An Optimal Design For IIR Allpass QMF With Complex Wavelet Application
Gamal F. Fahmy, Mamdouh F. Fahmy, Omar M. Fahmy · 2024
In this paper we present a novel design for stable QMF (Quadrature Mirror Filter) IIR filter bank structure that can be utilized in sub band coding, discrete/complex wavelet transform and different other signal processing applications. This paper presents a new IIR wavelet basis, the proposed IIR wavelet is composed of IIR allpass functions. It satisfies the PR and AC condition required for wavelet basis. As the synthesis bases involves IIR functions that are incomputable in real time domain, a technique is proposed to accurately simulate their responses in none real time. 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. Different methods for time revering operations are presented to calculate the final PR (Perfect Reconstruction) QMF output signal. Frequency response graphs for the developed filter design are illustrated along with time revered signal simulations.