# InverseShortTimeFourier

InverseShortTimeFourier[input]

reconstructs the signal from short-time Fourier data.

InverseShortTimeFourier[input,n]

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

InverseShortTimeFourier[input,n,d]

assumes partitions with offset d.

InverseShortTimeFourier[input,n,d,wfun]

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:
•  stfdata a ShortTimeFourierData object complexes a 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 MaxIterations Automatic maximum number of iterations SampleRate Automatic the sample rate of the result

# Examples

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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, https://reference.wolfram.com/language/ref/InverseShortTimeFourier.html.

#### Text

Wolfram Research (2019), InverseShortTimeFourier, Wolfram Language function, https://reference.wolfram.com/language/ref/InverseShortTimeFourier.html.

#### CMS

Wolfram Language. 2019. "InverseShortTimeFourier." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/InverseShortTimeFourier.html.

#### APA

Wolfram Language. (2019). InverseShortTimeFourier. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/InverseShortTimeFourier.html

#### BibTeX

@misc{reference.wolfram_2024_inverseshorttimefourier, author="Wolfram Research", title="{InverseShortTimeFourier}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/InverseShortTimeFourier.html}", note=[Accessed: 12-August-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_inverseshorttimefourier, organization={Wolfram Research}, title={InverseShortTimeFourier}, year={2019}, url={https://reference.wolfram.com/language/ref/InverseShortTimeFourier.html}, note=[Accessed: 12-August-2024 ]}