Editing Short-time Fourier transform (section)

{{Short description|Fourier-related transform suited to signals that change rather quickly in time}}

The '''short-time Fourier transform''' ('''STFT''') is a [[List of Fourier-related transforms|Fourier-related transform]] used to determine the sinusoidal frequency and phase content of local sections of a signal as it changes over time.<ref>{{cite journal |author1=Sejdić E. |author2=Djurović I. |author3=Jiang J. | year = 2009 | title = Time-frequency feature representation using energy concentration: An overview of recent advances | journal = Digital Signal Processing | volume = 19 | issue = 1| pages = 153–183 | doi=10.1016/j.dsp.2007.12.004|bibcode=2009DSP....19..153S }}</ref> In practice, the procedure for computing STFTs is to divide a longer time signal into shorter segments of equal length and then compute the Fourier transform separately on each shorter segment. This reveals the Fourier spectrum on each shorter segment.  One then usually plots the changing spectra as a function of time, known as a [[spectrogram]] or [[waterfall plot]], such as commonly used in [[Software Defined Radio|software defined radio]] (SDR) based spectrum displays. Full bandwidth displays covering the whole range of an SDR commonly use fast Fourier transforms (FFTs) with 2^24 points on desktop computers.{{citation needed|date=August 2024}}

[[File:Spectrogram-19thC.png|thumb|400px|A spectrogram visualizing the results of a STFT of the words "nineteenth century". Here, frequencies are shown increasing up the vertical axis, and time on the horizontal axis. The legend to the right shows that the color intensity increases with the density.]]