returns the spectrogram data of list.


uses partitions of length n.


uses partitions with offset d.


applies a smoothing window wfun to each partition.


pads partitions with zeros to length m prior to the computation of the transform.


returns spectrogram data of audio.

Details and Options

  • SpectrogramArray[list] returns the discrete Fourier transform (DFT) of partitions of list, also known as short-time Fourier transform (STFT).
  • Plot the spectrogram using Spectrogram.
  • SpectrogramArray[list] uses partitions of length and offset , where is Length[list].
  • The partition length n and offset d can be expressed as an integer number (interpreted as number of samples) or as time or sample quantities.
  • If necessary, fixed padding is used on the right to make all the partitions the same size.
  • In SpectrogramArray[list,n,d,wfun], the smoothing window wfun can be specified using a window function that will be sampled between and or a list of length n. The default window is DirichletWindow, which effectively does no smoothing.
  • SpectrogramArray works with numeric lists as well as Audio and Sound objects.
  • For multichannel sound objects, the spectrogram is computed over the sum of all channels.
  • SpectrogramArray accepts the FourierParameters option. The default setting is FourierParameters->{1,-1}.


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Basic Examples  (2)

Short-time Fourier transform of a sine wave:

Short-time Fourier transform of an audio signal:

Plot the result:

Scope  (1)

Magnitude spectrum of a single partition:

Plot of the magnitude of the SpectrogramArray data:

Apply a smoothing window function:

Applications  (2)

Short-time energy of an audio object:

Identify the numbers pressed on a phone keypad from a spectrogram:

Create a sound with digits seven and three:

Magnitude of the spectrogram array of the sound:

Find the peaks and calculate the frequencies:

Properties & Relations  (2)

Fourier of partitions of lists is equivalent to SpectrogramArray:

Compute the inverse of spectrogram of non-overlapping partitions:

Wolfram Research (2012), SpectrogramArray, Wolfram Language function, https://reference.wolfram.com/language/ref/SpectrogramArray.html (updated 2017).


Wolfram Research (2012), SpectrogramArray, Wolfram Language function, https://reference.wolfram.com/language/ref/SpectrogramArray.html (updated 2017).


Wolfram Language. 2012. "SpectrogramArray." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2017. https://reference.wolfram.com/language/ref/SpectrogramArray.html.


Wolfram Language. (2012). SpectrogramArray. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SpectrogramArray.html


@misc{reference.wolfram_2024_spectrogramarray, author="Wolfram Research", title="{SpectrogramArray}", year="2017", howpublished="\url{https://reference.wolfram.com/language/ref/SpectrogramArray.html}", note=[Accessed: 22-July-2024 ]}


@online{reference.wolfram_2024_spectrogramarray, organization={Wolfram Research}, title={SpectrogramArray}, year={2017}, url={https://reference.wolfram.com/language/ref/SpectrogramArray.html}, note=[Accessed: 22-July-2024 ]}