Digital filters: basics and design ; with 34 tables
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2000
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 361 S. Ill., graph. Darst. |
| ISBN: | 3540668411 |
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| 245 | 1 | 0 | |a Digital filters |b basics and design ; with 34 tables |c Dietrich Schlichthärle |
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| _version_ | 1804127808225542144 |
|---|---|
| adam_text | DIETRICH SCHLICHTHARLE
DIGITAL FILTERS
BASICS AND DESIGN
WITH 257 FIGURES AND 34 TABLES
SPRINGER
CONTENTS
CONTINUOUS-TIME SYSTEMS 1
.1 RELATIONS IN THE TIME DOMAIN 1
.2 RELATIONS IN THE FREQUENCY DOMAIN 2
.2.1 THE LAPLACE TRANSFORM 3
.2.2 THE FOURIER TRANSFORM 5
.3 TRANSFER FUNCTIONS 7
2 ANALOG FILTERS 13
2.1 THE IDEAL LOW-PASS FILTER 13
2.2 BUTTERWORTH FILTERS 15
2.3 CHEBYSHEV FILTERS 19
2.4 INVERSE CHEBYSHEV FILTERS 24
2.5 ELLIPTIC FILTERS 27
2.6 BESSEL FILTERS 33
2.7 FILTER FRANSFORMATIONS 41
2.7.1 LOW-PASS HIGH-PASS TRANSFORMATION 42
2.7.2 LOW-PASS BANDPASS TRANSFORMATION 43
2.7.3 LOW-PASS BANDSTOP TRANSFORMATION 45
2.7.4 FILTER TRANSFORMATIONS IN PRACTICE 46
3 DISCRETE-TIME SYSTEMS 51
3.1 DISCRETE-TIME CONVOLUTION 52
3.2 RELATIONS IN THE FREQUENCY DOMAIN 54
3.3 THE Z-TRANSFORM 58
3.3.1 DEFINITION OF THE Z-TRANSFORM 58
3.3.2 PROPERTIES OF THE Z-TRANSFORM 59
3.3.3 EXAMPLES 61
3.4 STABILITY CRITERION IN THE TIME DOMAIN 65
3.5 FURTHER PROPERTIES OF THE UNIT-SAMPLE RESPONSE H(N) 66
4 SAMPLING THEOREM 69
4.1 INTRODUCTION 69
4.2 SAMPLING 69
4.3 BAND-LIMITED SIGNALS 71
4.4 PRACTICAL ASPECTS OF SIGNAL CONVERSION 74
4.4.1 ANALOG-TO-DIGITAL CONVERSION 74
X
CONTENTS
4.4.2 DIGITAL-TO-ANALOG CONVERSION 76
4.5 MATHEMATICAL ANALYSIS OF THE D/A CONVERSION PROCESS 77
5 FILTER STRUCTURES 83
5.1 GRAPHICAL REPRESENTATION OF DISCRETE-TIME NETWORKS 83
5.2 FIR FILTERS 86
5.2.1 THE BASIC STRUCTURE OF FIR FILTERS 86
5.2.2 POLES AND ZEROS OF THE FIR FILTER 89
5.2.3 LINEAR-PHASE FILTERS 91
5.3 IIR FILTERS 95
5.3.1 AN INTRODUCTORY EXAMPLE 95
5.3.2 DIRECT-FORM FILTERS 96
5.3.3 POLES AND ZEROS 98
5.4 FURTHER PROPERTIES OF TRANSFER FUNCTIONS 101
5.4.1 STABILITY CONSIDERATIONS IN THE FREQUENCY DOMAIN 101
5.4.2 MINIMUM-PHASE FILTERS 103
5.5 STATE SPACE STRUCTURES 104
5.6 THE NORMAL FORM 109
5.7 DIGITAL LADDER FILTERS 110
5.7.1 LOSSLESS NETWORKS 112
5.7.2 READABILITY 113
5.7.3 KIRCHHOFF LADDER FILTERS 114
5.7.4 WAVE DIGITAL FILTERS 120
5.7.4.1 WAVE PARAMETERS 120
5.7.4.2 DECOMPOSITION OF THE ANALOG REFERENCE NETWORK INTO ONE-PORTS
AND MULTI-PORTS 126
5.7.4.3 THE REFLECTANCE OF CAPACITOR AND INDUCTOR 130
5.7.4.4 THE ROLE OF THE BILINEAR TRANSFORM 133
5.7.4.5 OBSERVANCE OF THE REALISABILITY CONDITION 135
5.7.4.6 SECOND-ORDER WAVE DIGITAL FILTER BLOCK 138
6 DESIGN OF IIR FILTERS 141
6.1 INTRODUCTION 141
6.2 PRESERVATION THEOREM OF THE CONVOLUTION 142
6.3 APPROXIMATION IN THE TIME DOMAIN 144
6.3.1 IMPULSE-INVARIANT DESIGN 145
6.3.2 STEP-INVARIANT DESIGN 151
6.3.3 RAMP-INVARIANT DESIGN 154
6.4 APPROXIMATION IN THE FREQUENCY DOMAIN 156
6.4.1 DIFFERENCE METHOD 157
6.4.2 BILINEAR TRANSFORM 160
6.4.3 PRACTICAL FILTER DESIGN USING THE BILINEAR TRANSFORM 165
6.4.4 IIR FILTER WITH BESSEL CHARACTERISTICS 169
6.4.4.1 DESIGN WITH PRESCRIBED DELAY T,, 172
6.4.4.2 DESIGN WITH GIVEN 3-DB CUTOFF FREQUENCY 173
CONTENTS
XI
7 DESIGN OF FIR FILTERS 177
7.1 INTRODUCTION 177
7.2 LINEAR-PHASE FILTERS 178
7.3 FREQUENCY SAMPLING 181
7.4 MINIMISATION OF THE MEAN-SQUARE ERROR 188
7.4.1 DIRECT SOLUTION 191
7.4.2 THE WINDOW METHOD 198
7.5 CHEBYSHEV APPROXIMATION 203
7.5.1 THE REMEZ EXCHANGE ALGORITHM 203
7.5.2 POLYNOMIAL INTERPOLATION 206
7.5.3 INTRODUCTION OF A WEIGHTING FUNCTION 210
