Random signal analysis:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Boston
De Gruyter
[2018]
Science Press Beijing [2018] |
| Series: | Information and computer engineering
volume 2 |
| Subjects: | |
| Online Access: | https://www.degruyter.com/doc/cover/9783110595369.jpg http://www.degruyter.com/search?f%5F0=isbnissn&q%5F0=9783110595369&searchTitles=true Inhaltsverzeichnis Inhaltsverzeichnis |
| Physical Description: | XIII, 308 Seiten Illustrationen, Diagramme |
| ISBN: | 9783110595369 |
Staff View
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Record in the Search Index
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| adam_text | CONTENTS
0 INTRODUCTION * 1
0.1 PROBABILITY SPACE * 1
0.1.1 RANDOMIZED TRIALS * 1
0.1.2 SAMPLE SPACE * 2
0.1.3 PROBABILITY SPACE * 2
0.2 CONDITIONAL PROBABILITY SPACE * 3
0.2.1 CONDITIONAL PROBABILITY* 3
0.2.2 MULTIPLICATION FORMULA * 4
0.2.3 TOTAL PROBABILITY FORMULA * 4
0.2.4 THE BAYESIAN FORMULA * 5
0.3 RANDOM VARIABLES * 6
0.3.1 THE CONCEPT OF RANDOM VARIABLES * 6
0.3.2 DISCRETE RANDOM VARIABLES * 7
0.3.3 CONTINUOUS RANDOM VARIABLES * 7
0.3.4 MULTIDIMENSIONAL RANDOM VARIABLES * 9
0.4 DISTRIBUTION OF RANDOM VARIABLE FUNCTIONS * 13
0.4.1 DISTRIBUTION OF DISCRETE RANDOM VARIABLE FUNCTIONS * 14
0.4.2 DISTRIBUTION OF CONTINUOUS RANDOM VARIABLE FUNCTIONS * 14
0.5 NUMERICAL CHARACTERISTICS OF RANDOM VARIABLES * 15
0.5.1 MATHEMATICAL EXPECTATIONS * 16
0.5.2 VARIANCE AND STANDARD DEVIATION * 17
0.5.3 COVARIANCE AND CORRELATION COEFFICIENTS * 18
0.5.4 THE MOMENT OF RANDOM VARIABLES * 18
0.6 CHARACTERISTIC FUNCTIONS OF RANDOM VARIABLES * 22
0.6.1 COMPLEX RANDOM VARIABLES* 22
0.6.2 CHARACTERISTIC FUNCTIONS OF RANDOM VARIABLES * 23
0.6.3 PROPERTIES OF CHARACTERISTIC FUNCTIONS * 24
0.6.4 RELATIONSHIP BETWEEN CHARACTERISTIC FUNCTIONS AND MOMENTS* 25
0.6.5 CHARACTERISTIC FUNCTIONS OF MULTIDIMENSIONAL RANDOM VARIABLES * 26
0.7 CHEBYSHEV INEQUALITY AND THE LIMIT THEOREM * 28
0.7.1 CHEBYSHEV INEQUALITY * 28
0.7.2 CENTRAL LIMIT THEOREM * 28
1 RANDOM PROCESSES * 33
1.1 BASIC CONCEPTS OF RANDOM PROCESSES * 33
1.1.1 DEFINITION OF RANDOM PROCESSES * 33
1.1.2 PROBABILITY DISTRIBUTION OF RANDOM PROCESSES * 36
1.1.3 THE MOMENT FUNCTION OF RANDOM PROCESSES * 40
1.1.4 CHARACTERISTIC FUNCTIONS OF RANDOM PROCESSES * 43
1.2 STATIONARY RANDOM PROCESSES * 45
1.2.1 CHARACTERISTICS AND CLASSIFICATION * 45
1.2.2 ERGODIC PROCESSES * 49
1.2.3 PROPERTIES OF CORRELATION FUNCTIONS * 56
1.2.4 CORRELATION COEFFICIENT AND CORRELATION TIME * 59
1.3 JOINT STATIONARY RANDOM PROCESSES * 61
1.3.1 JOINT PROBABILITY DISTRIBUTION AND MOMENT FUNCTIONS
OF TWO RANDOM PROCESSES * 61
