Editing Spectrogram (section)

==Generation==
Spectrograms of light may be created directly using an [[optical spectrometer]] over time.

Spectrograms may be created from a [[time-domain]] signal in one of two ways: approximated as a filterbank that results from a series of [[band-pass filter]]s (this was the only way before the advent of modern digital signal processing), or calculated from the time signal using the [[Fourier transform]]. These two methods actually form two different [[time–frequency representation]]s, but are equivalent under some conditions.

The bandpass filters method usually uses [[analog signal|analog]] processing to divide the input signal into frequency bands; the magnitude of each filter's output controls a transducer that records the spectrogram as an image on paper.<ref>{{cite web|url=https://www.sfu.ca/sonic-studio/handbook/Spectrograph.html|title=Spectrograph|website=www.sfu.ca|access-date=7 April 2018}}</ref>

Creating a spectrogram using the FFT is a [[Digital signal processing|digital process]]. Digitally [[sampling (signal processing)|sampled]] data, in the [[Time series|time domain]], is broken up into chunks, which usually overlap, and Fourier transformed to calculate the magnitude of the frequency spectrum for each chunk. Each chunk then corresponds to a vertical line in the image; a measurement of magnitude versus frequency for a specific moment in time (the midpoint of the chunk). These spectrums or time plots are then "laid side by side" to form the image or a three-dimensional surface,<ref>{{cite web|url=https://ccrma.stanford.edu/~jos/mdft/Spectrograms.html|title=Spectrograms|website=ccrma.stanford.edu|access-date=7 April 2018}}</ref> or slightly overlapped in various ways, i.e. [[Window function#Overlapping windows|windowing]]. This process essentially corresponds to computing the squared [[magnitude (mathematics)|magnitude]] of the [[short-time Fourier transform]] (STFT) of the signal <math>s(t)</math> — that is, for a window width <math>\omega</math>, <math>\mathrm{spectrogram}(t,\omega)=\left|\mathrm{STFT}(t,\omega)\right|^2</math>.<ref>{{cite web|url=http://zone.ni.com/reference/en-XX/help/371361E-01/lvanls/stft_spectrogram_core/#details|title=STFT Spectrograms VI – NI LabVIEW 8.6 Help|website=zone.ni.com|access-date=7 April 2018}}</ref>