`nufftn`

N-dimensional Fourier transform of data at nonuniform sample points.

Category: Mathematics > Fourier Analysis and Filtering

Syntax

Y = nufftn(X)

Same as fftn(X), for unit-spaced points.

Y = nufftn(X, t, f)

Sample points t and query frequencies f.

Description

It is the multidimensional version of nufft: the exponent is -2*pi*1i times the dot product of the sample coordinate with the query frequency. With the default points and frequencies the result matches fftn.

The number of sample points must equal the number of elements of X.

Input arguments

X: Sample values.
t: Sample coordinates: a matrix with one row per element of X and one column per dimension, or a cell array of one grid vector per dimension.
f: Query frequencies in the same two forms.

Output arguments

Y: Transform values at the query frequencies.

Example

Default grid equals fftn

X = [1 2; 3 4];
Y = nufftn(X)
max(abs(Y(:) - reshape(fftn(X), [], 1))) < 1e-12

Output

Y = 2×2

    10    -2
    -4     0
ans = logical
   1

Notes

MatLivre evaluates the sums directly instead of using a fast approximation.

nufftn