reconstructs the signal from short-time Fourier data.


assumes the spectrogram data was computed with partitions of length n.


assumes partitions with offset d.


assumes a smoothing window wfun was applied to each partition.

Details and Options

  • InverseShortTimeFourier computes an inverse of the short-time Fourier transform (STFT).
  • To compute the short-time Fourier transform of lists and audio signals, use ShortTimeFourier.
  • Possible types of input include:
  • stfdataa ShortTimeFourierData object
    complexesa 2D complex matrix representing the STFT of a signal
  • The inverse spectrogram array can be computed from the STFT if the offset d is smaller than half the size of the partition length n.
  • The following options can be given:
  • FourierParameters{1,-1}Fourier parameters to be used
    MaxIterationsAutomaticmaximum number of iterations
    SampleRateAutomaticthe sample rate of the result


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Basic Examples  (1)

Short-time Fourier transform and its inverse of an audio signal:

Scope  (5)

Data  (2)

If the input is a complex matrix, the data is assumed to be a full short-time Fourier transform:

Audio reconstruction from full short-time Fourier data:

Parameters  (3)

The partition size should be what was used for computing the short-time Fourier:

A different value cannot be used for the partition size:

If the input is a complex matrix, the partition size should be the same as its second dimension:

Any other value would be rejected:

By default, the offset used for short-time Fourier is used:

A different partition offset can be used and will result in time stretching:

If the input data is a matrix, by default an offset equal to 1/3 of the inferred partition size is used:

The smoothing window can be different from the value stored in the input data:

Applications  (2)

Zero out a time interval of the short-time Fourier transform:

Modify the short-time Fourier transform:

Perform the inverse transform:

Zero out some frequencies in the short-time Fourier transform of an audio signal:

Zero out some frequencies:

Perform the inverse transform:

Wolfram Research (2019), InverseShortTimeFourier, Wolfram Language function,


Wolfram Research (2019), InverseShortTimeFourier, Wolfram Language function,


@misc{reference.wolfram_2020_inverseshorttimefourier, author="Wolfram Research", title="{InverseShortTimeFourier}", year="2019", howpublished="\url{}", note=[Accessed: 02-March-2021 ]}


@online{reference.wolfram_2020_inverseshorttimefourier, organization={Wolfram Research}, title={InverseShortTimeFourier}, year={2019}, url={}, note=[Accessed: 02-March-2021 ]}


Wolfram Language. 2019. "InverseShortTimeFourier." Wolfram Language & System Documentation Center. Wolfram Research.


Wolfram Language. (2019). InverseShortTimeFourier. Wolfram Language & System Documentation Center. Retrieved from