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研究生:黃筱寧
研究生(外文):Hsiao-Ning Huang
論文名稱:高超取樣率及可變中心頻率之差和濾波器設計
論文名稱(外文):A HIGH OSR VARIABLE CENTER FREQUENCY DELTA-SIGMA MODULATOR
指導教授:劉皆成
學位類別:碩士
校院名稱:大同大學
系所名稱:通訊工程研究所
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:2006
畢業學年度:94
語文別:英文
論文頁數:120
中文關鍵詞:差和濾波器
外文關鍵詞:delta-sigma modulator
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雖然存在於真實世界的都是類比訊號,但這些訊號常常被希望以類比數位轉換器(ADC)轉換成數位訊號的形式。這是因為有一些處理程序只能在數位域被穩定執行。爲了達到這個目標,差積調變器這項技術因為具有高解析力而變的十分受歡迎。
傳統上,多重中心頻率的結合可以使用改變梳型濾波器(COMB FILTER)的級數來達到。但是目前情況下,梳型濾波的級數必需都是整數值,這條件導致一個限制產生:「並非任意位置的中心頻率都是可達到的」。因此在這裡我們用一種數位訊號處理所提出的方法來克服這個問題:「植入近似分數延遲濾波器來大約代表差積調變器內的分數延遲」。我們將分別使用 FIR和IIR的方法作為表示分數延遲濾波器的工具。如此一來,多頻帶差積調變器的雜訊塑型頻譜的中心頻率便可以位在任何你想要的地方,且此種調變器適用於多重音調訊號(MULTIPLE TONE SIGNAL)的類比轉數位過程。
除此之外,這種方法被引入多種分別具有不同優點的差積調變器架構以供選擇最適合設計需求的架構並證明該法可行性。
Although real world signals are analog, it is often desirable to convert them into the digital domain using an analog to digital converter (ADC). Some processing is only feasible in the digital domain such as intricate processing of the signal. In order to achieving the goal, one technique, delta-sigma modulator, has become quite-popular for high resolution.
Traditionally, many combinations of multiple center frequencies can be obtained by varying the order of the comb filters. However, the realistic fact that the comb filter order must be an integer value imposes a restriction in that not all center frequencies are attainable. The limitation can be overcome by another proposed DSP skill: embedding fractional delay filter to approximate the fractional delay within the modulator. We will use individual FIR and IIR methods to be a tool to represent approximation fractional delayer combined in the delta-sigma modulator. Thus Multi-band delta-sigma modulators whose noise-shaping spectrum center frequency can be located anywhere you want may be well suited for the simultaneous analog-to-digital conversion of multiple-tone signals.
Furthermore, the method demonstrates that the use of several kinds of delta-sigma modulator structures to choose the most suitable one to satisfy your design needs, and to prove the probability of the method.
ENGLISH ABSTRACT ………………………………………………………….…i
CHINESE ABSTRACT……………………………………………………………..ii
致謝………………………...………………………………………………………...iii
TABLE OF CONTENTS……………………………………………………………iv
LIST OF FIGURES………………………………………………………………....ix
LIST OF TABLES………………………………………………………………….xvi
CHAPTER
I INTRODUCTION ……………………………………………………….1
1.1 Motivation……………………………………………………………1
II METHODS APPROXIMATING FRACTIONAL DELAYER………..4
2.1 Overview……………………………………………………………..4
2.2 Preliminaries…………………………………………………………5
2.3 Fractional Delay Approximation Using FIR Filter………………….9
2.3.1 Maximally Flat FIR Fractional Delay Filter Design:
Lagrange Interpolation………………………………………10
2.3.2 Least Squared Error Solutions for FIR Filters……….14
2.3.3 Minimax Design of FIR Fractional Dela Filters…………...19
2.3.4 Summary of FIR Filter Design and Implementation……….. 27
2.4 Fractional Delay Approximation Using All-Pass Filters…………27
2.4.1 Maximally Flat Group Delay Design of All-Pass Filter……31
2.4.2 Least Squared Design of All-Pass Filters…………………..34
2.4.3 Equiripple Phase Error Design of All-Pass Filters… ……39
2.4.4 Summary of All-Pass Fractional Delay Filters……….43
III ANALOG TO DIGITAL (A/D) CONVERSION…………………...…44
3.1 Pulse Code Modulation (PCM) A/D Conversion…………………44
3.1.1 Nyquist Rate Conversion…………………………………..44
3.1.2 Sampling…………………………………………………...44
3.1.3 Quantization………………………………………………..46
3.1.4 Trading Resolution for Bandwidth…………………………47
3.1.5 Performance Modeling……………………………………..48
3.1.6 Limitation of Nyquist rate A/D Converters………………...50
3.2 Over-Sampled PCM Conversions………………………………...51
3.2.1 System Description………………… 51
3.2.2 Performance Modeling for Over-Sampled
PCM Converter..53
3.2.3 Performance Modeling for Discrete-Time Band-pass Over-
Sampled Delta-Sigma Modulation…………………...56

IV OVER-SAMPLED DELTA-SIGMA MODULATOR FOR A/D (ANALOG TO DIGITAL)
CONVERSION…………………………...59
4.1: Director Delta-Sigma Modulation A/D Conversion (Single-Band)
………………………………………..59
4.1.1 Single Use of Delta-Sigma Modulator NTF with a Fractional
Delay Order D (c=-1)………………………..60
4.1.2 Operation and Performance Modeling ……………..60
4.1.3 Preliminary Analysis ……………….66
4.1.4 FIR Fractional Delay Case………… ……………70
4.1.5 All-Pass Fractional Delay Case…………….72
4.1.6 Simulation Results………………………….……73
4.2: Noise-Shaping in Fractional Delay Filter Approach (Extended to
Multi-Band)……………………………………………………75
4.2.1 Fractional Delay and Simulation Result(c=+/-1)
………77
4.3: Delta-Sigma Modulator with Multiple Use of the NTF=(1+cz-D)
…………………………………………………………………………82
4.3.1: Delta-Sigma Modulator with Multiple Use of
Fractional Order of D of Noise Transfer
Function………………...83
4.3.2: Operation and Performance Modeling…….84
4.3.3: Fractional Delay Filters and Simulation
Result………..88
4.4: Other Types of Higher stages Delta-Sigma modulator………..91
4.4.1:Multi-Bit Delta-Sigma Modulator……………………..92
4.4.1.1 N-Bit Delta-Sigma Modulator …………92
4.4.1.2 Simulation Result…………………………….93
4.4.2:Multi-Stage (Cascade) Delta-Sigma Modulation ……...96
4.4.2.1 Cascade Delta-Sigma Modulator ……………96
4.4.2.2 Simulation Result ……………………………..99
4.4.3:Multi-Rate (Time-Interleaved) Delta-Sigma
Modulation ………………………………..101
4.4.3.1 Time-Interleaved Modulator (TIM) …102
4.4.3.2 Simulation Result……………………104
4.4.4: Multi-Path Multi-Rate Delta-Sigma Modulator……….107
4.4.4.1 N-Path Multi-Rate Delta-Sigma Modulator
Model ………………………108
4.4.4.2 Simulation Result…………………110
V CONCLUSION AND FUTURE WORK………………………………112
5.1: Conclusion…………………………………………………………112
5.2: Future Work………………………………………………………..120
REFERENCES……………………………………………………………………121
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