Hilbert transforms in signal processing:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston [u.a.]
Artech House
1996
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| Series: | The Artech House signal processing library
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 442 S. Ill., graph. Darst. |
| ISBN: | 0890068860 |
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| adam_text | HILBERT TRANSFORMS IN SIGNAL PROCESSING STEFAN L. HAHN ARTECH HOUSE
BOSTON * LONDON CONTENTS PREFACE XIII INTRODUCTION 1 CHAPTER 1 THEORY OF
THE ONE-DIMENSIONAL HILBERT TRANSFORMATION 3 1.1 THE CONCEPTS OF THE
HILBERT AND FOURIER TRANSFORMATIONS 3 1.2 ANALYTIC FUNCTIONS 5 1.3
CAUCHY INTEGRAL REPRESENTATION OF THE ANALYTIC FUNCTION: THE ANALYTIC
SIGNAL 7 1.4 EXAMPLES OF DERIVATION OF HILBERT TRANSFORMS IN THE TIME
DOMAIN 9 1.4.1 HARMONIC SIGNALS: COS(R), 1.4.2 THE HILBERT TRANSFORM OF
THE DELTA PULSE 10 1.4.3 THE HILBERT TRANSFORM OF A SQUARE PULSE 11 1.5
THE FOURIER TRANSFORM OF THE HILBERT TRANSFORM 12 1.6 SYMMETRY
PROPERTIES OF THE HILBERT TRANSFORM 13 1.7 THE DERIVATION OF HILBERT
TRANSFORMS BY MEANS OF FOURIER TRANSFORMS 14 1.7.1 THE HILBERT TRANSFORM
OF A GAUSSIAN PULSE 15 1.8 THE DERIVATION OF HILBERT TRANSFORMS USING
HARTLEY TRANSFORMS 16 1.9 HILBERT TRANSFORMS OF PERIODIC SIGNALS 19
1.9.1 THE METHOD BASED ON THE WOODWARD DEFINITION OF A PERIODIC SIGNAL
19 1.9.2 THE COTANGENT FORM OF THE HILBERT TRANSFORM OF THE PERIODIC
SIGNAL 21 1.9.3 THE HILBERT TRANSFORM OF THE FOURIER SERIES EXPANSION OF
A PERIODIC FUNCTION 22 1.9.4 THE DERIVATION OF THE HILBERT TRANSFORM OF
PERIODIC SIGNALS DIRECTLY FROM THE TIME-DOMAIN HILBERT INTEGRAL 25 1.10
HILBERT TRANSFORMS OF THE BESSEL FUNCTIONS OF THE FIRST KIND 27 1.10.1
DERIVATION OF THE HILBERT TRANSFORMS OF BESSEL FUNCTIONS USING FOURIER
TRANSFORMS 30 1.11 ONE-SIDED SPECTRA OF ANALYTIC SIGNALS AND ANALYTIC
SPECTRA OF CAUSAL SIGNALS 36 1.11.1 ONE-SIDED SPECTRA OF ANALYTIC
SIGNALS 37 1.11.2 ANALYTIC SPECTRA OF ONE-SIDED (CAUSAL) SIGNALS 39 1.12
INTEGRATION OF ANALYTIC SIGNALS 42 1.13 THE DEFINITIONS OF THE
INSTANTANEOUS AMPLITUDE, PHASE, AND FREQUENCY OF ANALYTIC SIGNALS 43
1.13.1 POLAR NOTATION OF ANALYTIC SIGNALS 44 1.13.2 THE INSTANTANEOUS
COMPLEX PHASE AND COMPLEX FREQUENCY 47 1.14 NEGATIVE INSTANTANEOUS
FREQUENCY OF THE ANALYTIC SIGNAL 51 REFERENCES 53 CHAPTER 2 PROPERTIES
OF THE HILBERT TRANSFORMATION DERIVATIONS AND APPLICATIONS 55 2.1
INTRODUCTION 55 2.2 LINEARITY 55 2.3 LINEARITY: A METHOD OF GENERATING
THE HILBERT TRANSFORM USING THE SAMPLES OF A FUNCTION 58 2.4 LINEARITY:
