PeriodogramArray
✖
PeriodogramArray

returns the squared magnitude of the discrete Fourier transform (power spectrum) of list.
pads partitions with zeros to length m prior to the computation of the transform.
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 allclose allBasic Examples (3)Summary of the most common use cases

https://wolfram.com/xid/0elue8loxiurxga-scln3d

Power spectrum of a noisy dataset:

https://wolfram.com/xid/0elue8loxiurxga-dshz3a

https://wolfram.com/xid/0elue8loxiurxga-l2d8p2

Power spectrum of a texture image:

https://wolfram.com/xid/0elue8loxiurxga-734bg4

Scope (5)Survey of the scope of standard use cases

https://wolfram.com/xid/0elue8loxiurxga-qrgvuj


https://wolfram.com/xid/0elue8loxiurxga-k6c0ax


https://wolfram.com/xid/0elue8loxiurxga-ct3s8s

Use a numerical array as a custom smoothing window:

https://wolfram.com/xid/0elue8loxiurxga-8abrhv

Increase the length of the discrete Fourier transform to smooth the power spectrum data:

https://wolfram.com/xid/0elue8loxiurxga-bpel4r

https://wolfram.com/xid/0elue8loxiurxga-j8c44c


https://wolfram.com/xid/0elue8loxiurxga-kg6jfo

Visualization of a 3D power spectrum of a modulated pulse:

https://wolfram.com/xid/0elue8loxiurxga-dyy4r6

https://wolfram.com/xid/0elue8loxiurxga-fuyjn0

Process the audio track of a video:

https://wolfram.com/xid/0elue8loxiurxga-l7x9gq

Options (1)Common values & functionality for each option
FourierParameters (1)
Change in the first Fourier parameter affects scaling:

https://wolfram.com/xid/0elue8loxiurxga-f1ahd7


https://wolfram.com/xid/0elue8loxiurxga-wgqio

Change in the second Fourier parameter does not affect the result:

https://wolfram.com/xid/0elue8loxiurxga-hug5gf

Properties & Relations (4)Properties of the function, and connections to other functions
Verification of Parseval's theorem:

https://wolfram.com/xid/0elue8loxiurxga-m0xfnq

Comparison with ListFourierSequenceTransform:

https://wolfram.com/xid/0elue8loxiurxga-crlh3e

https://wolfram.com/xid/0elue8loxiurxga-iihc9a

https://wolfram.com/xid/0elue8loxiurxga-gd8dkh

https://wolfram.com/xid/0elue8loxiurxga-0a4r4

With partitions longer than the list, a zero-padded version of the list is used:

https://wolfram.com/xid/0elue8loxiurxga-yohuy0

Use logarithmic scaling to visualize the power spectra of an image:

https://wolfram.com/xid/0elue8loxiurxga-05nurb


https://wolfram.com/xid/0elue8loxiurxga-mnfswz

Possible Issues (1)Common pitfalls and unexpected behavior
Wolfram Research (2012), PeriodogramArray, Wolfram Language function, https://reference.wolfram.com/language/ref/PeriodogramArray.html (updated 2024).
Text
Wolfram Research (2012), PeriodogramArray, Wolfram Language function, https://reference.wolfram.com/language/ref/PeriodogramArray.html (updated 2024).
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.
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
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: 23-May-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: 23-May-2025
]}