NO AMPLITUDE DISTORTION QMF IIR DEGITAL FILTER OF EVEN ORDER

概要

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Let (H_0(z), H_1(z)) and (F_0(z), F_1(z)) be respectively the analysis and the synthesis filters of a two-channel QMF filter bank. In, assuming that, F_0(z)=H_0(z) and F_1(z)=-H_1(z), H_1(z)=H_0(-z), zeros on the unit-circle and an odd filter order N then the QMF response T(z) is all-pass and H_0(z)=(a_0(z^2)+z^<-1>a_1(z^2))/2 as well as H_1(z)=(a_0(z^2)-z^<-1>a_1(z^2))/2 where a_0(z^2) and a_1(z^2) are real allpass transfer functions, fact that is used to derive an efficient filter structure. In the case where N is even, the previous relations are not valid; nevertheless, if we allow the QMF digital filter structure of Fig. 1 along with conditions F_0(z)=H_0(z), F_1(z)=H_1(z), H_1(z)=H_0(-z) and zeros on the unit-circle then here also T(z) is allpass. However, the previous real allpass decomposition in a_0(z^2)and a_1(z^2) does not exist, instead a more complicated complex allpass decomposition is derived in. For N even, we propose in this paper, a new real realization based on the orthogonal factorization of a sparse orthogonal state-space realization for the QMF analysis filters of even order. The QMF synthesis filters could be obtained with a simple flow diagram transposition of the corresponding analysis filters.
社団法人電子情報通信学会の論文
1997-08-13