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PeriodogramArray
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PeriodogramArray

Updated in 14.1

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

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averages the power spectra of non-overlapping partitions of length n.

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PeriodogramArray[list,n,d]

uses partitions with offset d.

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PeriodogramArray[list,n,d,wfun]

applies a smoothing window wfun to each partition.

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PeriodogramArray[list,n,d,wfun,m]

pads partitions with zeros to length m prior to the computation of the transform.

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PeriodogramArray[image,…]

returns the squared power spectrum of image.

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PeriodogramArray[audio,…]

returns the squared power spectrum of audio.

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PeriodogramArray[video,…]

returns the squared power spectrum of the first audio track in video.

Details and Options

Examples

open allclose all

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

Power spectrum of a list:

In[1]:=1
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https://wolfram.com/xid/0elue8loxiurxga-scln3d
Out[1]=1

Power spectrum of a noisy dataset:

In[1]:=1
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https://wolfram.com/xid/0elue8loxiurxga-dshz3a
In[2]:=2
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https://wolfram.com/xid/0elue8loxiurxga-l2d8p2
Out[2]=2

Power spectrum of a texture image:

In[1]:=1
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https://wolfram.com/xid/0elue8loxiurxga-734bg4
Out[1]=1

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

Specify the partition length:

In[1]:=1
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https://wolfram.com/xid/0elue8loxiurxga-qrgvuj
Out[1]=1

Use overlapping partitions:

In[2]:=2
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https://wolfram.com/xid/0elue8loxiurxga-k6c0ax
Out[2]=2

Smooth with a Hamming window:

In[3]:=3
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https://wolfram.com/xid/0elue8loxiurxga-ct3s8s
Out[3]=3

Use a numerical array as a custom smoothing window:

In[4]:=4
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https://wolfram.com/xid/0elue8loxiurxga-8abrhv
Out[4]=4

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

In[1]:=1
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https://wolfram.com/xid/0elue8loxiurxga-bpel4r
In[2]:=2
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https://wolfram.com/xid/0elue8loxiurxga-j8c44c
Out[2]=2

Power spectrum of an image:

In[1]:=1
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https://wolfram.com/xid/0elue8loxiurxga-kg6jfo

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

In[1]:=1
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https://wolfram.com/xid/0elue8loxiurxga-dyy4r6
In[2]:=2
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https://wolfram.com/xid/0elue8loxiurxga-fuyjn0
Out[2]=2

Process the audio track of a video:

In[1]:=1
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https://wolfram.com/xid/0elue8loxiurxga-l7x9gq
Out[1]=1

Options  (1)Common values & functionality for each option

FourierParameters  (1)

Change in the first Fourier parameter affects scaling:

In[1]:=1
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https://wolfram.com/xid/0elue8loxiurxga-f1ahd7
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0elue8loxiurxga-wgqio
Out[2]=2

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

In[3]:=3
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https://wolfram.com/xid/0elue8loxiurxga-hug5gf
Out[3]=3

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

Verification of Parseval's theorem:

In[1]:=1
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https://wolfram.com/xid/0elue8loxiurxga-m0xfnq
Out[2]=2

Comparison with ListFourierSequenceTransform:

In[1]:=1
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https://wolfram.com/xid/0elue8loxiurxga-crlh3e
In[2]:=2
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https://wolfram.com/xid/0elue8loxiurxga-iihc9a
In[3]:=3
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https://wolfram.com/xid/0elue8loxiurxga-gd8dkh
In[4]:=4
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https://wolfram.com/xid/0elue8loxiurxga-0a4r4
Out[4]=4

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

In[1]:=1
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https://wolfram.com/xid/0elue8loxiurxga-yohuy0
Out[1]=1

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

In[1]:=1
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https://wolfram.com/xid/0elue8loxiurxga-05nurb
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0elue8loxiurxga-mnfswz
Out[2]=2

Possible Issues  (1)Common pitfalls and unexpected behavior

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

In[1]:=1
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https://wolfram.com/xid/0elue8loxiurxga-gpqb2r
In[2]:=2
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https://wolfram.com/xid/0elue8loxiurxga-bp23lq
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0elue8loxiurxga-iccqzx
Out[3]=3

Neat Examples  (1)Surprising or curious use cases

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

In[1]:=1
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https://wolfram.com/xid/0elue8loxiurxga-ig4ly0
Out[3]=3
Wolfram Research (2012), PeriodogramArray, Wolfram Language function, https://reference.wolfram.com/language/ref/PeriodogramArray.html (updated 2024).
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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.

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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

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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 ]}

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@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 ]}

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@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 ]}