1.3.2 MOMENT FUNCTION OF JOINT STATIONARY RANDOM PROCESSES * 63
1.4 DISCRETE-TIME RANDOM PROCESS * 66
1.4.1 DEFINITION OF DISCRETE-TIME RANDOM PROCESSES * 66
1.4.2 PROBABILITY DISTRIBUTION OF DISCRETE-TIME RANDOM PROCESSES * 67
1.4.3 DIGITAL CHARACTERISTICS OF DISCRETE-TIME RANDOM PROCESSES * 69
1.4.4 PROPERTIES OF CORRELATION FUNCTIONS OF STATIONARY
DISCRETE-TIME RANDOM PROCESSES * 74
1.5 NORMAL RANDOM PROCESSES * 75
1.5.1 GENERAL NORMAL RANDOM PROCESSES
-----
76
1.5.2 STATIONARY NORMAL RANDOM PROCESSES * 78
1.5.3 VECTOR MATRIX REPRESENTATION OF NORMAL STOCHASTIC PROCESSES * 80
1.6 SPECTRAL ANALYSIS OF STATIONARY RANDOM PROCESSES * 82
1.6.1 CONCEPT OF SPECTRAL DENSITY * 82
1.6.2 DEFINITION OF POWER SPECTRAL DENSITY * 84
1.6.3 RELATION BETWEEN THE POWER SPECTRAL DENSITY
AND CORRELATION FUNCTIONS * 86
1.6.4 PROPERTIES OF POWER SPECTRAL DENSITY * 88
1.6.5 MUTUAL SPECTRAL DENSITY OF JOINT STATIONARY RANDOM PROCESSES * 91
1.6.6 POWER SPECTRAL DENSITY OF DISCRETE-TIME RANDOM PROCESSES * 93
1.7 WHITE NOISE * 95
2 LINEAR TRANSFORMATION OF RANDOM PROCESSES * 101
2.1 LINEAR TRANSFORMATION AND LINEAR SYSTEM OVERVIEW * 101
2.1.1 BASIC CONCEPTS OF LINEAR SYSTEMS * 101
2.1.2 RESEARCH TOPIC OF LINEAR TRANSFORMATION OF RANDOM PROCESSES * 106
2.2 DIFFERENTIATION AND INTEGRATION IN STOCHASTIC PROCESSES * 107
2.2.1 LIMIT OF THE RANDOM PROCESS * 107
2.2.2 CONTINUITY OF STOCHASTIC PROCESSES * 108
2.2.3 DIFFERENTIAL OF STOCHASTIC PROCESSES (DERIVATIVES)
-----
110
2.2.4 DIFFERENTIAL TRANSFORMATION OF STOCHASTIC PROCESSES * 113
2.2.5 INTEGRALS OF RANDOM PROCESSES * 117
2.2.6 INTEGRAL TRANSFORMATION OF RANDOM PROCESSES * 118
2.3 ANALYSIS OF RANDOM PROCESSES THROUGH CONTINUOUS-TIME SYSTEMS * 121
2.3.1 IMPULSE RESPONSE METHOD * 121
2.3.2 SPECTRUM METHOD * 124
2.4 WHITE NOISE THROUGH LINEAR SYSTEMS * 129
2.4.1 GENERAL RELATIONS * 129
2.4.2 NOISE EQUIVALENT PASSBAND * 130
2.4.3 WHITE NOISE THROUGH RC INTEGRAL CIRCUITS * 131
2.4.4 WHITE NOISE THROUGH IDEAL LOWPASS LINEAR SYSTEMS * 133
2.4.5 WHITE NOISE THROUGH IDEAL BANDPASS LINEAR SYSTEMS * 134
2.4.6 WHITE NOISE THROUGH A LINEAR SYSTEM WITH A GAUSSIAN BAND * 136
2.5 PROBABILITY DISTRIBUTION OF THE LINEAR TRANSFORMATION
OF RANDOM PROCESSES * 137
2.5.1 INPUT IS NORMAL AND OUTPUT IS STILL NORMAL * 138
2.5.2 INPUT IS A NON-NORMAL PROCESS OF A BROADBAND (RELATIVE TO SYSTEM S
PASSBAND), AND OUTPUT IS AN APPROXIMATE NORMAL PROCESS * 140
2.5.3 INPUT IS WHITE NOISE AND OUTPUT OF THE LIMITED BANDWIDTH SYSTEM
IS AN APPROXIMATE NORMAL PROCESS * 142
3 STATIONARY AND NARROWBAND RANDOM PROCESSES
* 149
3.1 NARROWBAND RANDOM PROCESSES REPRESENT
QUASI-SINUSOIDAL OSCILLATION * 149
3.1.1 FORMATION AND CHARACTERISTICS OF NARROWBAND
