A first course in Fourier analysis:
This book provides a meaningful resource for applied mathematics through Fourier analysis. It develops a unified theory of discrete and continuous (univariate) Fourier analysis, the fast Fourier transform, and a powerful elementary theory of generalized functions and shows how these mathematical ide...
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2007
|
| Edition: | Second edition |
| Subjects: | |
| Online Access: | BSB01 FHN01 UBY01 Volltext |
| Summary: | This book provides a meaningful resource for applied mathematics through Fourier analysis. It develops a unified theory of discrete and continuous (univariate) Fourier analysis, the fast Fourier transform, and a powerful elementary theory of generalized functions and shows how these mathematical ideas can be used to study sampling theory, PDEs, probability, diffraction, musical tones, and wavelets. The book contains an unusually complete presentation of the Fourier transform calculus. It uses concepts from calculus to present an elementary theory of generalized functions. FT calculus and generalized functions are then used to study the wave equation, diffusion equation, and diffraction equation. Real-world applications of Fourier analysis are described in the chapter on musical tones. A valuable reference on Fourier analysis for a variety of students and scientific professionals, including mathematicians, physicists, chemists, geologists, electrical engineers, mechanical engineers, and others |
| Item Description: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Physical Description: | 1 online resource (1 volume (various pagings)) |
| ISBN: | 9780511619700 |
| DOI: | 10.1017/CBO9780511619700 |
Staff View
MARC
| LEADER | 00000nmm a2200000zc 4500 | ||
|---|---|---|---|
| 001 | BV043943063 | ||
| 003 | DE-604 | ||
| 005 | 20230214 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 161206s2007 |||| o||u| ||||||eng d | ||
| 020 | |a 9780511619700 |c Online |9 978-0-511-61970-0 | ||
| 024 | 7 | |a 10.1017/CBO9780511619700 |2 doi | |
| 035 | |a (ZDB-20-CBO)CR9780511619700 | ||
| 035 | |a (OCoLC)876433965 | ||
| 035 | |a (DE-599)BVBBV043943063 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-12 |a DE-92 |a DE-706 | ||
| 082 | 0 | |a 515/.2433 |2 22 | |
| 084 | |a SK 450 |0 (DE-625)143240: |2 rvk | ||
| 100 | 1 | |a Kammler, David W. |d 1940- |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a A first course in Fourier analysis |c David W. Kammler |
| 250 | |a Second edition | ||
| 264 | 1 | |a Cambridge |b Cambridge University Press |c 2007 | |
| 300 | |a 1 online resource (1 volume (various pagings)) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 500 | |a Title from publisher's bibliographic system (viewed on 05 Oct 2015) | ||
| 505 | 8 | |a part 1. The mathematical core. Chapter 1. Fourier's representation for functions on R, Tp, Z, and PN. 1.1. Synthesis and analysis equations ; 1.2. Examples of Fourier's representation ; 1.3. The Parseval identities and related results ; 1.4. The Fourier-Poisson cube ; 1.5. The validity of Fourier's representation ; Chapter 2. Convolution of functions on R, Tp, Z, and PN. 2.1. Formal definitions of f * g, F x g ; 2.2. Computation of f * g ; 2.3. Mathematical properties of the convolution product ; 2.4. Examples of convolution and correlation ; Further reading ; Exercises ; Chapter 3. The calculus for finding Fourier transformations of functions on R. 3.1. Using the definition to find Fourier transformations ; 3.2. Rules for finding Fourier transformations ; 3.3. Selected applications of the Fourier transform calculus ; Further reading ; Exercises ; Chapter 4. The calculus for finding Fourier transforms of functions of Tp, Z, and PN. 4.1. Fourier series ; 4.2. | |
| 505 | 8 | |a Selected applications of Fourier series ; 4.3. Discrete Fourier transformations ; 4.4. Selected applications of the DFT calculus ; Further reading ; Exercises ; Chapter 5. Operator identities associated with Fourier analysis ; 5.1. the concept of an operator identity ; 5.2. Operators generated by powers of F ; 5.3. Operators related to complex conjugation ; 5.4. Fourier transforms of operators ; 5.5. Rules for Hartley transforms ; 5.6. Hilbert transforms ; Further reading ; Exercises ; Chapter 6. The fact Fourier transform. 6.1. Pre-FFT computation of the DFT ; 6.2. Deprivation of the FFT via DFT rules ; 6.3. The bit reversal permutation ; 6.4. Sparse matric factorization of F when N = 2m ; 6.5. Sparse matric factorization of H when N = 2m ; 6.6. Sparse matric factorization of F when N = P1P2...Pm ; 6.7. Kronecker product factorization of F ; Further reading ; Exercises ; Chapter 7. Generalized functions on R. 7.1. The concept of a generalized function ; 7.2. | |
