Abstract: The present invention relates to echo cancelling techniques and more particularly to an initialization device for an echo cancelling system. The invention comprises means for converting a pseudo-random sequence (u.sub.k) of length N into a sequence of emitted samples (e.sub.k) such that each sample e.sub.k is derived from u.sub.k by e.sub.k =2 u.sub.k -1, multiplying each sample u.sub.(N-M+1+k)mod N with each received sample s.sub.N+k and adding the results k varying between 0 and N-1. The result at instant kT, to within a multiplicative constant, of said additions is then H.sub.M (k), one of the N coefficients at the initial conditions of said echo cancelling device, M being between 0 and N, and k varying from 0 to N-1, with H.sub.M (k)=H.sub.M (k-1)+s.sub.N+k. u.sub.(N+k+1-M)mod N. The invention is applicable to the pulse response of any signal.