WOLFRAM

returns the squared magnitude of the discrete Fourier transform (power spectrum) of list.

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

Examples

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Basic Examples  (3)Summary of the most common use cases

Power spectrum of a list:

Out[1]=1

Power spectrum of a noisy dataset:

Out[2]=2

Power spectrum of a texture image:

Out[1]=1

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

Specify the partition length:

Out[1]=1

Use overlapping partitions:

Out[2]=2

Smooth with a Hamming window:

Out[3]=3

Use a numerical array as a custom smoothing window:

Out[4]=4

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

Out[2]=2

Power spectrum of an image:

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

Out[2]=2

Process the audio track of a video:

Out[1]=1

Options  (1)Common values & functionality for each option

FourierParameters  (1)

Change in the first Fourier parameter affects scaling:

Out[1]=1
Out[2]=2

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

Out[3]=3

Properties & Relations  (4)Properties of the function, and connections to other functions

Verification of Parseval's theorem:

Out[2]=2

Comparison with ListFourierSequenceTransform:

Out[4]=4

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

Out[1]=1

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

Out[1]=1
Out[2]=2

Possible Issues  (1)Common pitfalls and unexpected behavior

When averaging over partitions, Parseval's theorem may be violated:

Out[2]=2
Out[3]=3

Neat Examples  (1)Surprising or curious use cases

3D visualization of a stack of 2D power spectra of a modulated pulse:

Out[3]=3
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).

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 ]}

@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 ]}

@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 ]}