. . . "A digital filter in which the relation between an input data x(n) and an output data Y(n) is: ##EQU4## where n is an integer and a.sub.n-i is a multiplier, said filtercomprising first means for multiplying the input data x(n) by all the integers l ranging from 0 to 2.sup.M -1, where M is the bit number of either a binary coded weight data a.sub.i or its partial bit a.sub.ij (j=1, 2, . . . , K); a" . .