臺灣博碩士論文加值系統

分數延遲濾波器在訊號處理領域上有許多的應用，如通訊、語音訊號處理等等。利用複頻訊號處理技巧可以簡單地設計此分數延遲濾波器，在本論文中，我們討論二種已存在的方法，為多重相位分解和IFIR，以及提出一個新的方法是減點與內插濾波器的串聯，這所提出的方法是被建立在一般複頻技術的使用於分數延遲濾波器和減點與內插濾波器串聯的架構上，這提出的方法能被有效地實現在複頻系統裡而且也可以化簡成一個單一的FIR 分數延遲濾波器，且這個單一非時變的FIR 分數延遲濾波器有最寬廣的頻寬在群延遲裡。然而在減點與內插濾波器串聯的架構中，我們也利用一方法可以找出最佳的減點與內插因子，使得此架構總和的濾波器階數與運算複雜度為最低。

A fractional delay filter (FDF) has many applications in signal processing, such as communications, speech signal processing, etc. It can be designed simply by using multirate signal processing technique. In this thesis, we discussed two existed methods, polyphase decomposition and IFIR, and proposed a new method that is by cascading decimation and interpolation. The proposed method is based on the use of the general multirate technique for FDF and cascade of decimation and interpolation structure. The proposed method can be implemented efficiently in multirate system and also reduce it into one single FIR fractional delay filter and it has the widest group delay bandwidth. Thus, in cascading of decimation and interpolation structure, we also use a method to find the optimal decimator and expander factors that have the total filter order and complexity are minimum in this structure.

CHINESE ABSTRACT...............I
ENGLISH ABSTRACT...............II
ACKNOWLEDGEMENT................III
CONTENTS.......................IV
LIST OF FIGURES................VI
LIST OF TABLES.................XII

Page
CHAPTER 1 INTRODUCTION........................................................1

CHAPTER 2 FUNDAMENTALS OF MULTIRATE SYSTEMS.........................3
2.1 Introduction....................................................3
2.2 Basic Concepts of Multirate Systems.............................3
2.2.1 Decimation and interpolation..............................3
2.2.2 Transform domain analysis of decimators and expanders.....6
2.2.3 Decimation filter and interpolation filter................8
2.3 Useful Identities in Multirate Systems..........................9
2.3.1 Decimator and expander........................................9
2.3.2 Decimator and expander cascade...............................15
2.4 Polyphase......................................................17
2.4.1 Efficient structures for decimation and interpolation
filters..................................................19
2.4.1.1 Decimation filters....................................19
2.4.1.2 Interpolation filters.................................21
2.4.2 The polyphase identity...................................22
CHAPTER 3 INTERPOLATED FIR (IFIR) FILTERS DESIGN...................24
3.1 Introduction.................................................24
3.2 The Interpolated FIR (IFIR) Approach.........................24
3.2.1 The Principle of interpolated FIR (IFIR) filters.........25
3.2.2 Some important properties of IFIR........................29
3.2.2.1 Terminologies of IFIR filters.........................30
3.2.2.2 Passband ripple sizes considerations..................31
3.2.2.3 Tradeoff problem and some condition of IFIR technique.31
3.2.3 Design of IFIR technique for lowpass filter..............33
3.3 Multistage of IFIR technique Implementations...................36
3.3.1 Multistage design of interpolation and decimation
filters..................................................37
3.3.1.1 Multistage design of Interpolation filters............37
3.4 On Optimal IFIR Filter Design..................................44
3.4.1 The principle and design of Optimal IFIR filter..........44

CHAPTER 4 DESIGN of FRACTIONAL DELAY FILTER........................47
4.1 Introduction...................................................47
4.2 Principles of Fractional Delay Filters (FDF)...................47
4.2.1 Ideal solution...............................................50
4.3 Basic Concepts and Structure for Fractional Delay Filter by
Using Multirate techniques...................................52
4.3.1 Consideration of lowpass filter design...................55
4.4 Efficient Design of Fractional Delay filter on Multirate
techniques...................................................60
4.4.1 Polyphase method.........................................61
4.4.2 IFIR method..............................................66
4.4.3 Cascade of decimation and interpolation (CDI) method.....68
4.4.3.1 Lowpass Filter Requirements for One and Two-Stages....73
4.4.4 Considerations of computational complexity...............74
4.4.4.1 Analytic of complexity for the required Filter Order..74
4.4.4.2 Analytic of complexity for the filter operations
per second............................................75
4.4.4.3 Analytic of complexity for the storage requirements...76
4.4.4.4 A design example......................................76
4.4.5 Optimal design for one and two stage CDI structure.......80
4.4.5.1 Comparison of one-stage and two-stage CDI structure...87
4.4.6 Design of fractional delay filter using the CDI method...91
4.4.6.1 Single FIR fractional delay filter design............100
4.4.7 Complexity comparison the CDI method with other methods.104

CHAPTER 5 CONCLUSIONS.............................................111

REFERENCES........................................................113

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