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


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


uses partitions with offset d.


applies a smoothing window wfun to each partition.


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


returns the squared power spectrum of image.


returns the squared power spectrum of audio.

Details and Options


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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:

Introduced in 2012
Updated in 2014