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Wolfram Language & System Documentation Center
Periodogram
  • See Also
    • PeriodogramArray
    • ImagePeriodogram
    • Fourier
    • Spectrogram
    • DirichletWindow
    • FindRepeat
  • Related Guides
    • Fourier Analysis
    • Signal Visualization & Analysis
    • Signal Processing
    • Audio Analysis
    • Summation Transforms
    • Audio Representation
    • Video Analysis
    • Speech Computation
    • Audio Processing
    • Signal Transforms
    • Video Computation: Update History
    • See Also
      • PeriodogramArray
      • ImagePeriodogram
      • Fourier
      • Spectrogram
      • DirichletWindow
      • FindRepeat
    • Related Guides
      • Fourier Analysis
      • Signal Visualization & Analysis
      • Signal Processing
      • Audio Analysis
      • Summation Transforms
      • Audio Representation
      • Video Analysis
      • Speech Computation
      • Audio Processing
      • Signal Transforms
      • Video Computation: Update History

Periodogram[list]

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

Periodogram[list,n]

plots the mean of power spectra of non-overlapping partitions of length n.

Periodogram[list,n,d]

uses partitions with offset d.

Periodogram[list,n,d,wfun]

applies a smoothing window wfun to each partition.

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

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

Periodogram[{list1,list2,…},n,d,wfun,m]

plots power spectra of several lists.

Periodogram[audio,…]

plots the power spectrum of audio.

Periodogram[video,…]

plots the power spectrum of the first audio track in video.

Periodogram[{input1,input2,…},…]

plots the power spectra of all inputi.

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Options  
AspectRatio  
Axes  
AxesLabel  
Show More Show More
AxesOrigin  
AxesStyle  
DataRange  
FourierParameters  
ImageSize  
SampleRate  
ScalingFunctions  
Ticks  
TicksStyle  
Properties & Relations  
Possible Issues  
See Also
Related Guides
History
Cite this Page
BUILT-IN SYMBOL
  • See Also
    • PeriodogramArray
    • ImagePeriodogram
    • Fourier
    • Spectrogram
    • DirichletWindow
    • FindRepeat
  • Related Guides
    • Fourier Analysis
    • Signal Visualization & Analysis
    • Signal Processing
    • Audio Analysis
    • Summation Transforms
    • Audio Representation
    • Video Analysis
    • Speech Computation
    • Audio Processing
    • Signal Transforms
    • Video Computation: Update History
    • See Also
      • PeriodogramArray
      • ImagePeriodogram
      • Fourier
      • Spectrogram
      • DirichletWindow
      • FindRepeat
    • Related Guides
      • Fourier Analysis
      • Signal Visualization & Analysis
      • Signal Processing
      • Audio Analysis
      • Summation Transforms
      • Audio Representation
      • Video Analysis
      • Speech Computation
      • Audio Processing
      • Signal Transforms
      • Video Computation: Update History

Periodogram

Periodogram[list]

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

Periodogram[list,n]

plots the mean of power spectra of non-overlapping partitions of length n.

Periodogram[list,n,d]

uses partitions with offset d.

Periodogram[list,n,d,wfun]

applies a smoothing window wfun to each partition.

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

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

Periodogram[{list1,list2,…},n,d,wfun,m]

plots power spectra of several lists.

Periodogram[audio,…]

plots the power spectrum of audio.

Periodogram[video,…]

plots the power spectrum of the first audio track in video.

Periodogram[{input1,input2,…},…]

plots the power spectra of all inputi.

Details and Options

  • Periodogram shows the frequency content of a signal by plotting the magnitude squared of the discrete Fourier transform.
  • In Periodogram[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.
  • Periodogram[list,n] is equivalent to Periodogram[list,n,n,DirichletWindow,n].
  • Periodogram works with numeric lists as well as Audio and Sound objects.
  • For a multichannel sound object, Periodogram plots power spectra of all channels.
  • For real input data, Periodogram displays only the first half of the power spectrum due to the symmetry property of the Fourier transform.
  • Compute the effective power spectrum using PeriodogramArray.
  • Periodogram takes the following options:
  • FourierParameters {0,1}Fourier parameters
    SampleRate Automaticthe sample rate
    ScalingFunctions {"Linear","dB"}the scaling function
  • With the setting SampleRate->r, signal frequencies are shown in the range from 0 to r/2.
  • Possible settings for ScalingFunctions include:
  • Automaticautomatic scaling
    Nonelinear scaling for axis and absolute scaling for axis
    sy axis scaling
    {sx} axis scaling
    {sx,sy}different scaling functions for the and directions
  • Possible magnitude scalings sy include:
  • "Absolute"absolute scaling
    "dB" decibel scaling (default)
    {f,f-1}arbitrary scaling using the function f and its inverse
  • Possible frequency scalings sx include:
  • "Linear"linear scaling (default)
    "Log10" scaling
    {f,f-1}arbitrary scaling using the function f and its inverse
  • The scaling function can be "dB" or "Absolute", which correspond to the decibel and absolute power values, respectively.
  • Periodogram also accepts all options of ListLinePlot.

