臺灣博碩士論文加值系統

分數延遲濾波器是一種在不改變取樣頻率下，使輸入的離散訊號
產生非整數延遲的一種裝置，許多領域需運用到這樣的功能，如通
訊、語音訊號處理等等。在本篇論文中，我們從新探討了如何以FIR
的設計技巧來近似部分延遲濾波器，而近似的技巧是以多項式為基礎
的內插法。我們所使用的多項式為基礎的內插法，是線性、三次方
Lagrange 和變參數三次方內插法。而且我們還提出了一個技巧反轉
分數延遲濾波器的處理過程。我們稱為回解器。最後，我們將此分數
延遲濾波器和回解器應用在浮水印。

Fractional delay filter is a device that delays the discrete-time input signal in a noninteger sampling interval, when the sampling rate is unchanged. It finds applications in numerous fields of signal processing, including communications, speech processing, and so on. In this thesis, we present a review of FIR filter design techniques for bandlimited approximation of a fractional delay filter, and this technique is based on polynomial-based interpolations. The polynomial-based interpolation methods we used are linear interpolation, cubic Lagrange interpolation and variable parameter cubic interpolation. And we also proposed a technique to invert the process of the fractional delay filter. We call it "deconvolver." Finally, we use this fractional delay filter and deconvolver to implement watermarking.

CONTENTS
ABSTRACT (in Chinese)………………………………………………V
ABSTRACT (in English)……………………………………………VI
ACKNOWLEDGEMENT……………………………………………VII
CONTENTS…………………………………………………………VIII
LIST OF FIGURES…………………………………………………XI
LIST OF TABLES…………………………………………………XIV
Page
CHAPTER 1 INTRODUCTION……………………………………1
CHAPTER 2 POLYNOMIAL-BASED FD FILTER…………………3
2.1 Preliminaries………………………………………………………3
2.1.1 Notation and concepts………………………………………3
2.1.2 Ideal solution…………………………………………………6
2.1.3 Least squared integral error
design……………………………8
2.1.4 General least squares FIR approximation of a complex
frequency response……………………………………………11
2.2 Farrow Structure For Fractional Delay FIR
Filters……………….15
2.2.1 Introduction of the Farrow
structure…………………………15
2.2.2 Coefficients computation of the Farrow
structure…………16
2.2.3 Discussion……………………………………………………19
2.3 FD Filter Implementation By Using Lagrange Interpolation
(Maximally Flat FD FIR Filter)…………………………………20
2.3.1 Lagrange interpolation for fractional delay approximation
(maximally flat FD FIR filter)…………………………………..20
2.3.2 The Farrow structure of Lagrange FD filter…………………23
2.3.2.1 Corresponding to linear interpolation…………………..25
2.3.2.2 The cubic Lagrange interpolation………………………27
2.3.2.3 The variable parameter cubic interpolation………… …30
2.4 Summary of Polynomial-based FD Filters……………………….35
CHAPTER 3 A MICROPROCESSOR-BASED DECONVOLVER..36
3.1 Thoughts On The Inverting Process Of The Fractional
Delay Filter……………………………………………………36
3.2 Calculation Of The Fractional Delay d(n) By
Using A Mathematical Procedure………………………………39
3.3 Some Examples Of The Internal Operations Of
Microprocessor-based Deconvolvers……………………………42
3.4 The Polynomial Approximation Technique For The Impulse
Response hd(n) Of The Fractional Delay Filter………45
3.5 Simulation Of The Inverting Process Of The General
Fractional Delay Filter…………………………………………47
3.6 Summary Of Microprocessor-based Deconvolver………………52
CHAPTER 4 A WATERMARKING TECHNIQUE BASED
ON FRACTIONAL DELAY FILTERS AND
DECONVOLVERS……………………………………53
4.1 Introduction Of Watermarking……………………………………53
4.2 Implementation Of Watermarking By Using Fractional
Delay Filters………………………………………………………54
4.2.1 Proposed watermarking approaches…………………………55
4.2.1.1 Watermarking embedding method………………………55
4.2.1.2 Watermarking extracting method………………………56
4.2.2 Simulation results……………………………………………57
4.3 Discussion………………………………………………………66
CHAPTER 5 CONCLUSIONS………………………………………67
REFERENCE…………………………………………………………69

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