Fourier Transform

The Fourier transform is a mathematical transformation that is often used in acoustics where a sound intensity can be expressed either as a function of time or as a function of frequency.

The illustration from a discussion of sound timbre shows the application of a Fourier transform which takes a musical waveform as a function of time and transforms it into a function of frequency. This is typically done with the aid of a computer routine which calculates the transformation. It is typically called an FFT for "fast Fourier transform" and is very useful for the analysis of sounds.

When applied to optics, the Fourier transform may transform the light intensity at one point in space to the light intensity at some distant plane, with a typical example being the Fraunhofer diffraction of light from a single slit.