HILBERT TRANSFORMS OF HYPERBOLIC FUNCTIONS 59 2.5 ITERATION 60 2.6
DIFFERENTIATION 61 2.7 SUCCESSIVE ITERATION AND DIFFERENTIATION 62 2.8
DIFFERENTIATION OF THE CONVOLUTIONS 65 2.9 DIFFERENTIATION AND
MULTIPLICATION BY T. HILBERT TRANSFORMS OF HERMITE POLYNOMIALS AND
FUNCTIONS 67 2.9.1 HERMITE POLYNOMIALS 68 2.10 HILBERT TRANSFORMS OF
LEGENDRE POLYNOMIALS 74 2.10.1 HILBERT TRANSFORMS OF LEGENDRE
POLYNOMIALS BY FOURIER TRANSFORMS 80 2.11 AUTOCONVOLUTION,
AUTOCORRELATION, AND ENERGY EQUALITY 82 2.12 THE N-FOLD AUTOCONVOLUTION
86 2.13 THE HILBERT TRANSFORM OF A PRODUCT OF TWO SIGNALS 88 2.13.1
NONOVERLAPPING SPECTRA OF/(F) AND G(T) - BEDROSIAN S THEOREM 88 2.13.2
THE HILBERT TRANSFORM OF THE PRODUCT A(T)COS((O 0 T + TPO) [5] 91 2.14
THE HILBERT TRANSFORM OF A PRODUCT OF ANALYTIC SIGNALS 92 REFERENCES 93
CHAPTER 3 DISTRIBUTIONS IN THE THEORY OF THE HILBERT TRANSFORMATION AND
COMPLEX SIGNALS 95 3.1 INTRODUCTION 95 3.2 DEFINITION OF A DISTRIBUTION
IN TERMS OF FUNCTIONALS 96 3.3 THE COMPLEX DELTA DISTRIBUTION 97 3.3.1 A
CONVOLUTION DEFINITION OF THE ANALYTIC SIGNAL 99 3.3.2 THE CONCEPT OF
THE INVERSE DISTRIBUTION 100 3.4 THE POLAR NOTATION OF THE COMPLEX DELTA
DISTRIBUTION 101 3.5 OTHER NOTATIONS OF THE COMPLEX DELTA DISTRIBUTION
104 3.6 THE INTEGRAL AND THE DERIVATIVES OF THE COMPLEX DELTA
DISTRIBUTION IN TERMS OF THE CAUCHY APPROXIMATION FUNCTIONS 104 3.7 THE
INTEGRAL AND THE DERIVATIVES OF THE COMPLEX DELTA DISTRIBUTION 106 3.8
THE COMPLEX DELTA SAMPLING SEQUENCE 107 3.9 THE TWO-DIMENSIONAL COMPLEX
DELTA DISTRIBUTION 110 3.10 THE POLAR REPRESENTATION OF THE
TWO-DIMENSIONAL COMPLEX DELTA DISTRIBUTION 112 3.10.1 THE ILLUSTRATION
OF THE TWO-DIMENSIONAL COMPLEX DELTA DISTRIBUTION WITH APPROXIMATION
FUNCTIONS 114 3.11 THE TWO-DIMENSIONAL COMPLEX SAMPLING SEQUENCE 115
3.12 THE THREE-DIMENSIONAL COMPLEX DELTA DISTRIBUTION 116 REFERENCES 118
CHAPTER 4 THE DISCRETE HILBERT TRANSFORMATION 121 4.1 INTRODUCTION 121
4.2 THE DFT*DISCRETE FOURIER TRANSFORMATION 121 4.2.1 THE ILLUSTRATION
OF THE EVENESS AND ODDNESS OF SEQUENCES 124 4.2.2 THE DC AND AC PARTS OF
A SEQUENCE 125 4.3 EXAMPLES OF THE DERIVATION OF THE DFT FOR SELECTED
SIMPLE SIGNALS 127 4.3.1 THE DFT OF TRIGONOMETRIC FUNCTIONS 134 4.4 THE
Z-TRANSFORMATION 136 4.5 THE ELEMENTARY PROPERTIES OF THE DFT AND
Z-TRANSFORMATIONS 138 4.5.1 LINEARITY 138 4.5.2 ENERGY EQUALITY
(PARSEVAL S THEOREM) 139 4.5.3 CIRCULAR CONVOLUTION:
CONVOLUTION-TO-MULTIPLICATION THEOREM 140 4.5.4 SHIFTING PROPERTY 141
4.6 THE DISCRETE HILBERT TRANSFORMATION 141 4.6.1 ENERGY RELATIONS 145
