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研究生:張閔涵
研究生(外文):Min-Han Chang
論文名稱:可調式數位濾波器之設計
論文名稱(外文):Design of Variable Digital Filters
指導教授:徐忠枝
指導教授(外文):Jong-Jy Shyu
學位類別:碩士
校院名稱:國立高雄大學
系所名稱:電機工程學系碩士班
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2010
畢業學年度:98
語文別:英文
論文頁數:66
中文關鍵詞:可調式分數延遲濾波器可調式分數階微積分器FIR微積分器IIR微積分器權重式最小平方差逼近法Farrow架構
外文關鍵詞:Variable fractional-delay filtervariable fractional-order differintegratorFIR differintegratorIIR differintegratorweighted least-squares approachFarrow structure
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本篇論文主要在研究可調式數位濾波器之設計。近十幾年來在通訊、訊號處理、影像處理領域,可調式數位濾波器(Variable Digital Filters)都受到相當的重視與廣泛的應用。因為具有可調的參數,需要不同的響應或延遲可以立即地調控,不用再重新設計。依照可調的情況不同,我們將分為可調式分數延遲濾波器(Variable Fractional-Delay filters)與可調式分數階微積分器(Variable Fractional-Order differintegrators)二大類進行探討。我們提出了權重式最小平方差逼近法(Weighted Least-Squares Approach)來設計有限脈衝響應(Finite Impulse Response)、無限脈衝響應(Infinite Impulse Response)、全通(Allpass)濾波器。此設計不但可以達到我們預期的成果,在一定範圍內更呈現了極小的誤差。接著在可調式分數階微積分器方面,分別設計了FIR與IIR的微積分器(differintegrators)。只要調整適當的參數,即可作為微分器、積分器,甚至同時具有微分與積分的功能。更重要的是,Farrow架構(Farrow structure)已經可以成功地應用來實現上述可調式數位濾波器系統。
In this thesis, the major research is the design of variable digital filters. During the past decade, variable digital filters have received considerable attention because they were widely used in communication systems, signal processing and image processing. Different responses or delays can be immediately obtained by tuning the variable parameters without the need to design a new one. The designs of variable digital filters are often classified into two categories according to various adjustable situations, which are the variable fractional-delay (VFD) digital filters and the variable fractional-order (VFO) differintegrators. First, Weighted Least-Squares Approach (WLS) is proposed to design the FIR, IIR and Allpass variable fractional-delay filters. This method not only can achieve the desired performance but also minimize the errors in the design range. Then, the topic is focused on the variable fractional-order (VFO) differintegrators. Both FIR differintegrator and IIR differintegrator are designed. They can deal with derivatives or integrals or even compute derivatives and integrals in the same filter by simply adjusting proper parameters. Importantly, the Farrow structure has successfully been applied to implement the variable digital filter systems stated above.
Contents
Abstract (In Chinese) ………………………………………………………………………………..i
Abstract (In English) ………………………………………………………………………………..ii
Acknowledgement (In Chinese) ……………………………………………………………………iii
Contents ……………………………………………………………………………………………..iv
List of Figures .……………………………………………………………………………………...vi
Chapter 1. Introduction…………………………………………………………………………. 1
Chapter 2. Design of Variable Fractional-Delay FIR Filters ………………………………….. 2
2.1 Introduction ……………………………………………………………………………….2
2.2 Problem Formulation …………………………………………………………………….2
2.3 Using Weighted Least-Squares Approach to design VFD FIR filters …………………5
2.4 Numerical Example ………………………………………………………………………7
2.5 Conclusions ………………………………………………………………………………..9
Chapter 3. Design of Variable Fractional-Delay IIR Filters ………………………………… 10
3.1 Introduction ……………………………………………………………………………..10
3.2 Problem Formulation …………………………………………………………………..10
3.3 Using Weighted Least-Squares Approach to design VFD IIR filters ………………...12
3.4 Numerical Example ……………………………………………………………………..15
3.5 Conclusions ………………………………………………………………………………18
Chapter 4. Design of Variable Fractional-Delay Allpass Filters …………………………….. 19
4.1 Introduction ……………………………………………………………………………..19
4.2 Problem Formulation …………………………………………………………………..19
4.3 Using Weighted Least-Squares Approach to design VFD Allpass filters ……………22
4.4 Numerical Example ……………………………………………………………………..24
4.5 Conclusions ………………………………………………………………………………26
Chapter 5. Design of Variable Fractional-Order FIR Differintegrators ……………………. 27
5.1 Introduction ……………………………………………………………………………...27
5.2 Problem Formulation …………………………………………………………………...27
5.3 VFO FIR differintegrator, pure differentiator and pure integrator examples ……...33
5.4 Conclusions ………………………………………………………………………………37
Chapter 6. Design of Variable Fractional-Order IIR Differintegrators ……………………. 38
6.1 Introduction ……………………………………………………………………………….38
6.2 Problem Formulation ……………………………………………………………………..38
6.3 VFO IIR differintegrator, pure differentiator and pure integrator examples ………...45
6.4 Conclusions ………………………………………………………………………………..49
Chapter 7. Conclusions and Future works ……………………………………………………..50
Reference …………………………………………………………………………………………51
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