臺灣博碩士論文加值系統

埃根逼近法近來被廣泛地用來設計許多不同的濾波器。這個方法基本上是計算一個實數、對稱、恆正的矩陣的特徵向量而能有效地得到所需的濾波器係數。數位濾波器大致上有兩種形式：IIR(無限脈衝響應)及FIR(有限脈衝響應)。埃根逼近法目前已被用在線性相位的FIR濾波器，Hilbert轉換器，數位濾波器，及複係數FIR濾波器等的設計上。
由於IIR濾波器有極點，它的設計一般說來與FIR濾波器不同。整篇論文將著重於使用埃根逼近法來設計IIR濾波器。我們可以清楚地看見埃根逼近法在增加時域或頻域的限制上，是個非常方便的方法。
從第二章到第四章，我們簡述這個方法並將其延伸來設計有時域或頻域限制的濾波器如凹谷濾波器，Nyquist濾波器，Partial Response濾波器等等。我們也可以設計有線性限制的濾波器。在這些章節中，我們推導這些限制及濾波器轉換函數之間的關係，並且使用埃根逼近法來計算答案。在第五及第六章，我們推導埃根逼近法，並將之延伸以設計複係數及對數域IIR濾波器。在第七章，我們提出一個FIR的新架構，並將其最佳化的方法。最後在第八章，我們總結這篇論文並且提出一些未來可能的研究方向。

The eigenfilter approach is widely used to design kinds of digital filters recently. This method is based on the eigenvector computation of an appropriate symmetric, positive-definite matrix, and the solution can be found efficiently. There are two major kinds of implementation of digital filters: IIR (Infinite Impulse Response) and FIR (Finite Impulse Response). The eigenfilter approach has been used to effectively design linear phase FIR filters, FIR Hilbert transformers, and digital differentiators, and complex FIR filters.
With the existence of denominator, design of IIR digital filters is somewhat different from that of FIR filters. This dissertation is focus on digital IIR filter design based on eigenfilter approach. The effectiveness of this approach of adding time and frequency domain constraints is presented.
In chapter 2 to 4, we introduce this approach and extend it to design filters with time and frequency domain constraints such as notch filters, Nyquist filters, and partial response filters, or even the filters with linear constraints. We formulate the transfer function according to the constraints and implement the formulation with eigenfilter approach. In chapter 5 and 6, we formulate IIR complex filters and IIR log filters and apply eigenfilter approach to implement the filters. We will also present a new method to construct FIR filter with sub-filters optimally in chapter 7 and conclude this dissertation and suggest our future works in chapter 8.

CHAPTER 1 INTRODUCTION
CHAPTER 2 REVIEW OF IIR EIGENFILTER APPROACH
2.1 INTRODUCTION
2.2 DESIGN OF IIR EIGENFILTER
2.2.1 Problem Formulation
2.2.2 Iterative Phase Updating
2.2.3 Choice of the Weighting Function
2.2.4 Consideration of Filter Stability
2.2.5 Summary of Design Procedures
2.3 CONCLUSION
CHAPTER 3 DESIGN OF IIR EIGENFILTERS WITH TIME AND FREQUENCY DOMAIN CONSTRAINTS
3.1 INTRODUCTION
3.2 IIR EIGENFILTER WITH PRESCRIBED MAGNITUDE RESPONSE AND CONSTANT GROUP DELAY
3.2.1 Introduction
3.2.2 Problem Formulation
3.2.3 Experiment Examples
3.2.4 Conclusion
3.3 DESIGN OF IIR NOTCH FILTER
3.3.1 Introduction
3.3.2 Problem Formulation
3.3.3 Design Procedures and Experiment Remark
3.3.4 Experiment Examples
3.4 DESIGN OF IIR NYQUIST FILTER
3.4.1 Introduction
3.4.2 Problem Formulation
3.4.3 Design Procedures and Experiment Remark
3.4.4 Experiment Examples
3.5 DESIGN OF PARTIAL RESPONSE FILTER
3.5.1 Introduction
3.5.2 Problem Formulation
3.5.3 Design Procedures
3.5.4 Experiment Examples
3.6 CONCLUSION
CHAPTER 4 DESIGN OF IIR EIGENFILTERS WITH LINEAR CONSTRAINTS
4.1 INTRODUCTION
4.2 GENERAL PROBLEM FORMULATION
4.2.1 Formulation of General Constraint Matrix
4.2.2 General Design Procedure
4.3 DESIGN OF LOWPASS FILTER WITH MAXIMALLY FLAT CONDITION
4.3.1 Problem Formulation
4.3.2 Experiment Examples
4.3.3 Conclusion
4.4 DESIGN OF DIFFERENTIATOR WITH LINEAR CONSTRAINTS
4.4.1 Problem Formulation
4.4.2 Experiment Examples
4.4.3 Conclusion
4.5 CONCLUSION
CHAPTER 5 DESIGN OF IIR COMPLEX EIGENFILTERS
5.1 INTRODUCTION
5.2 DESIGN FORMULATION OF COMPLEX FILTERS
5.3 DESIGN REMARKS
5.4 EXPERIMENT EXAMPLES
5.5 CONCLUSION
CHAPTER 6 DESIGN OF IIR LOG EIGENFILTERS
6.1 INTRODUCTION
6.2 DESIGN FORMULATION OF LOG FILTERS
6.2.1 Problem Formulation
6.2.2 Design Remarks
6.2.3 Experiment Examples
6.3 DESIGN OF COMPLEX LOG FILTERS
6.3.1 Problem Formulation
6.3.2 Experiment Examples
6.4 CONCLUSION
CHAPTER 7 DESIGN OF FIR FILTERS WITH ARBITRARY BUILDING BLOCKS
7.1 INTRODUCTION
7.2 ORTHOGONALITY PRINCIPLE ON FIR FILTER DESIGN
7.3 DESIGN FORMULATION
7.4 EXPERIMENT EXAMPLES
7.5 CONCLUSION
CHAPTER 8 CONCLUSION AND FUTURE WORKS
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