STOCHASTIC PROCESSES * 149
3.1.2 EXPRESSION OF NARROWBAND STOCHASTIC PROCESSES * 150
3.2 ANALYTIC SIGNALS AND HILBERT TRANSFORMS * 151
3.2.1 COMPLEX SIGNALS OF SINUSOIDAL SIGNALS * 151
3.2.2 COMPLEX SIGNALS OF HIGH-FREQUENCY NARROWBAND SIGNALS * 152
3.2.3 ANALYTIC SIGNALS AND THE HILBERT TRANSFORM * 155
3.3 ANALYTIC COMPLEX STOCHASTIC PROCESS * 158
3.3.1 COMPLEX RANDOM VARIABLES * 158
3.3.2 COMPLEX RANDOM PROCESSES * 159
3.3.3 CORRELATION FUNCTION AND POWER SPECTRAL DENSITY
OF COMPLEX STOCHASTIC PROCESSES * 161
3.3.4 COMPLEX ENVELOPE AND STATISTICAL PROPERTIES
OF NARROWBAND RANDOM PROCESSES * 163
3.4 PROBABILITY DISTRIBUTION OF NARROWBAND NORMAL PROCESS
ENVELOPES AND PHASE * 168
3.4.1 PROBABILITY DISTRIBUTION OF THE NARROWBAND NORMAL NOISE
ENVELOPE AND PHASE * 169
3.4.2 PROBABILITY DISTRIBUTION OF THE ENVELOPE AND PHASE
OF A NARROWBAND NORMAL NOISE PLUS SINE (TYPE) SIGNAL * 174
3.5
3.5.1
3.5.2
3.5.3
4
4.1
4.2
4.2.1
4.2.2
4.2.3
4.2.4
4.2.5
4.3
4.3.1
4.3.2
4.3.3
4.4
4.4.1
4.4.2
4.5
4.5.1
4.5.2
4.5.3
4.6
5
5.1
5.1.1
5.1.2
5.1.3
5.1.4
PROBABILITY DISTRIBUTION OF NARROWBAND
RANDOM PROCESS ENVELOPING SQUARES * 179
PROBABILITY DISTRIBUTION OF NARROWBAND
NORMAL NOISE ENVELOPING SQUARES * 179
PROBABILITY DISTRIBUTION OF SYNTHESIS PROCESS ENVELOPING SQUARES
IN NARROWBAND NORMAL NOISE PLUS SINE (TYPE) SIGNALS * 180
X2 DISTRIBUTION AND NONCENTERED/2 DISTRIBUTION
-----
180
THE NONLINEAR TRANSFORMATION OF STATIONARY RANDOM PROCESSES
* 189
NONLINEAR TRANSFORMATION OVERVIEW * 189
DIRECT METHOD OF NONLINEAR TRANSFORMATION OF RANDOM PROCESSES * 192
STATIONARY NORMAL NOISE THROUGH FULL-WAVE SQUARE-LAW DEVICES * 192
COMMON NOISE AND SIGNALS THROUGH FULL-WAVE SQUARE-LAW DEVICE * 196
DETERMINATION OF THE OUTPUT POWER SPECTRUM WITH THE DIFFERENCE
BEAT METHOD AND THE SUM BEAT METHOD * 200
HERMITE POLYNOMIAL METHOD * 202
STATIONARY NORMAL NOISE THROUGH HALF-WAVE LINEAR DEVICES * 207
TRANSFORMATION METHOD OF RANDOM PROCESS
NONLINEAR TRANSFORMATION * 210
TRANSFER FUNCTION * 211
MOMENT FUNCTIONS OF NONLINEAR DEVICE OUTPUT PROCESSES * 215
THE PRICE METHOD * 220
SLOWLY CHANGING ENVELOPMENT METHOD FOR RANDOM PROCESS
NONLINEAR TRANSFORMATION * 224
SLOWLY CHANGING ENVELOPE METHOD WITHOUT LOAD REACTION * 224
SLOWLY CHANGING ENVELOPE METHOD WITH LOAD REACTION * 230
ANALYSIS OF RANDOM PROCESSES THROUGH A LIMITER * 237
EFFECT OF LIMITING ON PROBABILITY DISTRIBUTION * 237
EFFECT OF LIMITING ON THE POWER SPECTRUM * 241
NOISE AND SINUSOIDAL SIGNALS TOGETHER
THROUGH LIMITING IF AMPLIFIER* 245
CALCULATION OF SNR AT THE OUTPUT OF A RADIO SYSTEM * 247
NONSTATIONARY RANDOM PROCESSES
* 255
STATISTICAL DESCRIPTION OF NONSTATIONARY RANDOM SIGNALS * 255