| 505 | 8 | |a Common generalized functions ; 7.3. Manipulation of generalized functions ; 7.4. Derivatives and simple differential equations ; 7.5. The Fourier transform calculus for generalized functions ; 7.6. Limits of generalized functions ; 7.7. Periodic generalized functions ; 7.8. Alternative definitions for generalized functions ; Further reading ; Exercises -- | |
| 505 | 8 | |a Part 2. Selected applications. Chapter 8. Sampling. 8.1. Sampling and interpolation ; 8.2. Reconstruction of f from its samples ; 8.3. Reconstruction of f from samples of a1 * f, a2 * f, ... ; 8.4. Approximation of almost bandlimited functions ; Further reading ; Exercises ; Chapter 9. Partial differential equations. 9.1. Introduction ; 9.2. The wave equation ; 9.3. The diffusion equation ; 9.4. The diffraction equation ; 9.5. Fast computation of frames for movies ; Further reading ; Exercises ; Chapter 10. Wavelets. 10.1. The Haar wavelets ; 10.2. Support-limited wavelets ; 10.3. Analysis and synthesis with Daubechies wavelets ; 10.4. Filter banks ; Further reading ; Exercises ; Chapter 11. Musical tones. 11.1. Basic concepts ; 11.2. Spectrograms ; 11.3. Additive synthesis of tones ; 11.4. FM synthesis of tones ; 11.5. Synthesis of tones from noise ; 11.6. Music with mathematical structure ; Further reading ; Exercises ; Chapter 12. Probability. 12.1. | |
| 505 | 8 | |a Probability density functions of R ; 12.2. Some mathematical tools ; 12.3. The characteristic function ; 12.4. Random variables ; 12.5. The central limit theorem ; Further reading ; Exercises -- Appendices. Appendix 1. The impact of Fourier analysis ; Appendix 2. Functions and their Fourier transforms ; Appendix 3. The Fourier transform calculus ; Appendix 4. Operators and their Fourier transforms ; Appendix 5. The Whittaker-Robinson flow chart for harmonic analysis ; Appendix 6. FORTRAN code for a randix 2 FFT ; Appendix 7. The standard normal probability distribution ; Appendix 8. Frequencies of the piano keyboard | |
| 520 | |a This book provides a meaningful resource for applied mathematics through Fourier analysis. It develops a unified theory of discrete and continuous (univariate) Fourier analysis, the fast Fourier transform, and a powerful elementary theory of generalized functions and shows how these mathematical ideas can be used to study sampling theory, PDEs, probability, diffraction, musical tones, and wavelets. The book contains an unusually complete presentation of the Fourier transform calculus. It uses concepts from calculus to present an elementary theory of generalized functions. FT calculus and generalized functions are then used to study the wave equation, diffusion equation, and diffraction equation. Real-world applications of Fourier analysis are described in the chapter on musical tones. A valuable reference on Fourier analysis for a variety of students and scientific professionals, including mathematicians, physicists, chemists, geologists, electrical engineers, mechanical engineers, and others | ||
| 650 | 4 | |a Fourier analysis | |
| 650 | 0 | 7 | |a Harmonische Analyse |0 (DE-588)4023453-8 |2 gnd |9 rswk-swf |
| 655 | 7 | |8 1\p |0 (DE-588)4123623-3 |a Lehrbuch |2 gnd-content | |
| 689 | 0 | 0 | |a Harmonische Analyse |0 (DE-588)4023453-8 |D s |
| 689 | 0 | |8 2\p |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |n Druckausgabe |z 978-0-521-70979-8 |
| 776 | 0 | 8 | |i Erscheint auch als |n Druckausgabe |z 978-0-521-88340-5 |
| 856 | 4 | 0 | |u https://doi.org/10.1017/CBO9780511619700 |x Verlag |z URL des Erstveröffentlichers |3 Volltext |
| 912 | |a ZDB-20-CBO | ||
| 999 | |a oai:aleph.bib-bvb.de:BVB01-029352034 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 883 | 1 | |8 2\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 966 | e | |u https://doi.org/10.1017/CBO9780511619700 |l BSB01 |p ZDB-20-CBO |q BSB_PDA_CBO |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1017/CBO9780511619700 |l FHN01 |p ZDB-20-CBO |q FHN_PDA_CBO |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1017/CBO9780511619700 |l UBY01 |p ZDB-20-CBO |q UBY_PDA_CBO_Kauf22 |x Verlag |3 Volltext | |
