Design of minimum-order allpass-based IIR multi-notch filters

Abstract

The paper investigates the design methods for the minimum-order allpass-based infinite impulse response multi-notch filters. Monotonically decreasing nature of the stable allpass filter's phase response allows the formulation of the magnitude response specifications of the allpass-based multi-notch filter as the linear equality and inequality constraints in unknown allpass filter coefficients. As not all allpass filters satisfying mentioned constraints are of the same practical interest, several design methods minimizing various cost functions are proposed. One of these methods outperforms existing design methods in terms of stability margin, while utilization of other methods can result in higher area under the passbands squared magnitude response. Proposed methods are also compared with some of the existing infinite impulse response multi-notch filter design methods, whose lower complexity counterparts are derived by means of conclusions drawn and notations introduced while deriving the proposed design methods.