1. A coding process of the adaptive prediction differential PCM type comprising the steps of: forming an error signal e.sub.t from the difference between a sample of signal y.sub.t to be coded and a prediction signal p.sub.t of said signal in which t is a sampling time; quantizing said error signal e.sub.t ; coding the quantized signal; forming a restored error signal e.sub.t from one of said quantized and coded signals; forming a restored signal y.sub.t by adding said restored error signal e.sub.t to said prediction signal p.sub.t ; and forming said prediction signal p.sub.t from said restored signals y.sub.t and e.sub.t by first and second linear filtering operations; said first operation being performed using N successive samples of y.sub.t, namely, y.sub.t, y.sub.t-1,. .. , y.sub.t-N+1, and comprising taking a sequence of N samples from a first sequence formed by said N samples of y.sub.t and from a second sequence obtained by orthogonalizing said N samples of y.sub.t, and multiplying said sequence of N samples respectively by coefficients A1.sub.t, A2.sub.t,. .. , AN.sub.t, then summing the products obtained to obtain a prediction signal py.sub.t ; said second operation being performed using P successive samples of e.sub.t, namely, e.sub.t, e.sub.t-1,. .. , e.sub.t-p+1, and comprising multiplying said P successive samples respectively by coefficients B1.sub.t, B2.sub.t,. .. , BP.sub.t and summing the products obtained to obtain a prediction signal pe.sub.t ; adjusting sequentially said coefficients A1.sub.t, A2.sub.t,. .. , AN.sub.t and B1.sub.t, B2.sub.t,. .. , BP.sub.t at each time t so that the mean power of said error signal e.sub.t is minimized; and carrying out at least one of the two following operations (a) and (b): (a) forming a linear filtering of said signal y.sub.t by using N successive samples of y.sub.t, namely, y.sub.t, y.sub.t-1,. .. , y.sub.t-N+1, and comprising taking a sequence of N samples from a first sequence formed by said N samples of y.sub.t and from a second sequence formed by N derivative samples obtained by orthogonalizing said N samples of y.sub.t, and multiplying said sequence of samples by N coefficients equal to the said coefficients A1.sub.t, A2.sub.t,. .. , AN.sub.t, then adding the products obtained to supply a filtered signal py.sub.t, then forming on the basis of said signal py.sub.t and said signal py.sub.t previously obtained by the filtering of y.sub.t, a signal pAR.sub.t equal to .gamma..sub.AR py.sub.t +(1-.gamma..sub.AR)py.sub.t, in which .gamma..sub.AR is a regulatable coefficient between 0 and 1 (terminals included); (b) filtering the unquantized error signal e.sub.t by multiplying P successive samples of said signal e.sub.t, namely, e.sub.t, e.sub.t-1,. .. , e.sub.t-P+1, by P coefficients equal respectively to said coefficients B1.sub.t, B2.sub.t,. .. , BP.sub.t and adding the products obtained, to supply a filtered signal pe.sub.t, then forming on the basis of said signal pe.sub.t and the signal pe.sub.t obtained previously by filtering e.sub.t a signal pMA.sub.t which is equal to .gamma..sub.MA pe.sub.t +(1-.gamma..sub.MA)pe.sub.t, in which .gamma..sub.MA is a regulatable coefficient between 0 and 1 (terminals included), the coefficients .gamma..sub.AR and .gamma..sub.MA not being simultaneously zero; and after said operations (a) and (b) adding the signals pAR.sub.t and pMA.sub.t, then delaying one sampling time of the sum obtained, to supply said prediction signal p.sub.t.