Fourier transformation for pedestrians:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English German |
| Published: |
Berlin ; Heidelberg ; New York
Springer
2006
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 201 S. graph. Darst. 24 cm |
| ISBN: | 9783540231653 354023165X |
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Record in the Search Index
| _version_ | 1804135391686557696 |
|---|---|
| adam_text | T. BUTZ FOURIER TRANSFORMATION FOR PEDESTRIANS WITH 117 FIGURES 4Y
SPRINGER CONTENTS INTRODUCTION 1 1 FOURIER SERIES 3 1.1 FOURIER SERIES 3
1.1.1 EVEN AND ODD FUNCTIONS 3 1.1.2 DEFINITION OF THE FOURIER SERIES 4
1.1.3 CALCULATION OF THE FOURIER COEFFICIENTS 6 1.1.4 FOURIER SERIES IN
COMPLEX NOTATION 11 1.2 THEOREMS AND RULES 13 1.2.1 LINEARITY THEOREM 13
1.2.2 THE FIRST SHIFTING RULE 14 1.2.3 THE SECOND SHIFTING RULE 17 1.2.4
SCALING THEOREM 21 1.3 PARTIAL SUMS, BESSEL S INEQUALITY, PARSEVAL S
EQUATION 21 1.4 GIBBS PHENOMENON 24 1.4.1 DIRICHLET S INTEGRAL KERNEL
24 1.4.2 INTEGRAL NOTATION OF PARTIAL SUMS 26 1.4.3 GIBBS OVERSHOOT 27
PLAYGROUND 30 2 CONTINUOUS FOURIER TRANSFORMATION 33 2.1 CONTINUOUS
FOURIER TRANSFORMATION 33 2.1.1 EVEN AND ODD FUNCTIONS 33 2.1.2 THE
6-FUNCTION 34 2.1.3 FORWARD AND INVERSE TRANSFORMATION 35 2.1.4 POLAR
REPRESENTATION OF THE FOURIER TRANSFORM 40 2.2 THEOREMS AND RULES 42
2.2.1 LINEARITY THEOREM 42 2.2.2 THE FIRST SHIFTING RULE 42 2.2.3, THE
SECOND SHIFTING RULE 43 2.2.4 SCALING THEOREM 44 2.3 CONVOLUTION, CROSS
CORRELATION, AUTOCORRELATION, PARSEVAL S THEOREM 46 2.3.1 CONVOLUTION 46
2.3.2 CROSS CORRELATION 55 XII CONTENTS 2.3.3 AUTOCORRELATION 56 2.3.4
PARSEVAL S THEOREM 57 2.4 FOURIER TRANSFORMATION OF DERIVATIVES 58 2.5
PITFALLS 60 2.5.1 TURN 1 INTO 3 60 2.5.2 TRUNCATION ERROR 63
PLAYGROUND 66 3 WINDOW FUNCTIONS 69 3.1 THE RECTANGULAR WINDOW 69 3.1.1
ZEROS 70 3.1.2 INTENSITY AT THE CENTRAL PEAK 70 3.1.3 SIDELOBE
SUPPRESSION 71 3.1.4 3 DB-BANDWIDTH 72 3.1.5 ASYMPTOTIC BEHAVIOUR OF
SIDELOBES 73 3.2 THE TRIANGULAR WINDOW (FEJER WINDOW) 73 3.3 THE COSINE
WINDOW 74 3.4 THE COS 2 -WINDOW (HANNING) 75 3.5 THE HAMMING WINDOW 77
3.6 THE TRIPLET WINDOW 78 3.7 THE GAUSS WINDOW 79 3.8 THE KAISER-BESSEL
WINDOW 80 3.9 THE BLACKMAN-HARRIS WINDOW 81 3.10 OVERVIEW OVER WINDOW
FUNCTIONS 84 3.11 WINDOWING OR CONVOLUTION? 87 PLAYGROUND 88 4 DISCRETE
FOURIER TRANSFORMATION 89 4.1 DISCRETE FOURIER TRANSFORMATION 89 4.1.1
EVEN AND ODD SERIES AND WRAP-AROUND 89 4.1.2 THE KRONECKER SYMBOL OR THE
DISCRETE 5-FUNCTION . . 90 4.1.3 DEFINITION OF THE DISCRETE FOURIER
TRANSFORMATION 92 4.2 THEOREMS AND RULES 96 4.2.1 LINEARITY THEOREM 96
4.2.2 THE FIRST SHIFTING RULE 96 4.2.3 THE SECOND SHIFTING RULE 97 4.2.4
SCALING RULE/NYQUIST FREQUENCY 98 4.3 CONVOLUTION, CROSS CORRELATION,
AUTOCORRELATION, PARSEVAL S THEOREM 99 4.3.1 CONVOLUTION , 100 4.3.2