PROBABILITY DENSITY OF NONSTATIONARY RANDOM SIGNALS * 255
DIGITAL CHARACTERISTICS OF NONSTATIONARY RANDOM SIGNALS * 255
THE TIME-VARYING POWER SPECTRUM
AND THE SHORT-TIME POWER SPECTRUM * 258
THE WIENER PROCESS * 259
5.2 LINEAR TIME-VARYING SYSTEMS AND NONSTATIONARY RANDOM SIGNALS * 260
5.2.1 DESCRIPTION OF LINEAR TIME-VARYING
DISCRETE SYSTEM CHARACTERISTICS * 260
5.2.2 CHARACTERIZATION OF LINEAR TIME-VARYING CONTINUOUS SYSTEMS * 263
5.2.3 TIME-VARYING PARAMETERS OF AR, MA AND ARMA MODELS
NONSTATIONARY RANDOM SIGNALS * 264
5.3 WIGNER-VILLE SPECTRUM OF NONSTATIONARY RANDOM SIGNALS * 265
5.3.1 OVERVIEW OF TIME-FREQUENCY ANALYSIS * 265
5.3.2 WIGNER DISTRIBUTION AND THE WIGNER-VILLE SPECTRUM * 266
5.3.3 EXAMPLES OF WD APPLICATIONS * 268
5.3.4 WV SPECTRA OF LINEAR TIME-VARYING SYSTEM OUTPUTS * 270
5.4 WAVELET ANALYSIS OF NONSTATIONARY RANDOM SIGNALS * 273
5.4.1 CONTINUOUS WAVELET TRANSFORM * 273
5.4.2 TWO-DIMENSIONAL PHASE SPACE * 275
5.4.3 TIME-FREQUENCY CHARACTERISTICS OF THE DOUBLE-WINDOW
FUNCTION OF TPA,B(T) * 277
5.4.4 PHYSICAL MEANING OF THE CONTINUOUS WAVELET TRANSFORM * 280
5.4.5 APPLICATION OF THE WAVELET TRANSFORM IN RANDOM SIGNAL ANALYSIS *
281
5.5 NON-GAUSSIAN PROCESSING AND HIGHER-ORDER STATISTICS * 282
5.5.1 NON-GAUSSIAN SIGNAL PROCESSING * 282
5.5.2 HIGHER-ORDER MOMENTS AND HIGH-ORDER CUMULATES * 284
5.5.3 THE HIGHER-ORDER SPECTRUM * 287
5.5.4 NON-GAUSSIAN PROCESSES AND LINEAR SYSTEMS * 291
A APPENDIX * 295
A .L POWER SPECTRAL DENSITY OF NONSTATIONARY RANDOM PROCESSES * 295
A.2 PROOF OF A DOUBLE INTEGRAL FORMULA * 297
A.3 DERIVATION OF THE DETECTOR VOLTAGE TRANSFER COEFFICIENT* 299
A.3.1 HALF-WAVE LINEAR DETECTOR * 300
A.3.2 FULL-WAVE SQUARE-LAW DETECTOR * 301
A.4 DERIVATION OF THE STATISTICAL MEAN OF RANDOM PROCESSES
IN RICE DISTRIBUTION * 302
BIBLIOGRAPHY * 305
INDEX* 307
|
| any_adam_object | 1 |
| author | Yang, Jie Liu, Congfeng |
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| author_facet | Yang, Jie Liu, Congfeng |
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| dewey-search | 500 |
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| discipline | Allgemeine Naturwissenschaft Elektrotechnik / Elektronik / Nachrichtentechnik |
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| genre | (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV045520115 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T08:20:23Z |
| institution | BVB |
| isbn | 9783110595369 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030904430 |
| oclc_num | 1057471414 |
| open_access_boolean | |
| owner | DE-83 DE-11 DE-634 |
| owner_facet | DE-83 DE-11 DE-634 |
