USAGE    : w=fresolve(x,K,[w_GT]);
FUNCTION : Super-resolves the largest K peaks of the DFT of the signal x
using the formula published in a "Tips & Tricks" column of the IEEE
Signal Processing Magazine (2023). If the ground-truth frequencies, w_GT,
are given as input, comparisons with the super-resolved frequencies are  
shown as well, together with some visualization.
If the DFT has less than K peaks, a warning occurs.

INPUT    : * x, the samples of the signal
           * K, the number of peaks to resolve
           * w_GT, the ground-truth frequencies (optional), only needed
             for comparison with the super-resolved frequencies and plots
OUPUT    : * w, the (cyclic) frequency after super-resolution (in ]-pi,pi])

DATE     : October 2023
AUTHOR   : Thierry Blu, mailto:thierry.blu@m4x.org 
REFERENCE: Guo, R. & Blu, T.,"Super-Resolving a Frequency Band", 
           IEEE Signal Processing Magazine, 2023. To appear. 
__________________________________________________________________________

EXAMPLE OF USE

% Generation of N samples of a signal made of K frequencies
K=5;N=30;

% First, choosing frequencies (reasonably separated from each other)
sep=5;
w_GT=sort(2*pi*rand(sep*K,1));
w_GT=pi-w_GT(1:sep:end);

% Second, choosing amplitudes (with reasonably close absolute values)
a_GT=randn(K,2)*[1;1i];
a_GT=a_GT./abs(a_GT).*(1+0.1*rand(K,1));

% Third, building the samples of the signal
x=a_GT.'*exp(1i*w_GT*(0:(N-1)));

% Finally, super-resolving the K DFT peaks
w=fresolve(x,K,w_GT);