simple test for nufft not working

I have a very simple test code for using the nufft function:

%% define signal
t = [-1.0/(2*pi),1.0/(2*pi)];
X = [1.0,1.0];

%% compute the NFFT
f_k = -10:10;
Y_k = nufft(X,t,f_k);

Accroding to the equation given in the documentation the result of this test should be , but the result is just a real constant across . How do I need to modify my program to deliver the correct result, or is this a bug?

Answer 1

[Paul]

Hi Pieter,

I don't think that expression for Y(k) is correct. We can check symbolically

%% define signal
t = sym([-1.0,1.0]);
X = [1.0/(2*sym(pi)),1.0/(2*sym(pi))];
%% compute the NFFT
%f_k = sym(-10:10);
%Y_k = nufft(X,t,f_k)
syms f_k
% expression of Y(k) from the doc page for nufft
Yk = sum(X.*exp(-1j*2*sym(pi)*t*f_k))

Yk = 

Yk = simplify(Yk)

Yk = 

Subbing back in the values of f_k from the original problem

cos(2*pi*(-10:10))/pi

ans = 1×21

0.3183 0.3183 0.3183 0.3183 0.3183 0.3183 0.3183 0.3183 0.3183 0.3183 0.3183 0.3183 0.3183 0.3183 0.3183 0.3183 0.3183 0.3183 0.3183 0.3183 0.3183

which matches the result from nufft.

nufft(double(X),double(t),-10:10)

ans = 1×21

0.3183 0.3183 0.3183 0.3183 0.3183 0.3183 0.3183 0.3183 0.3183 0.3183 0.3183 0.3183 0.3183 0.3183 0.3183 0.3183 0.3183 0.3183 0.3183 0.3183 0.3183