:Fourier analysis/synthesis:

Pronunciation GBː ˈfʊriə, GA: ˈfʊriər

Fourier analysis is a mathematical technique used to transform a signal in the time domain to a frequency domain representation. In terms of speech research this essentially means the production of an amplitude-frequency spectrum by processing a sampled version of the speech pressure waveform of a sound. The equation used is known as a Discrete Fourier Transform (DFT). This is given below:

where X=a value in the frequency domain, x=a value in the time domain, N=the total number of time domain sample points.

A related technique, known as Fourier Synthesis, produces a sampled time domain representation from a frequency domain representation, using the Inverse DFT:

In practice one of a number of available computationally efficient algorithms is used to perform the transformations. These are known as Fast Fourier Transforms (FFT).