Applied Fourier analysis:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
San Diego u.a.
Harcourt, Brace, Jovanovich
1984
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| Edition: | 1. ed. |
| Series: | Harcourt Brace Jovanovich college outline series.
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 223 S. graph. Darst. |
| ISBN: | 0156016095 |
Staff View
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Record in the Search Index
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| adam_text | Titel: Applied Fourier analysis
Autor: Hsu, Hwei P
Jahr: 1984
CONTENTS CHAPTER 1 Fourier Series 1 1-1: Periodic Functions 1 1-2: Fourier Series 3 1-3: Properties of Sine and Cosine: Orthogonal Functions 3 1-4: Evaluation of Fourier Coefficients 5 1- 5: Approximation by Finite Fourier Series 9 CHAPTER 2 Analysis of Periodic Waveforms 22 2- 1: Waveform Symmetry 22 2-2: Fourier Coefficients of Symmetric Waveforms 25 2- 3: Fourier Expansion of a Function over a Finite Interval 29 CHAPTER 3 Discrete Frequency Spectra 40 3- 1: The Complex Form of Fourier Series 40 3-2: Orthogonality of Complex Exponential Functions 42 3-3: Complex Frequency Spectra 43 3- 4: Power Content of a Periodic Function: Parseval’s Theorem 45 CHAPTER 4 Generalized Functions 54 4- 1 : The Unit Impulse Function ô(t) 54 4-2: The Unit Step Function u{t ) 56 4-3: Generalized Derivatives 57 4-4: Generalized Derivative of a Discontinuous Function 59 4-5: Fourier Series of Derivatives of Discontinuous Periodic Functions 62 4- 6: Evaluation of Fourier Coefficients by Differentiation 63 CHAPTER 5 Fourier Transforms 75 5- 1: Fourier Transforms 75 5-2: Properties of Fourier Transforms 76 5-3: Differentiation and Integration Theorems 81 5-4: Parseval’s Formula 82 5-5: Multidimensional Fourier Transforms 83 vii
Vlii Contents CHAPTER 6 Generalized Fourier Transforms 97 6-1: Functions of Slow Growth 6-2: Generalized Fourier 97 Transforms 6-3: The Fourier Transform of a 98 Periodic Function 103 6-4: Integral Representation of d(t) 105 CHAPTER 7 Convolution and Correlation 115 7-1: Convolution 115 7-2: Convolution Theorems 117 7-3: Parseval’s Theorem 120 7-4: Correlation Functions 7-5: The Wiener-Khintchine 121 Theorem 123 CHAPTER 8 Applications to Signal Theory 8-1: Band-Limited and Duration- 136 Limited Signals 136 8-2: The Uncertainty Principle 136 8-3: Sampling Theorems 137 8-4: Modulation 141 8-5: Average Correlation Functions 8-6: Average Power Spectra: 143 Random Signals 8-7: Analytic Signals and Hilbert 145 Transforms 146 CHAPTER 9 Applications to Linear Systems 161 9-1: Linear Systems 9-2: Unit Impulse Response and 161 System Function 162 9-3: Operational System Function 164 9-4: Causal Systems 166 9-5: Response to Random Signals 168 CHAPTER 10 Applications to Boundary-Value Problems 10-1: Separation of Variables and 184 Fourier Series 184 10-2: Vibration 188 10-3: Heat Conduction 194 10-4: Potential Theory 197 FINAL EXAMINATION 214 APPENDIX A Three Forms of Fourier Series 217 APPENDIX B Summary of Symmetry Conditions 217 APPENDIX C Properties of the Fourier Transform 218 APPENDIX D List of Symbols 220 INDEX 221
|
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| ctrlnum | (OCoLC)10162639 (DE-599)BVBBV002191228 |
| dewey-full | 515/.2433 |
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| discipline | Mathematik |
| edition | 1. ed. |
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| id | DE-604.BV002191228 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:41:49Z |
| institution | BVB |
| isbn | 0156016095 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001439320 |
| oclc_num | 10162639 |
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| physical | VIII, 223 S. graph. Darst. |
| publishDate | 1984 |
| publishDateSearch | 1984 |
| publishDateSort | 1984 |
| publisher | Harcourt, Brace, Jovanovich |
| record_format | marc |
| series2 | Harcourt Brace Jovanovich college outline series. |
| spelling | Hsu, Hwei P. Verfasser aut Applied Fourier analysis 1. ed. San Diego u.a. Harcourt, Brace, Jovanovich 1984 VIII, 223 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Harcourt Brace Jovanovich college outline series. Análise de fourier larpcal Fourier analysis Harmonische Analyse (DE-588)4023453-8 gnd rswk-swf Harmonische Analyse (DE-588)4023453-8 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001439320&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hsu, Hwei P. Applied Fourier analysis Análise de fourier larpcal Fourier analysis Harmonische Analyse (DE-588)4023453-8 gnd |
| subject_GND | (DE-588)4023453-8 |
| title | Applied Fourier analysis |
| title_auth | Applied Fourier analysis |
| title_exact_search | Applied Fourier analysis |
| title_full | Applied Fourier analysis |
| title_fullStr | Applied Fourier analysis |
| title_full_unstemmed | Applied Fourier analysis |
| title_short | Applied Fourier analysis |
| title_sort | applied fourier analysis |
| topic | Análise de fourier larpcal Fourier analysis Harmonische Analyse (DE-588)4023453-8 gnd |
| topic_facet | Análise de fourier Fourier analysis Harmonische Analyse |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001439320&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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