How can I find the FFT of a time series when the samples are not equally spaced?

How do I find the FFT of a time series with nonuniformly spaced samples?

Answer 1

[MathWorks Support Team]

Starting in MATLAB R2020a, the function "nufft" can be used to find the nonuniform FFT of a signal. Please refer to the official documentation page for "nufft" for more information: 

https://www.mathworks.com/help/matlab/ref/double.nufft.html

In releases prior to MATLAB R2020a, you may use the following workaround:

 

To find the FFT of a time series when the samples are not equally spaced, you must first interpolate the data so all samples are equally spaced. You may use the "interp1" function to interpolate between the sampled points. You may then feed the results of "interp1" to the FFT function. Note that this is an approximation and you might lose some of the resolution. Please refer to the official documentation page for "interp1" for more information: 

https://www.mathworks.com/help/matlab/ref/interp1.html

If you are interested in the frequency spectrum mainly, there is also the alternative to use the "plomb" function from the Signal Processing Toolbox.

For additional ways of analyzing spectrum of nonuniformly spaced sample data, please refer to:

"Spectral Estimation from Nonconsecutive Data"

by N. Rozario and A. Papoulis

IEEE Trans. on Information Theory, vol IT-33, no. 6, November 1987

"On Nonuniform Sampling Expansions Using Entire Interpolating

Functions, and On the Stability of Besslel-Type Sampling Expansions"

by Michael D. Rawn,

IEEE Trans. on Information Theory, vol IT-35, no. 3, May 1989

[Walter Roberson]

Tao comments

I found it very useful

Answer 2

[Walter Roberson]

These days you use nufft