# 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[{audio1,audio2,},]

plots the power spectra of all audioi.

# Details and Options   • 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 Automatic the 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:
•  Automatic automatic scaling None linear 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 allclose all

## Basic Examples(3)

Power spectrum of a noisy dataset:

Periodogram of a Sound object:

Power spectrum of an Audio object:

## Scope(3)

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:

## Options(4)

### 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:

### 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:

## Properties & Relations(1)

Periodogram plots the magnitude 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: