Digital filters: theory, application and design of modern filters
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| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
Weinheim
Wiley-VCH
2012
|
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XI, 359 S. Ill., graph. Darst. |
| ISBN: | 9783527411481 3527411488 |
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Record in the Search Index
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IMAGE 1
V
CONTENTS
1 BACKGROUND AND INTRODUCTION 1
1.1 INTRODUCTION 1
1.2 HOW IS DIGITAL PROCESSING DONE? 2
1.3 WHAT IS FILTERING? 3
1.3.1 INTERSYMBOL INTERFERENCE 4 1.3.2 NOISE 4
1.4 LINEAR FILTERS 6
1.4.1 THE FIR FILTER 6
1.4.2 THE IIR FILTER 7
1.4.3 HOW AND WHERE FILTERS OPERATE 8 1.5 MULTIRATE FILTERS 8
1.5.1 ALTERING THE SAMPLING RATE BY A FRACTION 10 1.5.2 SUBBAND
DECOMPOSITION 11 1.6 A CLASSICAL FILTERING MODEL 12
1.7 AN OPTIMUM SOLUTION TO THE CLASSICAL PROBLEM 14 1.7.1 IMPROVING THE
OPTIMUM FILTER 15 1.8 CLASSES OF APPLICATIONS OF ADAPTIVE FILTERS 16
1.8.1 SYSTEM IDENTIFICATION 17 1.8.2 INVERSE MODELING 17
1.8.3 PREDICTION MODELING 17 1.8.4 INTERFERENCE CANCELING 17 1.9 CHAPTER
SUMMARY 18
2 DISCRETE TIME SIGNALS AND SYSTEMS 19
2.1 INTRODUCTION 19
2.1.1 DISCRETE TIME SIGNALS 19 2.2 OPERATIONS ON SIGNALS 22
2.3 SYMMETRY IN SIGNALS 27
2.3.1 ODD AND EVEN SEQUENCES 27
2.3.2 CONJUGATE SYMMETRIC AND CONJUGATE ANTISYMMETRIC SEQUENCES 28 2.4
ENERGY AND POWER SIGNALS 29
2.5 THE CONCEPT OF FREQUENCY IN DISCRETE TIME SYSTEMS 30 2.6 DISCRETE
TIME SYSTEMS 34
HTTP://D-NB.INFO/1017775443
IMAGE 2
V I CONTENTS
2.6.1 STATIC VERSUS DYNAMIC 35
2.6.2 TIME VARIANT VERSUS TIME INVARIANT 35 2.6.3 LINEAR VERSUS
NONLINEAR 36 2.6.4 CAUSAL VERSUS NONCAUSAL 37 2.6.5 STABLE VERSUS
NONSTABLE 38 2.7 ANALYSIS OF SHIFT-INVARIANT LINEAR SYSTEM 39
2.7.1 INPUT SEQUENCE AS A SUM OF SHIFTED WEIGHTED IMPULSES 39 2.7.2
RESPONSE TO A LINEAR SHIFT INVARIANT SYSTEM 40 2.8 THE CONVOLUTION SUM
41
2.8.1 PROPERTIES OF CONVOLUTION 41 2.8.1.1 COMMUTATIVE LAW 42 2.8.1.2
ASSOCIATIVE LAW 43 2.8.1.3 DISTRIBUTIVE LAW 43
2.9 SYSTEMS DESCRIBED BY DIFFERENCE EQUATIONS 44 2.9.1 SYSTEMS DESCRIBED
BY CONSTANT COEFFICIENT DIFFERENCE EQUATION 45 2.9.2 SOLUTION OF LINEAR
CONSTANT COEFFICIENT DIFFERENCE EQUATION 47 2.9.3 THE ZERO INPUT
RESPONSE 47
2.9.4 THE ZERO STATE RESPONSE 48
2.9.5 COMPLETE SOLUTION OF THE DIFFERENCE EQUATION 48 2.10 IMPULSE
RESPONSE TO A SYSTEM 51
2.11 EXAMPLES OF SOME DISCRETE TIME SYSTEMS 53 2.11.1 THE ACCUMULATOR 53
2.11.2 THE MOVING AVERAGE FILTER 53
2.11.3 MEDIAN FILTER 55
2.11.4 LINEAR INTERPOLATOR 56 2.12 CHAPTER SUMMARY 57
3 DISCRETE TIME SYSTEMS IN THE FREQUENCY DOMAIN 59 3.1 INTRODUCTION 59
3.2 CONTINUOUS TIME FOURIER TRANSFORM 59 3.2.1 DEFINITION O F THE
FOURIER TRANSFORM 60 3.3 SAMPLING AN ANALOG SIGNAL 63
3.4 DISCRETE TIME FOURIER TRANSFORM 62
3.4.1 DEFINITION OF THE DISCRETE TIME FOURIER TRANSFORM 62 3.4.2
PROPERTIES OF THE DTFT 64
3.4.2.1 LINEARITY 65
3.4.2.2 TIME REVERSAL 65 3.4.2.3 SHIFT IN THE TIME DOMAIN 66 3.4.2.4
SHIFT IN THE FREQUENCY DOMAIN 68 3.4.2.5 MULTIPLICATION BY A LINEAR RAMP
68
3.4.2.6 CONVOLUTION IN THE TIME DOMAIN 69 3.4.2.7 PARSEVAL'S RELATION 71
3.5 SAMPLING A CONTINUOUS TIME SIGNAL 71 3.5.1 NYQUIST SAMPLING THEOREM
72 3.5.2 RECONSTRUCTION OF THE SAMPLED SIGNAL 78
IMAGE 3
CONTENTS V I I
3.6 DISCRETE FOURIER TRANSFORM 80
3.6.1 DEFINITION 81
3.6.1.1 COMPUTING THE DFT FROM THE DEFINITION 84 3.6.2 RELATION BETWEEN
THE DTFT AND THE DFT 86 3.6.3 RELATION BETWEEN THE FOURIER TRANSFORM AND
THE DFT 88 3.7 PROPERTIES OF THE DFT 89
3.7.1 CIRCULAR SHIFT 89
3.7.2 SYMMETRY RELATIONS IN THE DFT 91 3.7.2.1 REAL AND IMAGINARY PARTS
OF THE DFT 91 3.7.2.2 DFT OF THE CONJUGATE OF X[N] 92 3.7.2.3 DFT OF THE
TIME-REVERSED SEQUENCE 92 3.7.2.4 DFT OF THE REAL AND THE IMAGINARY
PARTS OF THE SEQUENCE X[N] 92 3.7.2.5 DFT OF THE CONJUGATE SYMMETRIC AND
THE CONJUGATE ANTISYMMETRIC
PART OF THE SEQUENCE X{N] 92 3.8 THEOREMS OF THE DFT 93
3.8.1 THE DFT IS A LINEAR TRANSFORM 93 3.8.2 THE DFT OF A CIRCULAR SHIFT
IN TIME 94 3.8.3 THE IDFT OF A CIRCULAR SHIFT IN FREQUENCY 94 3.8.4
CIRCULAR CONVOLUTION 95 3.8.5 LINEAR CONVOLUTION USING THE CIRCULAR
CONVOLUTION 98 3.9 DFT OF REAL SEQUENCES 100
3.9.1 DFT OF A 2N POINT REAL SEQUENCE USING N POINT DFT 100 3.9.2 TWO N
POINT DFT OF REAL SEQUENCES USING A SINGLE N POINT DFT 101 3.10
CONVOLUTION OF VERY LONG SEQUENCES 102 3.10.1 OVERLAP AND ADD METHOD 102
3.10.2 OVERLAP AND SAVE METHOD 103 3.11 CHAPTER SUMMARY 107
4 THE Z-TRANSFORM 109
4.1 INTRODUCTION 109
4.2 DEFINITION OF THE Z-TRANSFORM 109
4.2.1 THE IMPORTANCE OF THE REGION OF CONVERGENCE 110 4.2.2 REGION OF
CONVERGENCE OF LEFT-AND RIGHT-SIDED SEQUENCES 112 4.3 THE INVERSE
Z-TRANSFORM 115
4.3.1 THE CAUCHY INTEGRAL THEOREM 115 4.3.2 PARTIAL FRACTION EXPANSION
117 4.3.2.1 COMPUTING RESIDUES USING MATLAB 121 4.3.3 LONG DIVISION 122
4.4 THEOREMS AND PROPERTIES OF THE Z-TRANSFORM 1 23 4.4.1 THE REGION OF
CONVERGENCE 124 4.4.2 LINEARITY 125
4.4.3 SHIFT IN THE TIME DOMAIN 126
4.4.4 SCALING IN THE FREQUENCY DOMAIN 126 4.4.5 CONJUGATION O F A
COMPLEX SEQUENCE 126 4.4.6 DIFFERENTIATION IN THE Z-DOMAIN 127
IMAGE 4
V I I I CONTENTS
4.4.7 CONVOLUTION OF TWO TIME DOMAIN SEQUENCES 127
4.4.8 SUMMARY OF Z-TRANSFORM THEOREMS AND PROPERTIES 128 4.5 APPLICATION
OF Z-TRANSFORMS TO SYSTEMS 129 4.6 RESPONSES TO TYPICAL POLE-ZERO
PATTERNS 130 4.6.1 FIRST-ORDER POLES 130
4.6.2 THE SECOND-ORDER POLES 130 4.7 INTRODUCTION TO TWO-DIMENSIONAL
Z-TRANSFORM 134 4.8 CHAPTER SUMMARY 135
4.8.1 DEFINITION O F Z-TRANSFORM 135 4.8.2 INVERSE OF THE Z-TRANSFORM J
35 4.8.3 THEOREMS AND PROPERTIES OF THE Z-TRANSFORM 136 4.8.4
APPLICATION OF Z-TRANSFORMS TO SYSTEMS 136
4.8.5 RESPONSES TO TYPICAL POLE-ZERO PATTERNS OF SYSTEMS 136 4.8.6
INTRODUCTION TO TWO-DIMENSIONAL Z-TRANSFORM 136
5 DISCRETE FILTER DESIGN TECHNIQUES 137
5.1 INTRODUCTION 137
5.2 DESIGN OF ANALOG FILTERS: A REVIEW 138 5.2.1 FILTER SPECIFICATIONS
138 5.2.2 THE BUTTERWORTH APPROXIMATION 140 5.2.3 THE CHEBYSHEV TYPE 1
APPROXIMATION 142 5.2.4 THE CHEBYSHEV TYPE 2 APPROXIMATION 143 5.2.5
SCALING THE FILTERS 144
5.2.6 TRANSFORMING FILTERS 146 5.3 DESIGN OF IIR FILTERS FROM ANALOG
FILTERS 150 5.3.1 IMPULSE INVARIANCE METHOD 151 5.3.2 BILINEAR TRANSFORM
METHOD 153 5.3.3 FREQUENCY TRANSFORMATIONS OF IIR DISCRETE FILTERS 159
5.4 DESIGN OF FIR FILTERS 163
5.4.1 LINEAR PHASE TRANSFER FUNCTIONS 164 5.4.2 REQUIREMENTS OF A LINEAR
PHASE TRANSFER FUNCTION 165 5.4.3 DESIGN OF FIR FILTERS USING WINDOWS
166 5.4.4 DESIGN OF FILTERS USING FREQUENCY SAMPLING 175 5.4.5 A
COMPARISON OF THE FIR AND THE IIR FILTERS 178 5.5 DESIGN OF WINDOWS 179
5.6 FIR FILTER DESIGN USING OPTIMIZATION TECHNIQUES 182 5.7 CHAPTER
SUMMARY 185
6 COMPUTING THE DFT 187
6.1 INTRODUCTION 187
6.2 DIRECT COMPUTATION OF THE DFT 188
6.3 THE GOERTZEL ALGORITHM 190
6.4 DECIMATION IN TIME ALGORITHM 191
6.5 DECIMATION IN FREQUENCY ALGORITHM 197 6.6 ALGORITHM WHEN N IS A
COMPOSITE NUMBER 202
IMAGE 5
CONTENTS I X
6.7 COMPUTING THE FFT OF ONLY A FEW SAMPLES 204
6.8 THE CHIRP Z-ALGORITHM 207
6.9 CHAPTER SUMMARY 213
7 MULT IRATE SIGNAL PROCESSING AND DEVICES 215 7.1 INTRODUCTION 215
7.2 TIME DOMAIN CHARACTERISTICS OF THE SAMPLING RATE ALTERATION DEVICES
216 7.2.1 THE UPSAMPLER 216
7.2.2 THE DOWNSAMPLER 217
7.3 FREQUENCY DOMAIN CHARACTERISTICS OF THE SAMPLING RATE ALTERATION
DEVICES 219 7.3.1 THE UPSAMPLER 219
7.3.2 THE DOWNSAMPLER 220
7.3.3 THE UPSAMPLER-DOWNSAMPLER CASCADE ARRANGEMENT 223 7.3.4 THE NOBLE
IDENTITIES 225
7.4 BASIC SAMPLING RATE CONVERTERS 227 7.4.1 INPUT-OUTPUT RELATIONS OF A
FRACTION RATE STRUCTURE 228 7.4.2 MULTISTAGE DESIGN OF FRACTION RATE
CONVERTER 229 7.4.2.1 SINGLE-STAGE DESIGN 230 7.4.2.2 MULTISTAGE DESIGN
231 7.4.3 APPLICATION OF SAMPLING RATE CONVERTER 233 7.5 POLYPHASE
DECOMPOSITION 234
7.6 COMPUTATIONALLY EFFICIENT INTERPOLATOR AND DECIMATOR 236 7.6.1
COMPUTATIONALLY EFFICIENT FRACTION RATE CONVERTERS 238 7.6.2 BUILDING AN
EFFICIENT FRACTION RATE CONVERTER 240 7.7 HALF BAND AND NYQUIST FILTERS
243
7.7.1 DESIGN OF LINEAR PHASE L-BAND FILTERS 245 7.8 CHAPTER SUMMARY 245
