Minimum phase wavelet by ARMA factorization

An algorithm is presented for computing a minimum phase wavelet, given only the causal part of its autocorrelation function r⁺ (k),k⩾0. The algorithm falls in the category of spectral factorization techniques, with the difference that instead of factoring the symmetric autocorrelation, its ARMA model is factored, and the ARMA model for symmetric autocorrelation is obtained directly from that of r ⁺ (k) via a simple identity. It is found that, at least in seismic context, this procedure works better than the conventional spectral factorization as it involves ARMA polynomials which are of much lower order than MA polynomials. The algorithm is supported by two theorems and a detailed numerical example. The treatment is essentially deterministic