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.

Details and Options

Examples

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Basic Examples  (3)

Power spectrum of a list:

Power spectrum of a noisy dataset:

Power spectrum of a texture image:

Scope  (4)

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:

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:

Wolfram Research (2012), PeriodogramArray, Wolfram Language function, https://reference.wolfram.com/language/ref/PeriodogramArray.html (updated 2016).

Text

Wolfram Research (2012), PeriodogramArray, Wolfram Language function, https://reference.wolfram.com/language/ref/PeriodogramArray.html (updated 2016).

CMS

Wolfram Language. 2012. "PeriodogramArray." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2016. 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_2023_periodogramarray, author="Wolfram Research", title="{PeriodogramArray}", year="2016", howpublished="\url{https://reference.wolfram.com/language/ref/PeriodogramArray.html}", note=[Accessed: 01-October-2023 ]}

BibLaTeX

@online{reference.wolfram_2023_periodogramarray, organization={Wolfram Research}, title={PeriodogramArray}, year={2016}, url={https://reference.wolfram.com/language/ref/PeriodogramArray.html}, note=[Accessed: 01-October-2023 ]}