Recursive digital low-pass filters with predetermined phase or group delay and Chebyshev stopband attenuation

A method is presented for determining the transfer function of recursive digital low-pass filters with a Chebyshev characteristic of its attenuation in the stopband and phase or group delay specifiable independently of the attenuation. If the maximally flat criterion is chosen for the approximation of a prescribed constant group delay, the transfer function will be obtained in an explicit form. In other cases, the group delay or phase prescription must first be approximated numerically, while the attenuation property can always be achieved explicitly without numerical optimization. A peculiarity of the method is that, in opposition to analog filters, one can obtain for a specific phase or group delay property several transfer functions, which differ in the numerator polynomial and thus in the minimum value of the attenuation in the stopband. The results will be demonstrated with the aid of an example.