可調式一維與二維數位梳型濾波器之設計

Abstract

諧音干擾 (Harmonic Interference) 往往存在於各種信號處理的工程中；例如心電圖信號，語音信號…等等。透過梳型濾波器 (Comb Filter)，我們可以有效率的濾除這些諧音干擾。由梳型濾波器的頻率響應可知，梳型濾波器的設計重點在於分數階延遲 (Fractional Delay)濾波器。這幾年來，分數階延遲可調式 (Variable Fractional Delay) 濾波器已經有重大突破，而且受到極大的重視。本篇論文，我們將深入研究如何把分數階延遲可調式濾波應用到梳型濾波器的設計之中；如此一來，這種新架構下的梳型濾波器將具有可調性；在本論文中，我們將之命名為：梳型可調式濾波器 (Tunable Comb Filter)。此外，把梳型濾波器放在一個回授路徑之中，即可得到相對應的多重帶通濾波器 (Multi-Bandpass Filter)；結合我們所推薦的梳型可調式濾波器與這個回授路徑，則可以架構出一個多重帶通可調式濾波器 (Tunable Multi-Bandpass Filter)。 除了一維的梳型濾波器外，本論文後半段則是研究二維的梳型濾波器。本研究的目的是找出二維梳型濾波器的頻率響應。在這個問題上，我們發現許多值得且必要考量的因素，例如: 相位控制，穩定性 (Stability)…等等。我們將提出一個新的二維梳型濾波器的頻率響應。 本論文的主要創新與貢獻歸納如下: 梳型可調式濾波器、多重帶通可調式濾波器、二維梳型濾波器的頻率響應。

In many applications of signal processing, the harmonic interference rejection is required. An example is to cancel the power line interference in the electrocardiogram (ECG) signal in the biomedical area. The goal of the cancellation can be usually achieved through the use of comb filter, which is periodic with the stopband notches at 0 Hz. So far, several methods have been developed to design comb filter, and some of them are related to the design of fractional delay. As for fractional delay, the method of variable fractional delay (VFD) design has achieved a great attention due to the on-lining tuning property. In this thesis, we will propose a new approach to transform the specification of comb filter design into that of VFD design. Under this approach, the designing problem is simplified to find the optimized coefficients of some induced delay from VFD filter, and thus the designed comb filter will tend to be on-line tunable. In addition, a feed-back path containing FIR comb filter will be proposed to design multi-bandpass filter. Through the on-line tuning property of FIR comb filter, the designed multi-bandpass filter will be on-line tunable also. After the investigation of one-dimensional (1-D) comb filter, two-dimensional (2-D) comb filter is worth our while. Since only few literatures are related to 2-D comb filter, the goal in this thesis is to find the transfer function of 2-D comb filter, which is more complicated than 1-D comb filter. Through a lot of experience, it is found that some important issues are necessary to consider detail for the goal. From these considerations, finally, we will derive the transfer function of 2-D comb filter. In this thesis, the primary achievements are: the connection between comb filter and VFD filter, the design of tunable comb filter, the design of tunable multi-bandpass filter, and a closed-from of 2-D comb filter.