Record in the Search Index
| _version_ | 1804176886636478464 |
|---|---|
| any_adam_object | |
| author | Kammler, David W. 1940- |
| author_facet | Kammler, David W. 1940- |
| author_role | aut |
| author_sort | Kammler, David W. 1940- |
| author_variant | d w k dw dwk |
| building | Verbundindex |
| bvnumber | BV043943063 |
| classification_rvk | SK 450 |
| collection | ZDB-20-CBO |
| contents | part 1. The mathematical core. Chapter 1. Fourier's representation for functions on R, Tp, Z, and PN. 1.1. Synthesis and analysis equations ; 1.2. Examples of Fourier's representation ; 1.3. The Parseval identities and related results ; 1.4. The Fourier-Poisson cube ; 1.5. The validity of Fourier's representation ; Chapter 2. Convolution of functions on R, Tp, Z, and PN. 2.1. Formal definitions of f * g, F x g ; 2.2. Computation of f * g ; 2.3. Mathematical properties of the convolution product ; 2.4. Examples of convolution and correlation ; Further reading ; Exercises ; Chapter 3. The calculus for finding Fourier transformations of functions on R. 3.1. Using the definition to find Fourier transformations ; 3.2. Rules for finding Fourier transformations ; 3.3. Selected applications of the Fourier transform calculus ; Further reading ; Exercises ; Chapter 4. The calculus for finding Fourier transforms of functions of Tp, Z, and PN. 4.1. Fourier series ; 4.2. Selected applications of Fourier series ; 4.3. Discrete Fourier transformations ; 4.4. Selected applications of the DFT calculus ; Further reading ; Exercises ; Chapter 5. Operator identities associated with Fourier analysis ; 5.1. the concept of an operator identity ; 5.2. Operators generated by powers of F ; 5.3. Operators related to complex conjugation ; 5.4. Fourier transforms of operators ; 5.5. Rules for Hartley transforms ; 5.6. Hilbert transforms ; Further reading ; Exercises ; Chapter 6. The fact Fourier transform. 6.1. Pre-FFT computation of the DFT ; 6.2. Deprivation of the FFT via DFT rules ; 6.3. The bit reversal permutation ; 6.4. Sparse matric factorization of F when N = 2m ; 6.5. Sparse matric factorization of H when N = 2m ; 6.6. Sparse matric factorization of F when N = P1P2...Pm ; 6.7. Kronecker product factorization of F ; Further reading ; Exercises ; Chapter 7. Generalized functions on R. 7.1. The concept of a generalized function ; 7.2. Common generalized functions ; 7.3. Manipulation of generalized functions ; 7.4. Derivatives and simple differential equations ; 7.5. The Fourier transform calculus for generalized functions ; 7.6. Limits of generalized functions ; 7.7. Periodic generalized functions ; 7.8. Alternative definitions for generalized functions ; Further reading ; Exercises -- Part 2. Selected applications. Chapter 8. Sampling. 8.1. Sampling and interpolation ; 8.2. Reconstruction of f from its samples ; 8.3. Reconstruction of f from samples of a1 * f, a2 * f, ... ; 8.4. Approximation of almost bandlimited functions ; Further reading ; Exercises ; Chapter 9. Partial differential equations. 9.1. Introduction ; 9.2. The wave equation ; 9.3. The diffusion equation ; 9.4. The diffraction equation ; 9.5. Fast computation of frames for movies ; Further reading ; Exercises ; Chapter 10. Wavelets. 10.1. The Haar wavelets ; 10.2. Support-limited wavelets ; 10.3. Analysis and synthesis with Daubechies wavelets ; 10.4. Filter banks ; Further reading ; Exercises ; Chapter 11. Musical tones. 11.1. Basic concepts ; 11.2. Spectrograms ; 11.3. Additive synthesis of tones ; 11.4. FM synthesis of tones ; 11.5. Synthesis of tones from noise ; 11.6. Music with mathematical structure ; Further reading ; Exercises ; Chapter 12. Probability. 12.1. Probability density functions of R ; 12.2. Some mathematical tools ; 12.3. The characteristic function ; 12.4. Random variables ; 12.5. The central limit theorem ; Further reading ; Exercises -- Appendices. Appendix 1. The impact of Fourier analysis ; Appendix 2. Functions and their Fourier transforms ; Appendix 3. The Fourier transform calculus ; Appendix 4. Operators and their Fourier transforms ; Appendix 5. The Whittaker-Robinson flow chart for harmonic analysis ; Appendix 6. FORTRAN code for a randix 2 FFT ; Appendix 7. The standard normal probability distribution ; Appendix 8. Frequencies of the piano keyboard |
