Deconvolve a symmetric sequence into minimum-phase and maximum-phase sequences
For approximating a minimum phase sequence from a finite length linear phase sequence (such as a windowed Sinc), here are some existing stackoverflow and dsp.stackexchange answers regarding a matlab minimum phase approximation script which uses cepstrum deconvolution:

https://stackoverflow.com/questions/16753508/cepstrum-deconvolution-matlab-code 

Derive minimum phase from magnitude 

And here's an earlier post on the same matlab script, with more comments, from the music-dsp mailing list:

http://www.music.columbia.edu/pipermail/music-dsp/2004-february/059372.html 

And the code:

x = [x; zeros(size(x))];
m = size(x,2);
n = size(x,1);
wn = [ones(1,m); 2*ones(n/2-1,m); ones(1,m);  zeros(n/2-1,m)];
y = real(ifft(exp(fft(wn.*real(ifft(log(abs(fft(x)))))))));
y = y(1:n/2;);


I've found that a greater amount of zero=padding of the original linear phase sequence may help improve the approximation.