A Novel Allpass IIR‐Based QMF Design With Applications in Complex Wavelets
Gamal F. Fahmy, Mamdouh F. Fahmy · International Journal of Circuit Theory and Applications · 2025
ABSTRACT IIR filter realizations in QMF structures has long suffered from stability problems. A novel design for quadrature mirror filter (QMF) IIR filter bank is presented and implemented in two different applications, namely, subband coding and discrete/complex wavelet transform. The proposed design is based on an allpass filter design for a stable IIR filter satisfying maximally flat passband amplitude conditions and prescribed regularity constraints. Then the proposed design is extended for QMF filter bank structure that can be applicable in different types of wavelets. Output samples of unstable filter realizations in the synthesis QMF part are calculated from inverse allpass filtering along with time‐reversed operations. A method for time‐reversing operations is presented to calculate the final PR (perfect reconstruction) QMF output signal. The proposed design is also extended to complex wavelets and is applied on both upper and lower trees and its dual transform structure. Frequency response graphs for the developed filter designs are presented along with time‐reversed signal simulations.