4.7 DISCRETE HILBERT TRANSFORMS OF SELECTED SEQUENCES 146 4.7.1 ENERGY
RELATIONS 146 4.7.2 THE HILBERT TRANSFORM OF THE KRONECKER DELTA SAMPLE
147 4.7.3 THE HILBERT TRANSFORMS OF TRIGONOMETRIC FUNCTIONS 149 4.7.4
ENERGY RELATIONS 149 4.7.5 THE HILBERT TRANSFORM OF A GAUSSIAN SEQUENCE
149 4.7.6 THE DHT OF A SAMPLED UNIPOLAR SQUARE PULSE 150 4.8 ITERATION
OF THE DISCRETE HILBERT TRANSFORMATION 153 4.8.1 ENERGY RELATION 155 4.9
THE SYSTEM THEORY DERIVATION OF THE DHT 4.10 THE COMPLEX ANALYTIC
DISCRETE SEQUENCE 4.11 CAUSAL DISCRETE-TIME SEQUENCES AND ANALYTIC
DISCRETE SPECTRA 4.12 THE BILINEAR TRANSFORMATION AND THE COTANGENT FORM
OF HILBERT TRANSFORMATIONS REFERENCES CHAPTER 5 HILBERT TRANSFORMERS 5.1
GENERAL FEATURES OF HILBERT TRANSFORMERS 5.1.1 TRANSFER FUNCTION AND
BANDWIDTH 5.2 PHASE-SPLITTER HILBERT TRANSFORMERS 5.2.1 ANALOG ALL-PASS
FILTERS 5.3 A SIMPLE METHOD OF DESIGN FOR HILBERT PHASE SPLITTERS 5.3.1
FIRST STEP 5.3.2 SECOND STEP 5.3.3 DELAY, PHASE DISTORTIONS, AND
EQUALIZATION 5.4 HILBERT TRANSFORMERS WITH TAPPED DELAY LINE FILTERS 5.5
BANDPASS HILBERT TRANSFORMERS 5.6 GENERATION OF HILBERT TRANSFORMS USING
SSB FILTERING 5.7 DIGITAL HILBERT TRANSFORMERS 5.7.1 THE TRANSFER
FUNCTION OF THE IDEAL NONCAUSAL HILBERT TRANSFORMER 5.7.2 TYPES OF
DIGITAL HILBERT TRANSFORMERS 5.8 FIR HILBERT TRANSFORMERS [15-18] 5.8.1
DESIGN 5.8.2 RECTANGULAR WINDOW 5.8.3 PARAMETERS OF THE GIE^) FUNCTION
5.8.4 IMPROVING THE RIPPLE DISTRIBUTION USING WINDOWS 5.8.5 TYPES OF
WINDOWS 5.8.6 ILLUSTRATION OF THE FUNCTIONS G(E^) OBTAINED BY USING
VARIOUS WINDOWS 5.8.7 COMPARISON OF THE PARAMETERS OF FIR HILBERT
TRANSFORMERS DESIGNED USING THE RECTANGULAR, KAISER, AND TSCHEBYSHEFF
WINDOWS 5.8.8 KAISER WINDOW WITH PREEMPHASIS 5.8.9 DESIGN OF FIR HILBERT
TRANSFORMERS WITH EVEN VALUES OF N 5.8.10 DERIVATION OF THE TRANSFER
FUNCTION (5.48) 5.9 FIR HILBERT TRANSFORMERS WITH HALFBAND FILTERS 5.10
RECAPITULATION OF THE DESIGN PROCEDURE OF FIR HILBERT TRANSFORMERS 5.11
DIGITAL ALL-PASS HILBERT TRANSFORMERS [23] 5.12 THE DESIGN OF HILBERT
TRANSFORMERS BY USE OF BILINEAR FREQUENCY TRANSFORMATION 225 5.13 IIR
DISCRETE-TIME HILBERT TRANSFORMERS 226 5.13.1 BUTTERWORTH PHASE
FUNCTIONS 229 5.14 DIFFERENTIATING HILBERT TRANSFORMERS 230 5.14.1
ANALOG RELATIONS 230 5.14.2 DISCRETE-TIME RELATIONS 230 5.14.3 THE
DESIGN OF THE FIR DIFFERENTIATING HILBERT TRANSFORMER 233 REFERENCES 239
CHAPTER 6 THE HILBERT TRANSFORM IN MODULATION THEORY 241 6.1
INTRODUCTION 241 6.1.1 DEFINITION 241 6.2 THE CONCEPT OF THE MODULATION
FUNCTION OF A HARMONIC CARRIER 242 6.2.1 THE MODIFIED MODULATION
