PeriodogramArray [list]
returns the squared magnitude of the discrete Fourier transform (power spectrum) of list.
PeriodogramArray [list,n]
averages the power spectra of non-overlapping partitions of length n.
PeriodogramArray [list,n,d]
uses partitions with offset d.
PeriodogramArray [list,n,d,wfun]
applies a smoothing window wfun to each partition.
PeriodogramArray [list,n,d,wfun,m]
pads partitions with zeros to length m prior to the computation of the transform.
PeriodogramArray [image,…]
returns the squared power spectrum of image.
PeriodogramArray [audio,…]
returns the squared power spectrum of audio.
PeriodogramArray [video,…]
returns the squared power spectrum of the first audio track in video.
PeriodogramArray
PeriodogramArray [list]
returns the squared magnitude of the discrete Fourier transform (power spectrum) of list.
PeriodogramArray [list,n]
averages the power spectra of non-overlapping partitions of length n.
PeriodogramArray [list,n,d]
uses partitions with offset d.
PeriodogramArray [list,n,d,wfun]
applies a smoothing window wfun to each partition.
PeriodogramArray [list,n,d,wfun,m]
pads partitions with zeros to length m prior to the computation of the transform.
PeriodogramArray [image,…]
returns the squared power spectrum of image.
PeriodogramArray [audio,…]
returns the squared power spectrum of audio.
PeriodogramArray [video,…]
returns the squared power spectrum of the first audio track in video.
Details and Options
- PeriodogramArray works with numeric arrays of any rank, 2D and 3D images, and sound objects.
- In PeriodogramArray [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.
- PeriodogramArray [list,n] is equivalent to PeriodogramArray [list,n,n,DirichletWindow ,n].
- PeriodogramArray [list,{n1,n2,…}] partitions a nested list into blocks of size n1×n2×….
- For multidimensional arrays, n is taken to be equivalent to {n,n,…}.
- PeriodogramArray works with numeric lists, as well as Audio and Sound objects.
- For multichannel sounds and images, PeriodogramArray is computed for each channel separately.
- PeriodogramArray accepts the FourierParameters option. The default setting is FourierParameters->{0,1}.
Examples
open all close allBasic Examples (3)
Power spectrum of a list:
Power spectrum of a noisy dataset:
Power spectrum of a texture image:
Scope (5)
Specify the partition length:
Use overlapping partitions:
Smooth with a Hamming window:
Use a numerical array as a custom smoothing window:
Increase the length of the discrete Fourier transform to smooth the power spectrum data:
Power spectrum of an image:
Visualization of a 3D power spectrum of a modulated pulse:
Process the audio track of a video:
Options (1)
FourierParameters (1)
Change in the first Fourier parameter affects scaling:
Change in the second Fourier parameter does not affect the result:
Properties & Relations (4)
Verification of Parseval's theorem:
Comparison with ListFourierSequenceTransform :
With partitions longer than the list, a zero-padded version of the list is used:
Use logarithmic scaling to visualize the power spectra of an image:
Possible Issues (1)
When averaging over partitions, Parseval's theorem may be violated:
Neat Examples (1)
3D visualization of a stack of 2D power spectra of a modulated pulse:
See Also
Periodogram ImagePeriodogram Fourier Partition SpectrogramArray DirichletWindow
Function Repository: IrregularPeriodogram WelchSpectralEstimate
Related Guides
History
Introduced in 2012 (9.0) | Updated in 2014 (10.0) ▪ 2016 (11.0) ▪ 2024 (14.1)
Text
Wolfram Research (2012), PeriodogramArray, Wolfram Language function, https://reference.wolfram.com/language/ref/PeriodogramArray.html (updated 2024).
CMS
Wolfram Language. 2012. "PeriodogramArray." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2024. https://reference.wolfram.com/language/ref/PeriodogramArray.html.
APA
Wolfram Language. (2012). PeriodogramArray. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/PeriodogramArray.html
BibTeX
@misc{reference.wolfram_2025_periodogramarray, author="Wolfram Research", title="{PeriodogramArray}", year="2024", howpublished="\url{https://reference.wolfram.com/language/ref/PeriodogramArray.html}", note=[Accessed: 24-November-2025]}
BibLaTeX
@online{reference.wolfram_2025_periodogramarray, organization={Wolfram Research}, title={PeriodogramArray}, year={2024}, url={https://reference.wolfram.com/language/ref/PeriodogramArray.html}, note=[Accessed: 24-November-2025]}