Magnitude approximation of IIR digital filters with constant group delay response

We present new techniques to approximate the magnitude response of IIR digital filters with nearly constant passband delay characteristics. A polynomial with a group delay response that approximates a constant value in the passband is chosen to be the denominator of the filter transfer function. The coefficients of the numerator polynomial are found such that the delay characteristic is unaffected, and the magnitude response either has desired degrees of flatness at ω=0 and/or ω=π or is flat in the passband and equiripple in the stopband. In the first case, the solution is shown to be analytical. In the second case, the well known Remez exchange algorithm is used to obtain the desired passband and stopband characteristics simultaneously