8 INTRODUCTION TO STOCHASTIC PROCESSES 247
8.1 INTRODUCTION 247
8.2 TYPES OF RANDOM VARIABLES, EXPECTED VALUE, AND MOMENTS 248 8.2.1
CONTINUOUS RANDOM VARIABLES 248 8.2.2 DISCRETE RANDOM VARIABLES 248
8.2.3 MIXED RANDOM VARIABLES 249 8.2.4 EXPECTED VALUE OPERATOR 249 8.2.5
VARIANCE 250
8.3 CORRELATION AND COVARIANCE 251
8.3.1 CORRELATION 251
8.3.2 COVARIANCE 252
8.3.3 CORRELATION MATRIX 253 8.3.4 COMPLEX VALUED RANDOM EXPERIMENTS 254
8.4 THE NOTION OF THE STOCHASTIC PROCESS 254 8.4.1 THE MEAN VALUE 256
IMAGE 6
X CONTENTS
8.4.2 THE AUTOCORRELATION 256
8.4.3 PROPERTIES O F AUTOCORRELATION 257 8.4.4 THE AUTOCOVARIANCE 257
8.4.5 STATIONARY PROCESS 258
8.4.6 ERGODIC PROCESS 259
8.4.7 POWER SPECTRUM DENSITY 259 8.4.8 PROPERTIES O F THE POWER SPECTRUM
DENSITY 259 8.5 THE CORRELATION MATRIX 260
8.6 WHITE NOISE PROCESS 263
8.7 STOCHASTIC PROCESS THROUGH A LINEAR SHIFT-INVARIANT FILTER 263 8.8
STOCHASTIC MODELS 266
8.8.1 THE AUTOREGRESSIVE MODEL 267 8.8.2 THE MOVING AVERAGE MODEL 268
8.8.3 THE AUTOREGRESSIVE MOVING AVERAGE PROCESS 269 8.8.4 CORRELATION
FUNCTION OF A STATIONARY AR PROCESS 270 8.8.5 YULE-WALKER EQUATIONS 271
8.8.6 RELATION BETWEEN THE FILTER PARAMETERS AND THE
AUTOCORRELATION SEQUENCE 272 8.9 CHAPTER SUMMARY 273
9 WEINER FILTERS 276
9.1 INTRODUCTION 276
9.2 THE PRINCIPLE OF ORTHOGONALITY 276
9.3 WEINER-HOPF EQUATIONS 279
9.4 SOLUTION OF THE WEINER-HOPF EQUATIONS IN THE TIME DOMAIN 280 9.4.1
ERROR PERFORMANCE SURFACE 281 9.4.2 MINIMUM MEAN SQUARE ERROR 283 9.5
SOLUTION OF THE WEINER-HOPF EQUATIONS IN THE FREQUENCY DOMAIN 284 9.5.1
INNOVATION REPRESENTATION OF A STOCHASTIC PROCESS 285 9.5.2 SOLUTION TO
THE ORIGINAL PROBLEM 287 9.5.3 THE MINIMUM MEAN SQUARE ERROR 291 9.5.3.1
SOLUTION IN THE FREQUENCY DOMAIN 293 9.5.3.2 SOLUTION IN THE TIME DOMAIN
294 9.6 CANONICAL FORM OF THE ERROR SURFACE 295
9.7 WEINER FILTERS WITH ADDITIONAL CONSTRAINTS 297 9.8 CHAPTER SUMMARY
299
10 ADAPTIVE FILTERS 301
10.1 INTRODUCTION 301
10.1.1 APPLICATIONS OF ADAPTIVE FILTERS 302 10.1.2 SYSTEM IDENTIFICATION
302 10.1.3 INVERSE MODELING 303
10.1.4 PREDICTION 304
10.1.5 INTERFERENCE CANCELING 304 10.2 ADAPTIVE DIRECT FORM FIR FILTERS
305
IMAGE 7
CONTENTS J X I
10.3 THE GRADIENT ALGORITHM 306
10.3.1 THE METHOD OF STEEPEST DESCENT 308 10.4 OTHER RELATED STOCHASTIC
GRADIENT ALGORITHMS 311 10.4.1 THE AVERAGE STOCHASTIC GRADIENT ALGORITHM
311 10.4.2 LOW-PASS FILTER OF THE GRADIENT 312
10.4.3 THE CONJUGATE GRADIENT ALGORITHM 312 10.4.4 THE ERROR SIGN
ALGORITHM 313 10.4.5 THE NORMALIZED LMS ALGORITHM 313 10.5 PROPERTIES OF
THE GRADIENT ALGORITHMS 314 10.5.1 EXAMPLES OF ADAPTIVE FILTERS USING
THE LMS ALGORITHM 316
