Abstract: A linear prediction analysis is performed for each frame of a speech signal to determine the coefficients of a short-Term synthesis filter. For each sub-frame, an excitations sequence which, when applied to the short-term synthesis filter generates a synthetic signal representative of the speech signal, is determined by means of an iterative process in which a symmetrical matrix B.sub.n, is gradually built up with each iteration. The matrix B.sub.n is reversed with each iteration by decomposing the pattern B.sub.n =L.sub.n .multidot.R.sub.n.sup.T with L.sub.n =R.sub.n .multidot.K.sub.n where L.sub.n and R.sub.n are triangular matrices and K.sub.n is a diagonal matrix, and matrix L.sub.n has only 1s on its main diagonal.