How to get a frequency vector in NUFFT MATLAB CODE?

The example is

t = [0:300 500.5:700.5];

S = 2*sin(0.1*pi*t) + sin(0.02*pi*t);

X = S + rand(size(t));

Y = nufft(X,t);

n = length(t);

f = (0:n-1)/n;

plot(f,abs(Y))

The frequency range here is [0,1],

My question is, for a noun-uniform (unknown) signal, How to calculate the frequency range? It is still 'f = (0:n-1)/n'?

I don not know how to get frequency vector for my data,that which is not in the normalized frequency range, In fact, it should be in the real frequency range (due to the non-uniform sampling rate).what the matlab code that i should use?

thanks so much .

[NGR MNFD]

Does anyone have an idea on my problem?

Answer 1

[Vinay]

Hi @NGR MNFD,

The ‘nufft’ uses the default frequencies with the form f(i) = (i-1)/n for a signal length of n. The nonuniform discrete Fourier transform treats the nonuniform sample points t and frequencies f as if they have a sampling period of 1 s and a sampling frequency of 1 Hz for the equivalent uniformly sampled data.

We can define the frequency vector by calculating average sampling frequency by taking the mean of the sampling intervals and calculating the normalized frequency vector as shown below

% calculate the sampling intervals
dt = diff(t);

% Estimate the average sampling frequency
fs_avg = 1 / mean(dt);

% Calculate the frequency vector
n = length(t);
f = (0:n-1) * (fs_avg / n);

Kindly refer to the below documentation of “nufft” for more details:

https://www.mathworks.com/help/releases/R2021b/matlab/ref/double.nufft.html

I hope this helps!