Fourier transform

Definition

A particular integral transform that when applied to a function of time (such as a signal), converts the function to one that plots the original function's frequency composition; the resultant function of such a conversion.

Etymology

Named after French mathematician and physicist Jean Baptiste Joseph Fourier, who initiated the study of what is now harmonic analysis.

Example Sentences

• "Fourier transforms are not limited to acting on functions of time, but the domain of the original function is commonly called the time domain."
• "The Fourier transform of a function of time is a complex function of frequency, whose magnitude (absolute value) represents the amount of that frequency present in the original function, and whose argument is the phase offset of the basic sinusoid in that frequency."
• "Since a separate integration is needed to give each point of the transformed function, the process would become extremely tedious if it were to be attempted manually and many ingenious devices have been invented for preforming Fourier transforms mechanically, electrically, acoustically and optically."