`nufft`

Fourier transform of data sampled at nonuniform points.

Category: Mathematics > Fourier Analysis and Filtering

Syntax

Y = nufft(X)

Same as fft(X), with unit-spaced sample points.

Y = nufft(X, t)

Samples are located at the points t; frequencies are the default (0:n-1)/n.

Y = nufft(X, t, f)

Evaluates the transform at the frequencies f.

Y = nufft(X, t, f, dim)

Operates along dimension dim.

Description

The result at frequency f(k) is the sum over j of X(j)*exp(-2*pi*1i*t(j)*f(k)). When the points t are evenly spaced and f is the default grid, this reduces to the ordinary DFT. The point of nufft is that t and f need not be uniform.

To analyze unevenly timed measurements, pass the measurement times as t and the frequencies of interest as f.

Input arguments

X: Sample values, vector or array.
t: Sample points, one per element of X along the operating dimension. Use [] for 0:n-1.
f: Frequencies at which to evaluate, in cycles per unit of t.
dim: Dimension to operate along.

Output arguments

Y: Transform values, one per frequency in f.

Examples

Uniform points reproduce fft

v = [1 2 3 4];
t = [0 0.25 0.5 0.75];
Y = nufft(v, t, 0:3);
max(abs(Y - fft(v))) < 1e-12

Output

ans = logical
   1

Irregular sample times

x = [0.1 0.4 0.7];
nufft([1 1 1], x, [0 1 2 3])