Abstract: In this transmission system using differential PCM, the local decoder, inporated in the loop of the encoder, and the remote decoder comprise identical filters (5) and (15) each constituted by a cascade arrangement of several filtering sections (F.sub.1 -F.sub.N) of the first and/or of the second order; each section may have one or two controllable coefficients, which are modified at each sampling instant by a modification term which depends upon the product of the difference signal (e) produced in the encoder and the gradient of the difference signal (e) with respect to the controllable coefficient. When the filtering sections (F.sub.1 -F.sub.N) are recursive, the gradients are obtained by applying a signal corresponding to the difference signal (e) to identical recursive sections (F'.sub.1 -F'.sub.N). When non-recursive filtering sections (H.sub.1 -H.sub.L) are used, the gradient calculation sections (H'.sub.1 -H'.sub.L) are recursive with a transfer function inverse to that of the sections (H.sub.1 -H.sub.