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.