Some properties of the lattice algorithm for the direct computation of the matricial spectral factor

The MA equivalent of the Levinson - Wiggins - Robinson algorithm computes the reflection matrices associated with the autocorrelation function of a stationary process and produces a sequence that converges towards the causal minimum phase spectral factor of a given matricial power spectrum. Here we intend to extend some of its properties known in the case of scalar signals to the case of vectorial signals : first it is shown that all the data computed during the recursion are bounded which may be useful for a fixed point implementation, and a method for performing this fixed point implementation is proposed ; second, it is shown that at each step of the recursion, the estimated spectral factor is minimum phase : this last result is based on the normalised form of the lattice algorithm.