Deconvolve a symmetric sequence into minimum-phase and maximum-phase sequences I learned in school that any real-valued, even-symmetric sequence can be expressed as the convolution of a minimum-phase sequence and its time-reverse, which is maximum-phase.  In my case, the real-valued, even-symmetric sequence is $sinc(x)$.  What causal, real-valued, minimum-phase sequence convolved with its time-reverse produces $sinc(x)$?

I am familiar with the traditional approach of computing the frequency-domain zeros and constructing the minimum-phase sequence from those inside the unit circle and half of the pairs on the unit circle.  However, in this case, the sequence has infinite length.  I would prefer a closed-form expression for the minimum-phase sequence function.

In practice, I will be using a windowed version of the sequence -- an FIR filter.  I would also like to learn how to deconvolve any real-valued, even-symmetric, finite sequence (FIR filter) into its minimum-phase component, whose frequency response magnitude is the square-root of the symmetric FIR.  I would like a time-domain method for doing this because there are precision problems with computing frequency domain zeros in very long sequences, such as a million taps.
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.