FUNCTION 243 6.3 CLASSIFICATION 244 6.3.1 LINEAR MODULATION 245 6.3.2
NONLINEAR MODULATION 245 6.4 TEST SIGNALS IN MODULATION 247 6.4.1 TEST
SIGNAL IN THE FORM OF A FOURIER SERIES 247 6.4.2 TEST SIGNALS WITH
RANDOM PHASES OF THE HARMONIC TERMS OF THE FOURIER SERIES 252 6.5 BASIC
THEORY OF AMPLITUDE MODULATION 253 6.5.1 AM MODULATORS 253 6.5.2
LOW-PASS-TO-BANDPASS FILTERING ANALOGY IN AM 256 6.5.3 AM*ENERGY
RELATIONS 258 6.6 BASIC THEORY OF ANGLE MODULATION 260 6.6.1
CLASSIFICATION 262 6.6.2 PHASE AND FREQUENCY MODULATORS 263 6.6.3
SPECTRA OF ANGLE MODULATION: HARMONIC MODULATING SIGNAL 263 6.6.4
FREQUENCY MODULATION BY THE HARMONIC SIGNAL 266 6.6.5 NARROWBAND PHASE
OR FREQUENCY MODULATION 266 6.6.6 WIDEBAND PHASE OR FREQUENCY MODULATION
267 6.6.7 ADIABATIC THEOREM 267 6.6.8 SPECTRA OF ANGLE MODULATION:
MULTITONE MODULATING SIGNAL 267 6.7 SINGLE-SIDEBAND LINEAR AM MODULATION
269 6.7.1 SINGLE-SIDEBAND MODULATORS 271 6.8 GENERAL FORMS OF
SINGLE-SIDEBAND MODULATIONS 272 6.8.1 BASIC RELATIONS 272 6.9 THE CSSB
SIGNAL FOR A LINEAR ENVELOPE DEMODULATOR 274 6.10 CSSB MODULATION FOR
SQUARE-LAW AM DEMODULATOR 277 6.11 SSB SIGNAL FOR A LINEAR FM
DEMODULATOR 280 6.11.1 APPLICATIONS OF THE CSSB SIGNALS 281 REFERENCES *
283 CHAPTER 7 THE HILBERT TRANSFORM IN SIGNAL AND SYSTEM THEORY 7.1
INTRODUCTION 7.2 HILBERT TRANSFORMS IN THE THEORY OF LINEAR SYSTEMS:
KRAMERS-KRONIG RELATIONS 7.2.1 CAUSALITY 7.2.2 PHYSICAL REALIZABILITY OF
TRANSFER FUNCTIONS 7.2.3 MINIMUM PHASE PROPERTY 7.3 AMPLITUDE PHASE
RELATIONS IN DLTI SYSTEMS 7.3.1 MINIMUM PHASE PROPERTY IN DLTI SYSTEMS
7.4 MEASUREMENT SYSTEMS USING THE AMPLITUDE PHASE RELATIONS OF LTI
SYSTEMS 7.5 THE KRAMERS-KRONIG RELATIONS IN LINEAR MACROSCOPIC
CONTINUOUS MEDIA 7.6 THE CONCEPT OF SIGNAL DELAY IN THE HILBERTIAN SENSE
7.7 THE HILBERT TRANSFORM IN THE THEORY OF SAMPLING 7.7.1 BANDPASS
FILTERING OF THE LOW-PASS SAMPLED SIGNAL 7.8 SAMPLING OF BANDPASS
SIGNALS 7.9 QUADRATURE SAMPLING OF A BANDPASS SIGNAL 7.10 LINEAR
TRANSFORMATIONS OF THE INTERPOLATORY EXPANSION 7.11 GENERATION OF A
RANDOM SIGNAL USING THE INTERPOLATION EXPANSION 7.12 COMPLEX ANALYTIC
RANDOM SIGNALS 7.12.1 SPECTRAL MOMENTS 7.12.2 THE INSTANTANEOUS PHASE
AND FREQUENCY OF GAUSSIAN LOW-PASS NOISE 7.13 INSTANTANEOUS SPECTRAL
MOMENTS DEFINED BY THE WIEGNER-VILLE TIME- FREQUENCY DISTRIBUTION 7.14
GENERATION OF TWO-DIMENSIONAL RANDOM FIELDS 7.14.1 GENERATION OF
TIME-VARIABLE TWO-DIMENSIONAL RANDOM FIELDS 7.15 THE DEFINITION OF
ELECTRICAL POWER IN TERMS OF HILBERT TRANSFORMS AND ANALYTIC SIGNALS
