The Journal of Korean Institute of Communications and Information Sciences (한국통신학회논문지)

The Korean Institute of Commucations and Information Sciences (한국통신학회)
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An Efficient Design Method of Linear-Phase Prototype Lowpass Filter for Near-Perfect Reconstruction Pseudo-QMF Banks

근접 완전재생 Pseudo-QMF 뱅크를 위한 선형위상 프로토타입 저역통과 필터의 효율적인 설계 방법

  • 전준현 (동국대학교 공과대학 IT 학부 정보통신공학과)
  • Published : 2008.03.31
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Abstract

M channel near-perfect-reconstruction(NPR) pseudo-QMF banks are a hybrid of conventional pseudo-QMF design and spectral factorization approach where the analysis and synthesis filters are cosine-modulated versions of the prototype-lowpass filter(p-LPF). However, p-LPF H(z) does not have linear-phase symmetry as well as magnitude-distortion optimization since it is obtained by spectral factorization of $2M^{-th}$ band filter $G(z)=z^{-(N-1)}H(z^{-1})H(z)$. A fair amount of attention, therefore, has been focused on the design of filter banks for reducing only alias-cancellation distortion without reconstructed-amplitude distortion. In this paper, we propose a new method for designing linear-phase p-LPF in NPR pseudo-QMF banks, which is based on Maxflat(maximally flat) FIR filters with closed-form transfer function. In addition, p-LPF H(z) is optimized in this approach so that the 2M-channel overall distortion response represented with $G(z)=H^2(z)$ approximately becomes an unit magnitude response. Through several examples of NPR pseudo-QMF banks, it is shown that the peek ripple of the overall magnitude distortion is less than $3.5{\times}10^{-4}\;({\simeq}-70dB)$ and analysis/synthesis filters have the sharp monotone-stopband attenuation exceeding 100 dB.

M채널 NPR(Near-Perfect Reconstruction) pseudo-QMF(Quadrature Mirror Filter) 뱅크의 설계는 일반적으로 SF(Spectral Factorization) 접근 방식을 혼합하여 많이 사용하며, 분리와 합성 필터들은 프로토타입 저역통과 필터(prototype lowpass filter : p-LPF)를 코사인 변조하여 사용한다. 그러나 이 방식은 $2M^{-th}$ 대역 필터 $G(z)=z^{-(N-1)}H(z^{-1})H(z)$의 SF 방식에 의해 p-LPF H(z)을 설계하기 때문에 p-LPF가 선형위상을 갖지 못할 뿐만 아니라 진폭왜곡이 최적화되지도 않았다. 따라서 대부분의 방법들이 재생 진폭왜곡 보다는 중첩상쇄왜곡을 줄이기 위한 p-LPF 설계를 제안하였다. 본 논문에서는 NPR pseudo-QMF 뱅크 구현에 필요한 p-LPF 설계를 위해 폐쇄형전달함수를 갖는 선형위상의 Maxflat(maximally flat) FIR 필터를 이용하는 새로운 방식을 제안하였다. 또한 폐쇄형주파수함수를 이용하여 $2M^{-th}$ 대역 필터 $G(z)=H^2(z)$로 표현되는 2M개 채널들의 전체진폭응답이 단일응답을 갖도록 p-LPF H(z)을 최적화하는 방법이 제안되었다. 실험 결과 시스템 최대진폭 왜곡이 $3.5{\times}10^{-4}\;({\simeq}-70dB)$보다 적고 각 분리 및 합성 필터들의 저지대역 감쇠가 -100dB 이상의 매우 뛰어난 NPR pseudo-QMF 뱅크 설계가 가능함이 증명되었다.

Keywords

References

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