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

The Korean Institute of Commucations and Information Sciences (한국통신학회)
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A New Closed-form Transfer Fuction for the Design of Wideband Lowpass MAXFLAT FIR filters with Zero Phase

제로 위상을 갖는 광대역 저역통과 MAXFLAT FIR 필터 설계를 위한 새로운 폐쇄형 전달 함수

  • 전준현 (동국대학교 정보산업대학 정보통신공학과)
  • Published : 2007.07.31
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Abstract

In general, the earlier linear-phase MAXFLAT(maximally flat) lowpass FIR filters have the main disadvantage of a gain response in the half frequency band $(0{\leq}w{\leq}{\pi}/2)$ by the closed form transfer functions used in design techniques for realizing them. Moreover, most of them has existent problems as follows : ripple error in the stopband, gentle-cutoff attenuation, phase and group delay and inexact cutoff frequency response. It is due to the approximation algorithms such as Chebyshev norm and Remez exchange which are used to approach MAXFLAT and linear-phase characteristics in frequency domain. In this paper, a new mathematically closed-form transfer function is introduced for the design of MAXFLAT lowpass FIR filters which have the zero-phase and wideband-gain response. In addition, we verify that the closed-form transfer function is easily realized due to our generalized formulas derived newly by using MAXFLAT conditions including an arbitrary cutoff point. This method is, therefore, useful for "simple and quick designs". Conclusively, we propose a technique for the design of new zero-phase wideband MAXFLAT lowpass FIR filters which can achieve sharp-cutoff attenuation exceeding 250 dB almost everywhere.

일반적으로 기존의 선형 위상을 갖는 저역통과 MAXFLAT FIR 필터 설계 방법들은 폐쇄형 전달함수의 특성으로 인하여 하프 주파수 대역 $(0{\leq}w{\leq}{\pi}/2)$에서 이득 응답을 갖는다. 더욱이 주파수 영역에서 MAXFLAT과 선형 위상 특성에 도달하기 위해 추정 알고리즘을 사용하기 때문에 설계 필터들은 저지대역에서의 리플 에러, 완만한 차단감쇠, 위상 및 그룹지연 그리고 부정확한 차단주파수와 같은 문제점들을 가지고 있다. 본 논문에서는 이러한 문제점들을 해결하기 위하여 제로 위상의 광대역 이득 응답을 갖는 MAXFLAT FIR 저역통과 필터 설계를 위한 새로운 수학적인 폐쇄형 전달함수를 제안하였다. 더욱이, 제안된 폐쇄형 전달함수는 임의의 차단 주파수를 포함한 MAXFLAT 조건들을 이용하여 새롭게 유도한 일반화한 공식들로 쉽게 실현됨이 증명되었다. 따라서 제안방식은 간단하고 빠른 설계에 적합하다. 결론적으로 제안된 설계 기술은 제로 위상과 광대역 이득 응답을 갖는 MAXFLAT FIR 저역통과 필터 실현이 가능하며, 설계된 필터들은 모두 250dB가 넘는 최대 차단 감쇠를 갖는 것을 알 수가 있다.

Keywords

References

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