| physical | XIII, 308 Seiten Illustrationen, Diagramme |
| publishDate | 2018 |
| publishDateSearch | 2018 |
| publishDateSort | 2018 |
| publisher | De Gruyter Science Press Beijing |
| record_format | marc |
| series | Information and computer engineering |
| series2 | Information and computer engineering |
| spelling | Yang, Jie Verfasser (DE-588)1169057551 aut Random signal analysis Jie Yang, Congfeng Liu Berlin ; Boston De Gruyter [2018] Science Press Beijing [2018] © 2018 XIII, 308 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Information and computer engineering volume 2 Stochastisches Signal (DE-588)4140374-5 gnd rswk-swf Signalanalyse (DE-588)4181260-8 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Stochastisches Signal (DE-588)4140374-5 s Signalanalyse (DE-588)4181260-8 s DE-604 Liu, Congfeng Verfasser (DE-588)1169057977 aut Erscheint auch als Online-Ausgabe, PDF 978-3-11-059380-8 Erscheint auch als Online-Ausgabe, EPUB 978-3-11-059297-9 Information and computer engineering volume 2 (DE-604)BV045435920 2 X:MVB https://www.degruyter.com/doc/cover/9783110595369.jpg X:MVB http://www.degruyter.com/search?f%5F0=isbnissn&q%5F0=9783110595369&searchTitles=true B:DE-101 application/pdf http://d-nb.info/1152830414/04 Inhaltsverzeichnis DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030904430&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Yang, Jie Liu, Congfeng Random signal analysis Information and computer engineering Stochastisches Signal (DE-588)4140374-5 gnd Signalanalyse (DE-588)4181260-8 gnd |
| subject_GND | (DE-588)4140374-5 (DE-588)4181260-8 (DE-588)4123623-3 |
| title | Random signal analysis |
| title_auth | Random signal analysis |
| title_exact_search | Random signal analysis |
| title_full | Random signal analysis Jie Yang, Congfeng Liu |
| title_fullStr | Random signal analysis Jie Yang, Congfeng Liu |
| title_full_unstemmed | Random signal analysis Jie Yang, Congfeng Liu |
| title_short | Random signal analysis |
| title_sort | random signal analysis |
| topic | Stochastisches Signal (DE-588)4140374-5 gnd Signalanalyse (DE-588)4181260-8 gnd |
| topic_facet | Stochastisches Signal Signalanalyse Lehrbuch |
| url | https://www.degruyter.com/doc/cover/9783110595369.jpg http://www.degruyter.com/search?f%5F0=isbnissn&q%5F0=9783110595369&searchTitles=true http://d-nb.info/1152830414/04 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030904430&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV045435920 |
| work_keys_str_mv | AT yangjie randomsignalanalysis AT liucongfeng randomsignalanalysis |
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