CROSS CORRELATION 103 4.3.3 AUTOCORRELATION 104 4.3.4 PARSEVAL S THEOREM
104 4.4 THE SAMPLING THEOREM 105 4.5 DATA MIRRORING 109 CONTENTS XIII
4.6 ZERO-PADDING 112 4.7 FAST FOURIER TRANSFORMATION (FFT) 118
PLAYGROUND 126 5 FILTER EFFECT IN DIGITAL DATA PROCESSING 131 5.1
TRANSFER FUNCTION 131 5.2 LOW-PASS, HIGH-PASS, BAND-PASS, NOTCH FILTER
132 5.3 SHIFTING DATA 139 5.4 DATA COMPRESSION 141 5.5 DIFFERENTIATION
OF DISCRETE DATA 141 5.6 INTEGRATION OF DISCRETE DATA 143 PLAYGROUND 147
APPENDIX: SOLUTIONS 149 REFERENCES 197 INDEX 199 I
|
| adam_txt |
T. BUTZ FOURIER TRANSFORMATION FOR PEDESTRIANS WITH 117 FIGURES 4Y
SPRINGER CONTENTS INTRODUCTION 1 1 FOURIER SERIES 3 1.1 FOURIER SERIES 3
1.1.1 EVEN AND ODD FUNCTIONS 3 1.1.2 DEFINITION OF THE FOURIER SERIES 4
1.1.3 CALCULATION OF THE FOURIER COEFFICIENTS 6 1.1.4 FOURIER SERIES IN
COMPLEX NOTATION 11 1.2 THEOREMS AND RULES 13 1.2.1 LINEARITY THEOREM 13
1.2.2 THE FIRST SHIFTING RULE 14 1.2.3 THE SECOND SHIFTING RULE 17 1.2.4
SCALING THEOREM 21 1.3 PARTIAL SUMS, BESSEL'S INEQUALITY, PARSEVAL'S
EQUATION 21 1.4 GIBBS' PHENOMENON 24 1.4.1 DIRICHLET'S INTEGRAL KERNEL
24 1.4.2 INTEGRAL NOTATION OF PARTIAL SUMS 26 1.4.3 GIBBS' OVERSHOOT 27
PLAYGROUND 30 2 CONTINUOUS FOURIER TRANSFORMATION 33 2.1 CONTINUOUS
FOURIER TRANSFORMATION 33 2.1.1 EVEN AND ODD FUNCTIONS 33 2.1.2 THE
6-FUNCTION 34 2.1.3 FORWARD AND INVERSE TRANSFORMATION 35 2.1.4 POLAR
REPRESENTATION OF THE FOURIER TRANSFORM 40 2.2 THEOREMS AND RULES 42
2.2.1 LINEARITY THEOREM 42 2.2.2 THE FIRST SHIFTING RULE 42 2.2.3, THE
SECOND SHIFTING RULE 43 2.2.4 SCALING THEOREM 44 2.3 CONVOLUTION, CROSS
CORRELATION, AUTOCORRELATION, PARSEVAL'S THEOREM 46 2.3.1 CONVOLUTION 46
2.3.2 CROSS CORRELATION 55 XII CONTENTS 2.3.3 AUTOCORRELATION 56 2.3.4
PARSEVAL'S THEOREM 57 2.4 FOURIER TRANSFORMATION OF DERIVATIVES 58 2.5
PITFALLS 60 2.5.1 "TURN 1 INTO 3" 60 2.5.2 TRUNCATION ERROR 63
PLAYGROUND 66 3 WINDOW FUNCTIONS 69 3.1 THE RECTANGULAR WINDOW 69 3.1.1
ZEROS 70 3.1.2 INTENSITY AT THE CENTRAL PEAK 70 3.1.3 SIDELOBE
SUPPRESSION 71 3.1.4 3 DB-BANDWIDTH 72 3.1.5 ASYMPTOTIC BEHAVIOUR OF
SIDELOBES 73 3.2 THE TRIANGULAR WINDOW (FEJER WINDOW) 73 3.3 THE COSINE
WINDOW 74 3.4 THE COS 2 -WINDOW (HANNING) 75 3.5 THE HAMMING WINDOW 77
3.6 THE TRIPLET WINDOW 78 3.7 THE GAUSS WINDOW 79 3.8 THE KAISER-BESSEL
WINDOW 80 3.9 THE BLACKMAN-HARRIS WINDOW 81 3.10 OVERVIEW OVER WINDOW
FUNCTIONS 84 3.11 WINDOWING OR CONVOLUTION? 87 PLAYGROUND 88 4 DISCRETE
FOURIER TRANSFORMATION 89 4.1 DISCRETE FOURIER TRANSFORMATION 89 4.1.1
EVEN AND ODD SERIES AND WRAP-AROUND 89 4.1.2 THE KRONECKER SYMBOL OR THE
"DISCRETE 5-FUNCTION" . . 90 4.1.3 DEFINITION OF THE DISCRETE FOURIER
TRANSFORMATION 92 4.2 THEOREMS AND RULES 96 4.2.1 LINEARITY THEOREM 96
4.2.2 THE FIRST SHIFTING RULE 96 4.2.3 THE SECOND SHIFTING RULE 97 4.2.4