Examples

open all close all

Basic Examples  (3)

Power spectrum of a noisy dataset:

Periodogram of a Sound object:

Power spectrum of an Audio object:

Scope  (4)

Bartlett's method averages over non-overlapping partitions:

Average overlapping partitions:

Welch's method averages over smoothed overlapping partitions:

Pad each partition to increase plot density:

Power spectrum of two dual-tone multi-frequency (DTMF) signals:

Periodogram of a multichannel audio object:

Periodogram of the audio track of a video:

Options  (33)

AspectRatio  (3)

By default, Periodogram uses a fixed height-to-width ratio for the plot:

Make the height the same as the width with AspectRatio1:

AspectRatioFull adjusts the height and width to tightly fit inside other constructs:

Axes  (3)

By default, Axes are drawn:

Use AxesFalse to turn off axes:

Turn on each axis individually:

AxesLabel  (3)

No axes labels are drawn by default:

Place a label on the axis:

Specify axes labels:

AxesOrigin  (2)

The position of the axes is determined automatically:

Specify an explicit origin for the axes:

AxesStyle  (3)

Change the style for the axes:

Specify the style of each axis:

Use different styles for the ticks and the axes:

DataRange  (1)

Use DataRange to display the power spectrum on the normalized frequency range {0,Pi} radians per unit time:

FourierParameters  (1)

Changing the a parameter in FourierParameters will change the scaling:

ImageSize  (7)

Use named sizes such as Tiny, Small, Medium and Large:

Specify the width of the plot:

Specify the height of the plot:

Allow the width and height to be up to a certain size:

Specify the width and height for a graphic, padding with space if necessary:

Setting AspectRatioFull will fill the available space:

Use maximum sizes for the width and height:

Use ImageSizeFull to fill the available space in an object:

Specify the image size as a fraction of the available space:

SampleRate  (1)

By default, Periodogram assumes a sampling rate of one sample per time unit:

Specify a different sample rate:

ScalingFunctions  (1)

By default, Periodogram shows the decibel values of magnitude:

Show the absolute values of the periodogram magnitude:

Ticks  (4)

Ticks are placed automatically in each plot:

Use TicksNone to not draw any tick marks:

Place tick marks at specific positions:

Draw tick marks at the specified positions with the specified labels:

TicksStyle  (4)

Specify the overall tick style, including the tick labels:

Specify the overall tick style for each of the axes:

Specify tick marks with scaled lengths:

Customize each tick with position, length, labeling and styling:

Properties & Relations  (1)

Periodogram plots the magnitude squared of the Fourier transform:

Possible Issues  (2)

When an explicit DataRange is specified, the SampleRate setting is ignored:

For very large partitions with a smoothing window, timing is increased due to sampling of the window:

Specify a smaller partition size:

Timing will be even worse with no partitioning:

See Also

PeriodogramArray  ImagePeriodogram  Fourier  Spectrogram  DirichletWindow  FindRepeat

Function Repository: IrregularPeriodogram

Related Guides

    ▪
  • Fourier Analysis
  • ▪
  • Signal Visualization & Analysis
  • ▪
  • Signal Processing
  • ▪
  • Audio Analysis
  • ▪
  • Summation Transforms
  • ▪
  • Audio Representation
  • ▪
  • Video Analysis
  • ▪
  • Speech Computation
  • ▪
  • Audio Processing
  • ▪
  • Signal Transforms
  • ▪
  • Video Computation: Update History

History

Introduced in 2012 (9.0) | Updated in 2014 (10.0) ▪ 2016 (11.0) ▪ 2024 (14.1)

Wolfram Research (2012), Periodogram, Wolfram Language function, https://reference.wolfram.com/language/ref/Periodogram.html (updated 2024).

Text

Wolfram Research (2012), Periodogram, Wolfram Language function, https://reference.wolfram.com/language/ref/Periodogram.html (updated 2024).

CMS

Wolfram Language. 2012. "Periodogram." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2024. https://reference.wolfram.com/language/ref/Periodogram.html.

APA

Wolfram Language. (2012). Periodogram. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Periodogram.html

BibTeX

@misc{reference.wolfram_2025_periodogram, author="Wolfram Research", title="{Periodogram}", year="2024", howpublished="\url{https://reference.wolfram.com/language/ref/Periodogram.html}", note=[Accessed: 04-February-2026]}

BibLaTeX

@online{reference.wolfram_2025_periodogram, organization={Wolfram Research}, title={Periodogram}, year={2024}, url={https://reference.wolfram.com/language/ref/Periodogram.html}, note=[Accessed: 04-February-2026]}

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