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Exponential decay fitting with Discrete Fourier transform (DFT)

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Deo
Deo 2017-4-17
关闭： Deo 2017-5-5
Hi
My Matlab version is R2016b.
I am trying to make Matlab code for exponential decay fitting with discrete fourier transform.
Details are shown in the article below. (I need only DFT part)
http://aip.scitation.org/doi/full/10.1063/1.2839918
Below is summary for the only required parts,
And below is a part of my code for this. Because of "iwt" part is negative than what matlab fft function uses (please see "More About" -> "Discrete Fourier Transform of Vector" section of this hyperlink for fft) and k should be k-1, I modified that way. I am still confusing about sign for phase or angle(phase). "tau" is reciprocal of beta. (tau = 1/beta).
elseif fit_method == 1
tic;
nfft = 1024;
dt = 10^-8;
F = fft(xy(:,2),nfft);
k = [1:1:nfft]';
wt = -2*pi.*(k-1)/nfft;
phase = angle(F);
tau = dt./log((cot(phase).*sin(wt))+cos(wt));
fit_success = 0;
toc;
However, the result is bad, and I do not understand what is my mistake.
Please help me to solve this issue.
xy is two column double data. First column is time data from 0 to 175 microsecond with interval of 10 nanosecond. Second column data is intensity (amplitude) data having exponential decay shape.
Thanks

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