An adaptive digital filter which is used, for instance, for a prediction filter in an ADPCM modulator and an ADPCM demodulator, for providing stable operation and minimum phase shift response has been found. The filter (FIG. 4, FIG. 5) has three parallel branches (A,B,C), two (A,B) of them have a plurality of series connected non-recursive filter elements (A.sub.1 -A.sub.n, B.sub.1 -B.sub.n) each of which has degree not larger than three relating to an operator (Z.sup.-1), and third branch (C) is merely a conductive line. Tap coefficients (c.sub.1, c.sub.2, . . . , d.sub.1, d.sub.2, . . . ) of non-recursive filter elements change according to solutions of the transfer function of the filter. A numerator and/or a denominator of the transfer function of the present filter is a Chebychev polynominal relating to an operator (Z.sup.-1), and has a zero point and/or a pole. The solutions (w.sub.i, v.sub.i) of a numerator and a denominator locate alternately on a unit circle (FIG. 6) on a Z.sup.-1 plane. When solutions of the transfer function do not locate alternately on said unit circle, tap coefficients (c.sub.1, c.sub.2, . . . , d.sub.1, d.sub.2, . . . ) are not updated, since non-alternate solutions do not assure stable operation and/or minimum phase shift response of the filter.