7.15.1 HARMONIC WAVEFORMS OF VOLTAGE AND CURRENT 7.15.2 THE NOTION OF
COMPLEX POWER 7.15.3 GENERALIZATION OF THE NOTION OF POWER 7.16
GENERALIZATION OF THE NOTION OF POWER FOR SIGNALS WITH FINITE AVERAGE
POWER REFERENCES CHAPTER 8 MULTIDIMENSIONAL COMPLEX SIGNALS AND
APPLICATIONS 8.1 INTRODUCTION 8.2 THE DEFINITION OF THE MULTIDIMENSIONAL
COMPLEX SIGNAL 8.2.1 THE FREQUENCY-DOMAIN DEFINITION OF THE
N-DIMENSIONAL COMPLEX SIGNAL 8.2.2 SIGNAL DOMAIN DEFINITION OF THE
N-DIMENSIONAL COMPLEX SIGNAL 335 8.3 THE DEFINITION OF THE
TWO-DIMENSIONAL COMPLEX SIGNAL 336 8.3.1 THE KERNEL OF THE
TWO-DIMENSIONAL FOURIER TRANSFORMATION WRITTEN IN TERMS OF HILBERT
TRANSFORMS 337 8.4 SEPARABLE TWO-DIMENSIONAL SIGNALS 339 8.5 CONJUGATE
TWO-DIMENSIONAL ANALYTIC SIGNALS 340 8.6 THE POLAR NOTATION OF
TWO-DIMENSIONAL COMPLEX SIGNALS 341 8.6.1 LOCAL AMPLITUDES AND PHASES
FOR SEPARABLE TWO-DIMENSIONAL SIGNALS 343 8.7 EXAMPLES OF SEPARABLE
COMPLEX TWO-DIMENSIONAL SIGNALS 344 8.8 EXAMPLES OF NONSEPARABLE
TWO-DIMENSIONAL COMPLEX SIGNALS 348 8.9 IMAGE DECOMPOSITION AND
RECONSTRUCTION USING AMPLITUDE AND PHASE PATTERNS 358 8.10
THREE-DIMENSIONAL COMPLEX SIGNALS 360 8.11 MULTIDIMENSIONAL MODULATION
THEORY 363 8.11.1 THE N-DIMENSIONAL MODULATION FUNCTION 364 8.11.2 THE
TWO-DIMENSIONAL MODULATION THEORY - 364 8.11.3 TWO-DIMENSIONAL AMPLITUDE
MODULATION 365 8.11.4 THE SINGLE-QUADRANT MODULATION SQM 366 8.11.5
TWO-DIMENSIONAL PHASE MODULATION 367 REFERENCES 368 CHAPTER 9
MULTIDIMENSIONAL HILBERT AND FOURIER TRANSFORMATIONS 369 9.1
INTRODUCTION 369 9.2 EVENNESS AND ODDNESS OF MULTIDIMENSIONAL REAL
SIGNALS 369 9.3 SIGNAL DOMAIN DEFINITION OF THE N-DIMENSIONAL HILBERT
TRANSFORMATION 373 9.4 TWO-DIMENSIONAL HILBERT TRANSFORMATIONS 374 9.5
PARTIAL HILBERT TRANSFORMATIONS 375 9.6 THE DERIVATION OF N-DIMENSIONAL
HILBERT TRANSFORMS BY MEANS OF N-DIMENSIONAL FOURIER TRANSFORMS 376 9.7
THE TWO-DIMENSIONAL DISCRETE HILBERT TRANSFORMATION: TWO- DIMENSIONAL
DHT 379 9.7.1 PROPERTIES OF THE ONE-DIMENSIONAL DHT 380 9.7.2 THE
TWO-DIMENSIONAL DISCRETE HILBERT TRANSFORM 380 9.7.3 PROPERTIES OF THE
TWO-DIMENSIONAL DHT [4] 381 9.7.4 ENERGY RELATIONS 385 9.8 STARK S
EXTENSION OF BEDROSIAN S THEOREM 391 9.9 TABLES OF TWO-DIMENSIONAL
HILBERT TRANSFORMS 394 REFERENCES 395 APPENDIX A TABULATION OF HILBERT
PAIRS 397 APPENDIX B THE DERIVATION OF THE DERIVATIVE OF THE LOGARITHMIC
AND 6{F) DISTRIBUTIONS 405 APPENDIX C SUPPLEMENT TO CHAPTER 4 407 C.I
THE FOURIER SERIES REPRESENTATION OF THE DFT 407 C.2 CALCULATION OF THE
DHT USING THE DISCRETE HARTLEY TRANSFORMATION 408 APPENDIX D DETAILS OF
