InverseSpectrogram [data]
reconstructs the signal from the magnitude spectrogram data.
InverseSpectrogram [img]
reconstructs the signal, assuming that the image img is the magnitude spectrogram.
InverseSpectrogram [input,n]
assumes the spectrogram data was computed with partitions of length n.
InverseSpectrogram [input,n,d]
assumes partitions with offset d.
InverseSpectrogram [input,n,d,wfun]
assumes a smoothing window wfun was applied to each partition.
InverseSpectrogram
InverseSpectrogram [data]
reconstructs the signal from the magnitude spectrogram data.
InverseSpectrogram [img]
reconstructs the signal, assuming that the image img is the magnitude spectrogram.
InverseSpectrogram [input,n]
assumes the spectrogram data was computed with partitions of length n.
InverseSpectrogram [input,n,d]
assumes partitions with offset d.
InverseSpectrogram [input,n,d,wfun]
assumes a smoothing window wfun was applied to each partition.
Details and Options
- InverseSpectrogram approximates an inverse of the magnitude spectrogram.
- To compute the short-time Fourier transform of lists and audio signals, use ShortTimeFourier .
- InverseSpectrogram assumes that real matrix input is a magnitude spectrogram without the redundant part. This means that the window size used was 2(size-1), where size is the second dimension of the input matrix.
- The inverse spectrogram can be computed from the spectrogram if the offset d is smaller than half the size of the partition length n.
- The following options can be given:
-
- Possible method settings include:
-
Automatic uses automatic method"GriffinLim" iteratively approximates the phase"SPSI" uses single-pass spectrogram inversion"Hybrid" uses the SPSI as the inital phase for Griffin–Lim
- The "Hybrid" method is used by default.
Examples
open all close allBasic Examples (3)
Generate an audio signal, assuming a cellular automaton evolution to be the magnitude spectrum:
data = CellularAutomaton[60, {{1}, 0}, 255];
ArrayPlot[data]Audio[InverseSpectrogram[data], SampleRate -> 8000]Reconstruct a signal from a magnitude spectrum:
InverseSpectrogram[{...}]Spectrogram[%]Construct an Audio object from an Image :
InverseSpectrogram[[image]]//AudioCompute the spectrogram of the resulting signal:
Spectrogram[%, PlotRange -> All, AspectRatio -> 1]Scope (3)
The partition size must match the value inferred from the input data:
data = List[...];The inferred partition size is 2×(size-1), where size is the second dimension of the input matrix:
size = Dimensions[data][[2]]InverseSpectrogram[data, 2(size - 1)]//SpectrogramBy default, the partition offset is of the inferred partition size:
data = List[...];InverseShortTimeFourier[data]//SpectrogramSpecify a different partition offset:
InverseSpectrogram[data, Automatic, 40]//SpectrogramSpecify a smoothing window:
data = List[...];InverseShortTimeFourier[data, Automatic, Automatic, DirichletWindow]//SpectrogramOptions (2)
MaxIterations (1)
Use the MaxIterations option to control the quality of the result and the speed of the operation:
AbsoluteTiming[res = InverseSpectrogram[List[...], Method -> "GriffinLim", MaxIterations -> 1];][[1]]
Spectrogram[res]AbsoluteTiming[res = InverseSpectrogram[List[...], Method -> "GriffinLim", MaxIterations -> 10000];][[1]]
Spectrogram[res]Method (1)
The "Griffin-Lim" method uses an iterative algorithm to approximate the original signal:
data = List[...];InverseSpectrogram[data, Method -> "GriffinLim"]//SpectrogramThe "SPSI" method approximates the signal in a non-iterative way, which is relatively fast:
InverseSpectrogram[data, Method -> "SPSI"]//SpectrogramThe "Hybrid" method uses the result of the "SPSI" method as the starting guess for iterative method "Griffin-Lim", which may converge faster:
InverseSpectrogram[data, Method -> "Hybrid"]//SpectrogramApplications (2)
Reconstruct an Audio object from its magnitude spectrum:
sp = List[...];
MatrixPlot[Log[sp]]Audio[InverseSpectrogram[sp, 1024, 256, HannWindow], SampleRate -> 16000]Construct an Audio object from image data:
img = [image];Convert the image to grayscale and rotate appropriately:
data = ColorConvert[ImageRotate[img, -Pi / 2], "Grayscale"]//ImageData;Reconstruct the signal with the assumption that the image was its spectrogram:
InverseSpectrogram[img]//AudioCompute the spectrogram of the resulting signal:
Spectrogram[%, PlotRange -> All, AspectRatio -> 1]Properties & Relations (1)
Compute the spectrogram of a signal and its approximate inverse:
data = Table[Cos[( i/4) + ((i/20))^2], {i, 2000}];
Spectrogram[data]Compute the short-time Fourier transform:
stft = SpectrogramArray[data];Discard the redundant part and take the absolute value to get the magnitude spectrogram:
spectrogram = Abs[stft[[All, 1 ;; Floor[Last[Dimensions[stft]] / 2 + 1]]]];Use InverseSpectrogram to compute the approximated inverse of the spectrogram:
InverseSpectrogram[spectrogram]//SpectrogramPossible Issues (1)
The partition size must match the value inferred for the input data:
data = List[...];
Dimensions[data]The inferred partition size is 2×(size-1), where size is the second dimension of the input matrix:
InverseSpectrogram[data, 2(127 - 1)]//HeadSignal reconstruction cannot be done with other partition sizes:
InverseSpectrogram[data, 80]//HeadRelated Guides
History
Text
Wolfram Research (2019), InverseSpectrogram, Wolfram Language function, https://reference.wolfram.com/language/ref/InverseSpectrogram.html.
CMS
Wolfram Language. 2019. "InverseSpectrogram." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/InverseSpectrogram.html.
APA
Wolfram Language. (2019). InverseSpectrogram. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/InverseSpectrogram.html
BibTeX
@misc{reference.wolfram_2026_inversespectrogram, author="Wolfram Research", title="{InverseSpectrogram}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/InverseSpectrogram.html}", note=[Accessed: 14-August-2026]}
BibLaTeX
@online{reference.wolfram_2026_inversespectrogram, organization={Wolfram Research}, title={InverseSpectrogram}, year={2019}, url={https://reference.wolfram.com/language/ref/InverseSpectrogram.html}, note=[Accessed: 14-August-2026]}