Exponential decay fitting with Discrete Fourier transform (DFT)

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