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.
- 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.
See also: Discrete Fourier Transform, Fourier, Baron Jean Baptiste Joseph.
Subjects: Analysis Signal Processing
- Further reading:
- Fourier Transform and Its Applications, , McGraw-Hill Book Company Ltd
- Fast Fourier Transform and Its Applications, , Prentice-Hall
- Weblinks:
- Acoustics and Vibrations Animations A collection of animations produced by Daniel A. Russell, Ph.D., Associate Professor of Applied Physics at Kettering University.