THE CALCULATION OF THE PHASE FUNCTION OF IIR HILBERT TRANSFORMERS 411
D.I CALCULATION OF THE COEFFICIENTS A(I) 413 D.2 THE PROBLEM OF THE
VALUE OF/(TIN (D.14) 416 APPENDIX E DERIVATION OF THE SPECTRUM OF THE
CSSB SIGNAL FOR LINEAR AMPLITUDE 419 APPENDIX F DERIVATION OF THE
FOURIER SPECTRUM OF THE AF-DIMENSIONAL HILBERT TRANSFORM 425 ABOUT THE
AUTHOR 427 INDEX 429
|
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| discipline | Elektrotechnik Mathematik Elektrotechnik / Elektronik / Nachrichtentechnik |
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| id | DE-604.BV011339634 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:08:04Z |
| institution | BVB |
| isbn | 0890068860 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007618974 |
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| physical | XIV, 442 S. Ill., graph. Darst. |
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| record_format | marc |
| series2 | The Artech House signal processing library |
| spelling | Hahn, Stefan L. Verfasser aut Hilbert transforms in signal processing Stefan L. Hahn Boston [u.a.] Artech House 1996 XIV, 442 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier The Artech House signal processing library Signalverarbeitung (DE-588)4054947-1 gnd rswk-swf Hilbert-Transformation (DE-588)4375311-5 gnd rswk-swf Signalverarbeitung (DE-588)4054947-1 s Hilbert-Transformation (DE-588)4375311-5 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007618974&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hahn, Stefan L. Hilbert transforms in signal processing Signalverarbeitung (DE-588)4054947-1 gnd Hilbert-Transformation (DE-588)4375311-5 gnd |
| subject_GND | (DE-588)4054947-1 (DE-588)4375311-5 |
| title | Hilbert transforms in signal processing |
| title_auth | Hilbert transforms in signal processing |
| title_exact_search | Hilbert transforms in signal processing |
| title_full | Hilbert transforms in signal processing Stefan L. Hahn |
| title_fullStr | Hilbert transforms in signal processing Stefan L. Hahn |
| title_full_unstemmed | Hilbert transforms in signal processing Stefan L. Hahn |
| title_short | Hilbert transforms in signal processing |
| title_sort | hilbert transforms in signal processing |
| topic | Signalverarbeitung (DE-588)4054947-1 gnd Hilbert-Transformation (DE-588)4375311-5 gnd |
| topic_facet | Signalverarbeitung Hilbert-Transformation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007618974&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT hahnstefanl hilberttransformsinsignalprocessing |