Design of allpass-based IIR multi-notch filters with identical pole radiuses

A design method for the allpass-based infinite impulse response multi-notch filters with identical pole radiuses is derived in the paper. According to the standard procedure when design of the allpass-based filters is considered, the multi-notch filters? magnitude response specifications are first formulated as the phase response specifications of the corresponding allpass filter. Then, for the specified identical pole radiuses, it is shown that unknown allpass filter coefficients can be obtained determined from the square system of linear equations. On the other hand, the minimum value of the pole radius, such that specifications of the the magnitude response are satisfied in all passbands, can be determined using the bisection method. Results of comparison with some of the existing design methods lead to the conclusion that proposed filters have higher area under the squared passbands magnitude response compared to filters with the same maximum pole radius. Furthermore, utilization of the proposed method can result in transfer functions that have the lowest possible maximum pole radius.