Musimathics: the mathematical foundations of music 2 The mathematical foundations of music
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge, Mass. [u.a.]
MIT Press
2007
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 562 S. graph. Darst. |
| ISBN: | 0262122855 9780262122856 |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804136449469054976 |
|---|---|
| adam_text | Contents
Foreword by John Chowning
Preface
Acknowledgments
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
1.10
1.11
1.12
1.13
1.14
Summary
2
2.1
2.2
2.3
2.4 de Moivre s
2.5
2.6
2.7
Graphing Complex Signals
2.8
Spectra of Complex Sampled Signals
2.9
Multiplying Phasors
2.10
Graphing Complex Spectra
2.11
Analytic Signals
Summary
3
Spectral Analysis and Synthesis
3.1
Introduction to the Fourier Transform
3.2
Discrete Fourier Transform
3.3
Discrete Fourier Transfom in Action
3.4
Inverse Discrete Fourier Transform
3.5
Analyzing Real-World Signals
3.6
Windowing
3.7
Fast Fourier Transform
3.8
Properties of the Discrete Fourier Transform
3.9
A Practical Hubert Transform
Summary
4
Convolution
4.1
Rolling Shutter Camera
4.2
Defining Convolution
4.3
Numerical Examples of Convolution
4.4
Convolving Spectra
4.5
Convolving Signals
4.6
Convolution and the Fourier Transform
4.7
Domain Symmetry between Signals and Spectra
4.8
Convolution and Sampling Theory
4.9
Convolution and Windowing
4.10
Correlation Functions
Summary
Suggested Reading
5
Filtering
5.1
Tape Recorder as a Model of Filtering
5.2
Introduction to Filtering
5.3
A Simple Filter
5.4
Finding the Frequency Response
5.5
Linearity and Time
5.6
FIR Filters
Contents
86
87
89
92
95
100
103
103
114
125
134
138
141
145
147
154
156
159
159
161
163
168
172
180
180
185
187
191
193
194
195
195
199
201
203
217
218
Contents ix
5.7 IIR Filters 218
5.8
5.9 Time Domain
5.10
5.11
5.12
5.13
Summary
6
6.1
6.2
6.3
Summary
7
7.1
7.2
7.3
7.4
Summary
8
8.1
8.2
8.3
8.4
8.5
8.6
8.7
8.8
8.9
8.10
8.11
8.12
8.13
8.14
8.15
Summary
Suggested Reading
x
9
9.1
9.2
9.3
9.4
9.5
9.6
9.7
9.8
Summary
10
10.1
10.2
10.3
10.4
10.5
Summary
Suggested Reading
Epilogue
Appendix
A.I About Algebra
A.2 About Trigonometry
A.3 Series and Summations
A.4 Trigonometric Identities
A.5 Modulo Arithmetic and Congruence
A.
A.7 Walsh-Hadamard Transform
A.8 Sampling, Reconstruction, and the Sine Function
A.9 Fourier Shift Theorem
A.
A.I
Notes
Glossary
References
Index of Equations and Mathematical Formulas
Subject Index
|
| adam_txt |
Contents
Foreword by John Chowning
Preface
Acknowledgments
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
1.10
1.11
1.12
1.13
1.14
Summary
2
2.1
2.2
2.3
2.4 de Moivre's
2.5
2.6
2.7
Graphing Complex Signals
2.8
Spectra of Complex Sampled Signals
2.9
Multiplying Phasors
2.10
Graphing Complex Spectra
2.11
Analytic Signals
Summary
3
Spectral Analysis and Synthesis
3.1
Introduction to the Fourier Transform
3.2
Discrete Fourier Transform
3.3
Discrete Fourier Transfom in Action
3.4
Inverse Discrete Fourier Transform
3.5
Analyzing Real-World Signals
3.6
Windowing
3.7
Fast Fourier Transform
3.8
Properties of the Discrete Fourier Transform
3.9
A Practical Hubert Transform
Summary
4
Convolution
4.1
Rolling Shutter Camera
4.2
Defining Convolution
4.3
Numerical Examples of Convolution
4.4
Convolving Spectra
4.5
Convolving Signals
4.6
Convolution and the Fourier Transform
4.7
Domain Symmetry between Signals and Spectra
4.8
Convolution and Sampling Theory
4.9
Convolution and Windowing
4.10
Correlation Functions
Summary
Suggested Reading
5
Filtering
5.1
Tape Recorder as a Model of Filtering
5.2
Introduction to Filtering
5.3
A Simple Filter
5.4
Finding the Frequency Response
5.5
Linearity and Time
5.6
FIR Filters
Contents
86
87
89
92
95
100
103
103
114
125
134
138
141
145
147
154
156
159
159
161
163
168
172
180
180
185
187
191
193
194
195
195
199
201
203
217
218
Contents ix
5.7 IIR Filters 218
5.8
5.9 Time Domain
5.10
5.11
5.12
5.13
Summary
6
6.1
6.2
6.3
Summary
7
7.1
7.2
7.3
7.4
Summary
8
8.1
8.2
8.3
8.4
8.5
8.6
8.7
8.8
8.9
8.10
8.11
8.12
8.13
8.14
8.15
Summary
Suggested Reading
x
9
9.1
9.2
9.3
9.4
9.5
9.6
9.7
9.8
Summary
10
10.1
10.2
10.3
10.4
10.5
Summary
Suggested Reading
Epilogue
Appendix
A.I About Algebra
A.2 About Trigonometry
A.3 Series and Summations
A.4 Trigonometric Identities
A.5 Modulo Arithmetic and Congruence
A.
A.7 Walsh-Hadamard Transform
A.8 Sampling, Reconstruction, and the Sine Function
A.9 Fourier Shift Theorem
A.
A.I
Notes
Glossary
References
Index of Equations and Mathematical Formulas
Subject Index |
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| discipline | Mathematik Musikwissenschaft |
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| spelling | Loy, Gareth 1945- Verfasser (DE-588)124732763 aut Musimathics the mathematical foundations of music 2 The mathematical foundations of music Gareth Loy Cambridge, Mass. [u.a.] MIT Press 2007 XIV, 562 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematik (DE-588)4037944-9 gnd rswk-swf Akustik (DE-588)4000988-9 gnd rswk-swf Akustik (DE-588)4000988-9 s Mathematik (DE-588)4037944-9 s DE-604 (DE-604)BV021760055 2 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015599932&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
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| title | Musimathics the mathematical foundations of music |
| title_auth | Musimathics the mathematical foundations of music |
| title_exact_search | Musimathics the mathematical foundations of music |
| title_exact_search_txtP | Musimathics the mathematical foundations of music |
| title_full | Musimathics the mathematical foundations of music 2 The mathematical foundations of music Gareth Loy |
| title_fullStr | Musimathics the mathematical foundations of music 2 The mathematical foundations of music Gareth Loy |
| title_full_unstemmed | Musimathics the mathematical foundations of music 2 The mathematical foundations of music Gareth Loy |
| title_short | Musimathics |
| title_sort | musimathics the mathematical foundations of music the mathematical foundations of music |
| title_sub | the mathematical foundations of music |
| topic | Mathematik (DE-588)4037944-9 gnd Akustik (DE-588)4000988-9 gnd |
| topic_facet | Mathematik Akustik |
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