| ctrlnum | (ZDB-20-CBO)CR9780511619700 (OCoLC)876433965 (DE-599)BVBBV043943063 |
| dewey-full | 515/.2433 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.2433 |
| dewey-search | 515/.2433 |
| dewey-sort | 3515 42433 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511619700 |
| edition | Second edition |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>07098nmm a2200565zc 4500</leader><controlfield tag="001">BV043943063</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20230214 </controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">161206s2007 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780511619700</subfield><subfield code="c">Online</subfield><subfield code="9">978-0-511-61970-0</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1017/CBO9780511619700</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(ZDB-20-CBO)CR9780511619700</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)876433965</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV043943063</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-12</subfield><subfield code="a">DE-92</subfield><subfield code="a">DE-706</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515/.2433</subfield><subfield code="2">22</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 450</subfield><subfield code="0">(DE-625)143240:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Kammler, David W.</subfield><subfield code="d">1940-</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">A first course in Fourier analysis</subfield><subfield code="c">David W. Kammler</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">Second edition</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Cambridge</subfield><subfield code="b">Cambridge University Press</subfield><subfield code="c">2007</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (1 volume (various pagings))</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Title from publisher's bibliographic system (viewed on 05 Oct 2015)</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">part 1. The mathematical core. Chapter 1. Fourier's representation for functions on R, Tp, Z, and PN. 1.1. Synthesis and analysis equations ; 1.2. Examples of Fourier's representation ; 1.3. The Parseval identities and related results ; 1.4. The Fourier-Poisson cube ; 1.5. The validity of Fourier's representation ; Chapter 2. Convolution of functions on R, Tp, Z, and PN. 2.1. Formal definitions of f * g, F x g ; 2.2. Computation of f * g ; 2.3. Mathematical properties of the convolution product ; 2.4. Examples of convolution and correlation ; Further reading ; Exercises ; Chapter 3. The calculus for finding Fourier transformations of functions on R. 3.1. Using the definition to find Fourier transformations ; 3.2. Rules for finding Fourier transformations ; 3.3. Selected applications of the Fourier transform calculus ; Further reading ; Exercises ; Chapter 4. The calculus for finding Fourier transforms of functions of Tp, Z, and PN. 4.1. Fourier series ; 4.2. </subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">Selected applications of Fourier series ; 4.3. Discrete Fourier transformations ; 4.4. Selected applications of the DFT calculus ; Further reading ; Exercises ; Chapter 5. Operator identities associated with Fourier analysis ; 5.1. the concept of an operator identity ; 5.2. Operators generated by powers of F ; 5.3. Operators related to complex conjugation ; 5.4. Fourier transforms of operators ; 5.5. Rules for Hartley transforms ; 5.6. Hilbert transforms ; Further reading ; Exercises ; Chapter 6. The fact Fourier transform. 