1. An adaptive auto-orthogonalizing equalizer operating in the discrete frequency domain, comprising: a filter with N cells operating in the discrete frequency domain by the overlap-save method, giving at its output a sequence of filtered samples; a decision element, which is serially connected to said filter, to receive the sequence of filtered samples and to assign each of them to the nearest level out of a predetermined levels set (decision); a control circuit, which is connected to said filter and to the output of said decision element and at each iteration, corresponding to the successive reception of input data blocks, to receive the discrete Fourier transform of an input sample vector, said filtered sample sequence and a decided symbol sequence, and uses them in order to vary the gains of said filter cells; characterized in that said control circuit comprises: a first estimator (S.sub.A) having its input connected to said filter and to the output of said decision element, and having its output connected to the output of a second estimator (S.sub.B) and to the input of a projector (P.sub.S), said first estimator (S.sub.A) estimating a vector (.gradient..epsilon.).sub.k which is proportional to the gradient of the mean square value of the difference between the samples at the filter output and the corresponding decided symbols (mean square error); a second estimator (S.sub.B) having the input connected to the filter and its output connected to the output of said first estimator (S.sub.A) and to the input of said projector (P.sub.S), said second estimator (S.sub.B) estimating a matrix (.phi..phi..sup.H).sub.k by which to multiply the output vector from said first estimator (S.sub.A) in order to transform it into another vector of which the direction passes as close as possible to the point corresponding to the absolute minimum of the function of the cell gain vector C, which represents the mean square error if C is the discrete Fourier transform of a real vector with N-M final zeroes, M being the number of cells of the filter operating in the time domain and equivalent to the filter under examination; and a projector (P.sub.S) having its input connected with the outputs of said first and second estimators (S.sub.A, S.sub.B) and having its output connected to a circuit for adjusting the cell gain vector (C.sup.k), said projector (P.sub.S) receiving as input the vector (U.sub.k) represented by the product of the matrix (.phi..phi..sup.H).sub.k and the vector (.gradient..epsilon.).sub.k and providing as output a vector which is the transform of a real vector with N-M final zeroes, and a circuit for adjusting the cell gain vector (C.sup.k), which subtracts from said vector (C.sup.k) a vector (R.sub.k) proportional to the output vector from said projector (P.sub.S).