SCALING RULE/NYQUIST FREQUENCY 98 4.3 CONVOLUTION, CROSS CORRELATION,
AUTOCORRELATION, PARSEVAL'S THEOREM 99 4.3.1 CONVOLUTION , 100 4.3.2
CROSS CORRELATION 103 4.3.3 AUTOCORRELATION 104 4.3.4 PARSEVAL'S THEOREM
104 4.4 THE SAMPLING THEOREM 105 4.5 DATA MIRRORING 109 CONTENTS XIII
4.6 ZERO-PADDING 112 4.7 FAST FOURIER TRANSFORMATION (FFT) 118
PLAYGROUND 126 5 FILTER EFFECT IN DIGITAL DATA PROCESSING 131 5.1
TRANSFER FUNCTION 131 5.2 LOW-PASS, HIGH-PASS, BAND-PASS, NOTCH FILTER
132 5.3 SHIFTING DATA 139 5.4 DATA COMPRESSION 141 5.5 DIFFERENTIATION
OF DISCRETE DATA 141 5.6 INTEGRATION OF DISCRETE DATA 143 PLAYGROUND 147
APPENDIX: SOLUTIONS 149 REFERENCES 197 INDEX 199 I |
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| index_date | 2024-07-02T14:49:24Z |
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| isbn | 9783540231653 354023165X |
| language | English German |
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| physical | XIII, 201 S. graph. Darst. 24 cm |
| publishDate | 2006 |
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| spelling | Butz, Tilman 1945- Verfasser (DE-588)120405792 aut Fourier transformation for pedestrians T. Butz Berlin ; Heidelberg ; New York Springer 2006 XIII, 201 S. graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Fourier, Transformations de Fourier transformations Fourier-Transformation (DE-588)4018014-1 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Fourier-Transformation (DE-588)4018014-1 s 1\p DE-604 Paralle Sprachausgabe deutsch Butz, Tilman Fouriertransformation für Fußgänger HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014822780&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Butz, Tilman 1945- Fourier transformation for pedestrians Fourier, Transformations de Fourier transformations Fourier-Transformation (DE-588)4018014-1 gnd |
| subject_GND | (DE-588)4018014-1 (DE-588)4123623-3 |
| title | Fourier transformation for pedestrians |
| title_auth | Fourier transformation for pedestrians |
| title_exact_search | Fourier transformation for pedestrians |
| title_exact_search_txtP | Fourier transformation for pedestrians |
| title_full | Fourier transformation for pedestrians T. Butz |
| title_fullStr | Fourier transformation for pedestrians T. Butz |
| title_full_unstemmed | Fourier transformation for pedestrians T. Butz |
| title_short | Fourier transformation for pedestrians |
| title_sort | fourier transformation for pedestrians |
| topic | Fourier, Transformations de Fourier transformations Fourier-Transformation (DE-588)4018014-1 gnd |
| topic_facet | Fourier, Transformations de Fourier transformations Fourier-Transformation Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014822780&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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