6.1. Pre-FFT computation of the DFT ; 6.2. Deprivation of the FFT via DFT rules ; 6.3. The bit reversal permutation ; 6.4. Sparse matric factorization of F when N = 2m ; 6.5. Sparse matric factorization of H when N = 2m ; 6.6. Sparse matric factorization of F when N = P1P2...Pm ; 6.7. Kronecker product factorization of F ; Further reading ; Exercises ; Chapter 7. Generalized functions on R. 7.1. The concept of a generalized function ; 7.2. </subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">Common generalized functions ; 7.3. Manipulation of generalized functions ; 7.4. Derivatives and simple differential equations ; 7.5. The Fourier transform calculus for generalized functions ; 7.6. Limits of generalized functions ; 7.7. Periodic generalized functions ; 7.8. Alternative definitions for generalized functions ; Further reading ; Exercises -- </subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">Part 2. Selected applications. Chapter 8. Sampling. 8.1. Sampling and interpolation ; 8.2. Reconstruction of f from its samples ; 8.3. Reconstruction of f from samples of a1 * f, a2 * f, ... ; 8.4. Approximation of almost bandlimited functions ; Further reading ; Exercises ; Chapter 9. Partial differential equations. 9.1. Introduction ; 9.2. The wave equation ; 9.3. The diffusion equation ; 9.4. The diffraction equation ; 9.5. Fast computation of frames for movies ; Further reading ; Exercises ; Chapter 10. Wavelets. 10.1. The Haar wavelets ; 10.2. Support-limited wavelets ; 10.3. Analysis and synthesis with Daubechies wavelets ; 10.4. Filter banks ; Further reading ; Exercises ; Chapter 11. Musical tones. 11.1. Basic concepts ; 11.2. Spectrograms ; 11.3. Additive synthesis of tones ; 11.4. FM synthesis of tones ; 11.5. Synthesis of tones from noise ; 11.6. Music with mathematical structure ; Further reading ; Exercises ; Chapter 12. Probability. 12.1. </subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">Probability density functions of R ; 12.2. Some mathematical tools ; 12.3. The characteristic function ; 12.4. Random variables ; 12.5. The central limit theorem ; Further reading ; Exercises -- Appendices. Appendix 1. The impact of Fourier analysis ; Appendix 2. Functions and their Fourier transforms ; Appendix 3. The Fourier transform calculus ; Appendix 4. Operators and their Fourier transforms ; Appendix 5. The Whittaker-Robinson flow chart for harmonic analysis ; Appendix 6. FORTRAN code for a randix 2 FFT ; Appendix 7. The standard normal probability distribution ; Appendix 8. Frequencies of the piano keyboard</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">This book provides a meaningful resource for applied mathematics through Fourier analysis. It develops a unified theory of discrete and continuous (univariate) Fourier analysis, the fast Fourier transform, and a powerful elementary theory of generalized functions and shows how these mathematical ideas can be used to study sampling theory, PDEs, probability, diffraction, musical tones, and wavelets. The book contains an unusually complete presentation of the Fourier transform calculus. It uses concepts from calculus to present an elementary theory of generalized functions. FT calculus and generalized functions are then used to study the wave equation, diffusion equation, and diffraction equation. Real-world applications of Fourier analysis are described in the chapter on musical tones. A valuable reference on Fourier analysis for a variety of students and scientific professionals, including mathematicians, physicists, chemists, geologists, electrical engineers, mechanical engineers, and others</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Fourier analysis</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Harmonische Analyse</subfield><subfield code="0">(DE-588)4023453-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="655" ind1=" " ind2="7"><subfield code="8">1\p</subfield><subfield code="0">(DE-588)4123623-3</subfield><subfield code="a">Lehrbuch</subfield><subfield code="2">gnd-content</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Harmonische Analyse</subfield><subfield code="0">(DE-588)4023453-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">2\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Druckausgabe</subfield><subfield code="z">978-0-521-70979-8</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Druckausgabe</subfield><subfield code="z">978-0-521-88340-5</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1017/CBO9780511619700</subfield><subfield code="x">Verlag</subfield><subfield code="z">URL des Erstveröffentlichers</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-20-CBO</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-029352034</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">2\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1017/CBO9780511619700</subfield><subfield