10.5.2 COMPUTING TIME TO CONVERGENCE 319 10.5.3 SUMMARY OF THE LMS
ALGORITHM 320 10.6 THE RECURSIVE LEAST SQUARES ALGORITHM 321 10.6.1
DEFINITIONS 321
10.6.2 RECURSIVE COMPUTATION OF D M (N) AND R XX 323 10.6.3 THE RLS
ALGORITHM 325 10.6.4 SUMMARY OF THE RLS ALGORITHM 326 10.7 CHAPTER
SUMMARY 332
FURTHER READING 334
APPENDIX A: MATHEMATICAL IDENTITIES 337
APPENDIX B: TRANSFORM TABLES 339 B.L FOURIER SERIES 339
B.2 FOURIER TRANSFORM 340
B.3 LAPLACE TRANSFORM 341
B.4 Z-TRANSFORM 342
B.5 DISCRETE FOURIER TRANSFORM 344
APPENDIX C: INTRODUCTION TO MATLAB 345 C.L INTRODUCTION 345
C.2 NUMBERS AND DATA REPRESENTATION 345 C.3 CONTROL FLOW 347
C.4 SPECIAL OPERATORS AND PREDEFINED VARIABLES C.5 DRAWING PLOTS IN
MATLAB 349 C.6 SOME SPECIAL COMMANDS USED IN THIS BOOK
INDEX 353 |
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| publisher | Wiley-VCH |
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| spelling | Kapadia, Rajiv J. Verfasser aut Digital filters theory, application and design of modern filters Rajiv J. Kapadia Weinheim Wiley-VCH 2012 XI, 359 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Digitalfilter (DE-588)4070477-4 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Digitalfilter (DE-588)4070477-4 s DE-604 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3932668&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024975087&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kapadia, Rajiv J. Digital filters theory, application and design of modern filters Digitalfilter (DE-588)4070477-4 gnd |
| subject_GND | (DE-588)4070477-4 (DE-588)4123623-3 |
| title | Digital filters theory, application and design of modern filters |
| title_auth | Digital filters theory, application and design of modern filters |
| title_exact_search | Digital filters theory, application and design of modern filters |
| title_full | Digital filters theory, application and design of modern filters Rajiv J. Kapadia |
| title_fullStr | Digital filters theory, application and design of modern filters Rajiv J. Kapadia |
| title_full_unstemmed | Digital filters theory, application and design of modern filters Rajiv J. Kapadia |
| title_short | Digital filters |
| title_sort | digital filters theory application and design of modern filters |
| title_sub | theory, application and design of modern filters |
| topic | Digitalfilter (DE-588)4070477-4 gnd |
| topic_facet | Digitalfilter Lehrbuch |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=3932668&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024975087&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT kapadiarajivj digitalfilterstheoryapplicationanddesignofmodernfilters |