:

Half wave rectified sine wave given by:

This can be expressed as the fourier series:

The full wave rectified sine wave given by

This can be expressed as the fourier series:

Acknowledgement

We would like to thank B. Kanmani (Department of Telecommunication Engineering, BMS College of Engineering, Bangalore, India) for corrections to this page.

Subjects: Analysis Signal Processing