New fast split-type algorithm for adaptive autoregressive spectral analysis

A fast time iterative algorithm is derived for the estimation of the backward predictor based on the simultaneous minimization of the forward-backward error powers. The algorithm belongs in the split-type type family and the involved internal variables are all symmetric. This is achieved by defining two symmetric vectors whose combination results in the forward-backward least-squares (FBLS) predictor without multiplications being involved. The time update of these two externally imposed symmetric vectors can be carried out using only symmetric quantities. The overall complexity of the new algorithm is 6.5 multiplications per time recursion. A saving on the order of 30% is achieved compared to the algorithm of N. Kalouptsidis and S. Theodoridis (1987)