# ImagePeriodogram

ImagePeriodogram[image]

shows the squared magnitude of the discrete Fourier transform (power spectrum) of image.

ImagePeriodogram[image,n]

shows the average of power spectra of non-overlapping partitions of size n×n.

ImagePeriodogram[image,n,d]

uses partitions with offset d.

ImagePeriodogram[image,n,d,wfun]

applies a smoothing window wfun to each partition.

ImagePeriodogram[image,n,d,wfun,m]

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

# Details and Options • ImagePeriodogram logarithmically scales the power spectrum of the image and adjusts the values so that they range from 0 to 1.
• In ImagePeriodogram[image,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.
• ImagePeriodogram[image,n] is equivalent to ImagePeriodogram[image,n,n,DirichletWindow,n].
• ImagePeriodogram[image,{n1,n2}] partitions image into blocks of size n1×n2.
• For 3D images, ImagePeriodogram[image,{n1,n2,n3}] partitions image into blocks of size n1×n2×n3.
• For multichannel images, ImagePeriodogram returns a multichannel image where each channel is the power spectrum computed for each channel separately.
• ImagePeriodogram accepts the Alignment option that determines the location of the zero frequency term. The default is . With Alignment->{Left,Top}, the zero frequency term is placed at the top-left corner of the image.

# Examples

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## Basic Examples(3)

Power spectrum of an image of a disk:

Power spectrum of a color image:

Power spectrum of a 3D image of the hydrogen wave function:

## Options(1)

### Alignment(1)

By default, the power spectrum is centered:

Use Alignment->{Left,Top} to avoid centering:

Centering can be switched off for one dimension:

## Properties & Relations(2)

Create the image periodogram from the power spectrum data:

Use PeriodogramArray to change the default visualization settings of the image power spectrum: