AbstractThis paper proposes group‐delay response approximation method based on the ARMA filter, an extension of digital filter approximation by statistical design. Since the denominator and numerator coefficient sequences are in opposite order in recursive group‐delay filters, obtaining either coefficient sequence leads to the other. the approximation described here replaces group‐delay response with the magnitude‐squared response via the complex cepstrum. It is then approximated by an auto‐regressive (AR) filter to obtain the denominator coefficient sequence by linear prediction; reversing this sequence gives the numerator coefficient sequence. A design procedure using the FFT and Levinson‐Durbin algorithm gives a solution much faster than the previous method of solution by means of iterated calculations, in addition to which it is easy to assure that the approximation is stable. A coefficient series allowing realization of a low‐coefficient‐sensitivity recursive structure is directly obtained in the design procedure. Examples of group‐delay equalization and results of radar signal simulation are presented as applications of the approximation method. Finally, some additional problems are considered in connection with the difficulty of obtaining a high‐order approximation with large g