1. Process for the blind equalisation of the effects of a transmission channel on a digital speech signal ({s.sub.n (t)}) passing through said transmission channel, said process involving at least: transforming said digital speech signal into a set of cepstral vectors, the set of cepstral vectors being representative of said digital speech signal over a given horizon; calculating a reference cepstrum ({R.sub.n (i)}) representative, for each of the cepstral vectors of said set of cepstral vectors of the long-term cepstrum of said speech signal, said reference cepstrum ({R.sub.n (i)}) consisting of a constant cepstrum signal for each of the cepstral vectors representative in the digital speech signal and in the set of cepstral vectors of the long-term cepstrum in the speech signal; subjecting each of the cepstral vectors to adaptive filtering on the basis of said reference cepstrum, in order to generate a set of equalised cepstral vectors ({C.sub.n (i)}) in which the effects of said transmission channel are substantially suppressed, said set of equalised cepstral vectors being representative of an equalised digital speech signal.