補償無乘法數位濾波器有限精準度之演算法設計技巧

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姓名

李逸仙(I-Hsien Lee ) 查詢紙本館藏

畢業系所

電機工程研究所

論文名稱

補償無乘法數位濾波器有限精準度之演算法設計技巧
(Algorithm-Level Impairment Compensation Techniques for Finite-Precision Multilper-less Digital Filters)

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摘要(中)

在無乘法器數位濾波器的實現當中,符號化二進位方法及座標角度旋轉演算法被用來代替乘法的運算。然而，因為這兩種方所造成係數或角度分布不均勻的問題，使得在量化上會造成嚴重的誤差，為了克服這個問題，設計者必須使用更多的非零位元或是微旋轉去達到濾波器的規格需求，但這樣的方法卻增加了硬體實現上的複雜度。
在這篇論文當中，我們提出了改良的非相關性轉換方法和改良式角度旋轉器，這些方法提供了系統化的解決方案以避免遭遇前面所提問題。在修正的非相關性轉換方法中，我們先壓縮係數的動態範圍，再將這些經過處理的係數量化至符號化二進位方法所可以表示的位置上。與修正的非相關性轉換方法不同的是，在角度方面，我們的做法是引入數種旋轉技巧去延展可能的角度分布。這些方法減少了在達到需求規格下硬體所需要的複雜度。
在前面的討論中，我們提出了補償無乘法數位濾波器實現上缺陷的方法。事實上，我們還可以進一步的藉由用更少的硬體去重新量化濾波器的係數或角度以達到降低硬體複雜度的目的。為了系統化的達到這個目標，我們針對這些組成係數或角度的基本單元做反放置的程序。經由這種方式可以提供無乘法數位濾波器設計中對於加法器數量很好的控制能力。因此，當我們藉由結合這些技巧，我們可以利用較少的加法器達到所設定的規格。

摘要(英)

Sign-Power-of-Two (SPT) scheme and CORDIC algorithm are introduced to replace the multiplicative and rotation operation in multiplier-less filter realization. However, these approaches will make up serious quantization errors since the distribution of SPT numbers and reachable angle are very non-uniform. To facilitate these problems, the designers have to employ more nonzero digits or micro-rotations to maintain filter specification but these approaches also increase the hardware complexity of the multiplier-less filters.
In this thesis, we propose the Modified DECOR (MDECOR) transformation and the Modified Angle Rotator; they provide systematic solution in avoiding the aforementioned problem. In MDECOR transformation, we compress the dynamic range firstly, then, quantizing these processed coefficients into SPT numbers. Different from MDECOR transformation, we extend the angle constellation by introducing several rotation techniques to compensate the impairment in angle domain. Both of these approaches help to save the hardware complexity to attend the desired specification.
In the above description, we propose the ways to compensate the impairment in multiplier-less filter design. In fact, we can further reduce the cost by reconstructing filter coefficients or angles with less hardware complexity. In order to achieving this propose systematically, we apply the de-allocation procedure on the elementary terms of filter coefficients or angles. It provides good control on the number of adders employed in multiplier-less filter design. As a result, it is capable of designing filter that meet the specification with fewer adders by integrating all these techniques.

關鍵字(中)

★ 去相關性
★ 反放置
★ 座標數位旋轉器
★ 數位濾波器
★ 無乘法器
★ 符號二進位
★ 角度量化

關鍵字(英)

★ Angle Quantization
★ CORDIC
★ De-allocation
★ DECOR Transformation
★ Digital Filter
★ multiplier-less
★ SPT

論文目次

CHAPTER 1 INTRODUCTION1
1.1BACKGROUND1
1.2MOTIVATION AND OBJECTIVE3
1.3THESIS ORGANIZATION6
CHAPTER 2 IMPAIRMENT COMPENSATION OF MULTIPLIER-LESS FIR FILTER STRUCTURE7
2.1MULTIPLIER-LESS FIR FILTER STRUCTURE7
2.1.1Basic FIR Filter Structure7
2.1.2SPT Multiplier8
2.1.3Problems of SPT quantization9
2.1.4An Alternative Way10
2.2REVIEW OF DIFFERENTIAL COEFFICIENT METHOD (DCM)10
2.2.1Time-domain Representation10
2.2.2z-domain Representation13
2.3REVIEW OF DECOR TRANSFORMATION14
2.4MODIFIED DECOR (MDECOR) TRANSFORMATION15
2.4.1Motivation of MDECOR15
2.4.2Quantization Problem in DECOR Transformation16
2.4.3Modified DECOR Transformation18
2.5SUMMARY20
CHAPTER 3 IMPAIRMENT COMPENSATION OF MULTIPLIER-LESS IIR FILTER STRUCTURE21
3.1BASIC IIR FILTER STRUCTURE AND ITS PROBLEM21
3.1.1Direct Form IIR Filter21
3.1.2Finite Wordlength Effect in Direct Form IIR Filter22
3.2DIGITAL LATTICE FILTER STRUCTURE25
3.2.1Basic Lattice IIR Filter25
3.2.2Normalized Lattice IIR Filter26
3.3THE IMPLEMENTATION OF NORMALIZED LATTICE FILTER27
3.3.1Vector Rotation27
3.3.2Conventional CORDIC28
3.3.3Angle Recoding Technique28
3.3.4VLSI Structure of Each Micro-Rotation29
3.4MODIFIED ANGLE ROTATOR30
3.4.1Angle Quantization30
3.4.2Pre-Rotation Operation32
3.4.3Extend Elementary Angle Set (EEAS)33
3.4.4Modified Angle Rotator and Its Performance34
3.5DATA PATH RESCALING36
3.5.1Scaling Phase in CORDIC Algorithm36
3.5.2Signal Pre-Scaling36
3.5.3Data path Rescaling37
3.6SUMMARY37
CHAPTER 4 OPTIMIZATION OF THE PROPOSED MULTIPLIER-LESS DIGITAL FILTER39
4.1FILTER OPTIMIZATION39
4.1.1Review of Filter Optimization39
4.1.2Modification of Trellis Allocation Algorithm40
4.2REVIEW OF TRELLIS SEARCH ALGORITHM40
4.2.1Normalized Peak Ripple (NPR)40
4.2.2Trellis Allocation Strategy41
4.3MDECOR BASED TRELLIS DE-ALLOCATION ALGORITHM45
4.3.1Problems of Trellis Allocation Algorithm45
4.3.2Trellis De-allocation Algorithm46
4.4ANGLE DOMAIN DE-ALLOCATION ALGORITHM48
4.4.1Discrete Coefficient and Angle48
4.4.2Problem of Angle Optimization in Trellis (De-) allocation Algorithm48
4.4.3De-allocation Algorithm in Angle Optimization50
4.5SUMMARY51
CHAPTER 5 SIMULATION RESULT52
5.1PERFORMANCE COMPARISON OF MULTIPLIER-LESS FIR FILTER52
5.1.1Impairment Compensation by MDECOR52
5.1.2Coefficient optimization by Trellis De-allocation55
5.2PERFORMANCE COMPARISON OF MULTIPLIER-LESS IIR FILTER56
5.2.1Impairment Compensation by Proposed Angle Rotation56
5.2.2Angle Optimization by De-allocation58
CHAPTER 6 CONCLUSIONS61

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指導教授

蔡宗漢(Tsung-Han Tsai)

審核日期

2001-6-26

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