7.5.4 CASE 2, 3 AND 4 FILTERS 213
7.5.5 MINIMUM-PHASE FIR FILTERS 215
7.6 MAXIMALLY FLAT (MAXFLAT) DESIGN 219
8 EFFECTS OF FINITE REGISTER LENGTH 227
8.1 CLASSIFICATION OF THE EFFECTS 227
8.2 NUMBER REPRESENTATION 227
8.2.1 FIXED-POINT NUMBERS 228
8.2.2 FLOATING-POINT NUMBERS 231
8.3 QUANTISATION 233
8.3.1 FIXED-POINT NUMBERS 233
8.3.2 FLOATING-POINT NUMBERS 238
8.4 SYSTEM NOISE BEHAVIOUR 241
8.4.1 SIGNAL-TO-NOISE RATIO 241
8.4.2 NOISE FILTERING BY LSI SYSTEMS 243
8.4.3 OPTIMUM USE OF THE DYNAMIC RANGE 245
8.5 NOISE OPTIMISATION WITH FIXED-POINT ARITHMETIC 247
8.5.1 NOISE BEHAVIOUR OF FIRST- AND SECOND-ORDER FILTER BLOCKS 247
8.5.2 SHAPING OF THE NOISE SPECTRUM 255
8.5.3 NOISE IN A CASCADE OF SECOND-ORDER FILTER BLOCKS 260
8.6 FINITE COEFFICIENT WORDLENGTH 264
8.6.1 COEFFICIENT SENSITIVITY 265
8.6.2 GRAPHICAL REPRESENTATION OF THE POLE DENSITY 267
8.6.3 INCREASED POLE DENSITY AT LOW AND HIGH FREQUENCIES 272
8.6.4 FURTHER REMARKS CONCERNING COEFFICIENT SENSITIVITY 277
8.6.5 A CONCLUDING EXAMPLE 278
8.7 LIMIT CYCLES 281
8.7.1 NONLINEARITIES IN ACTUAL IMPLEMENTATIONS 282
8.7.2 STABILITY OF THE LINEAR FILTER 284
8.7.3 STABILITY WITH QUANTISATION AND OVERFLOW CORRECTION 289
8.7.4 A CONSTRUCTIVE APPROACH FOR THE DETERMINATION OF STABILITY 290
8.7.4.1 THE LINEAR SYSTEM 290
8.7.4.2 STABILITY OF THE NONLINEAR SYSTEM 292
8.7.5 A SEARCH ALGORITHM IN THE STATE PLANE 304
8.7.6 SUMMARY 311
XII CONTENTS
9 OVERSAMPLING AND NOISE SHAPING 313
9.1 D/A CONVERSION 313
9.1.1 INTERPOLATION 314
9.1.2 NOISE FILTERING 316
9.1.3 NOISE SHAPING 317
9.2 A/D CONVERSION 320
9.2.1 OVERSAMPLING AND DECIMATION 320
9.2.2 NOISE FILTERING 322
9.2.3 OVERSAMPLING AS CONVERTER 323
10 APPENDIX 327
10.1 SYMBOLS AND ABBREVIATIONS 327
10.2 REFERENCES 329
10.3 FILTER DESIGN TABLES 331
10.4 FILTER DESIGN ROUTINES 346
INDEX 359
|
| any_adam_object | 1 |
| author | Schlichthärle, Dietrich |
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| discipline | Elektrotechnik Elektrotechnik / Elektronik / Nachrichtentechnik |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:39:14Z |
| institution | BVB |
| isbn | 3540668411 |
| language | English |
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| physical | XII, 361 S. Ill., graph. Darst. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Springer |
| record_format | marc |
| spelling | Schlichthärle, Dietrich Verfasser aut Digital filters basics and design ; with 34 tables Dietrich Schlichthärle Berlin [u.a.] Springer 2000 XII, 361 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Digitalfilter (DE-588)4070477-4 gnd rswk-swf Digitalfilter (DE-588)4070477-4 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008931546&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Schlichthärle, Dietrich Digital filters basics and design ; with 34 tables Digitalfilter (DE-588)4070477-4 gnd |
| subject_GND | (DE-588)4070477-4 |
| title | Digital filters basics and design ; with 34 tables |
| title_auth | Digital filters basics and design ; with 34 tables |
| title_exact_search | Digital filters basics and design ; with 34 tables |
| title_full | Digital filters basics and design ; with 34 tables Dietrich Schlichthärle |
| title_fullStr | Digital filters basics and design ; with 34 tables Dietrich Schlichthärle |
| title_full_unstemmed | Digital filters basics and design ; with 34 tables Dietrich Schlichthärle |
| title_short | Digital filters |
| title_sort | digital filters basics and design with 34 tables |
| title_sub | basics and design ; with 34 tables |
| topic | Digitalfilter (DE-588)4070477-4 gnd |
| topic_facet | Digitalfilter |
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