code="l">BSB01</subfield><subfield code="p">ZDB-20-CBO</subfield><subfield code="q">BSB_PDA_CBO</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1017/CBO9780511619700</subfield><subfield code="l">FHN01</subfield><subfield code="p">ZDB-20-CBO</subfield><subfield code="q">FHN_PDA_CBO</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1017/CBO9780511619700</subfield><subfield code="l">UBY01</subfield><subfield code="p">ZDB-20-CBO</subfield><subfield code="q">UBY_PDA_CBO_Kauf22</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield></record></collection> |
| genre | 1\p (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV043943063 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:18Z |
| institution | BVB |
| isbn | 9780511619700 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029352034 |
| oclc_num | 876433965 |
| open_access_boolean | |
| owner | DE-12 DE-92 DE-706 |
| owner_facet | DE-12 DE-92 DE-706 |
| physical | 1 online resource (1 volume (various pagings)) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO FHN_PDA_CBO ZDB-20-CBO UBY_PDA_CBO_Kauf22 |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Cambridge University Press |
| record_format | marc |
| spelling | Kammler, David W. 1940- Verfasser aut A first course in Fourier analysis David W. Kammler Second edition Cambridge Cambridge University Press 2007 1 online resource (1 volume (various pagings)) txt rdacontent c rdamedia cr rdacarrier Title from publisher's bibliographic system (viewed on 05 Oct 2015) part 1. The mathematical core. Chapter 1. Fourier's representation for functions on R, Tp, Z, and PN. 1.1. Synthesis and analysis equations ; 1.2. Examples of Fourier's representation ; 1.3. The Parseval identities and related results ; 1.4. The Fourier-Poisson cube ; 1.5. The validity of Fourier's representation ; Chapter 2. Convolution of functions on R, Tp, Z, and PN. 2.1. Formal definitions of f * g, F x g ; 2.2. Computation of f * g ; 2.3. Mathematical properties of the convolution product ; 2.4. Examples of convolution and correlation ; Further reading ; Exercises ; Chapter 3. The calculus for finding Fourier transformations of functions on R. 3.1. Using the definition to find Fourier transformations ; 3.2. Rules for finding Fourier transformations ; 3.3. Selected applications of the Fourier transform calculus ; Further reading ; Exercises ; Chapter 4. The calculus for finding Fourier transforms of functions of Tp, Z, and PN. 4.1. Fourier series ; 4.2. Selected applications of Fourier series ; 4.3. Discrete Fourier transformations ; 4.4. Selected applications of the DFT calculus ; Further reading ; Exercises ; Chapter 5. Operator identities associated with Fourier analysis ; 5.1. the concept of an operator identity ; 5.2. Operators generated by powers of F ; 5.3. Operators related to complex conjugation ; 5.4. Fourier transforms of operators ; 5.5. Rules for Hartley transforms ; 5.6. Hilbert transforms ; Further reading ; Exercises ; Chapter 6. The fact Fourier transform. 6.1. Pre-FFT computation of the DFT ; 6.2. Deprivation of the FFT via DFT rules ; 6.3. The bit reversal permutation ; 6.4. Sparse matric factorization of F when N = 2m ; 6.5. Sparse matric factorization of H when N = 2m ; 6.6. Sparse matric factorization of F when N = P1P2...Pm ; 6.7. Kronecker product factorization of F ; Further reading ; Exercises ; Chapter 7. Generalized functions on R. 7.1. The concept of a generalized function ; 7.2. Common generalized functions ; 7.3. Manipulation of generalized functions ; 7.4. Derivatives and simple differential equations ; 7.5. The Fourier transform calculus for generalized functions ; 7.6. Limits of generalized functions ; 7.7. Periodic generalized functions ; 7.8. Alternative definitions for generalized functions ; Further reading ; Exercises -- Part 2. Selected applications. Chapter 8. Sampling. 8.1. Sampling and interpolation ; 8.2. Reconstruction of f from its samples ; 8.3. Reconstruction of f from samples of a1 * f, a2 * f, ... ; 8.4. Approximation of almost bandlimited functions ; Further reading ; Exercises ; Chapter 9. Partial differential equations. 9.1. Introduction ; 9.2. The wave equation ; 9.3. The diffusion equation ; 9.4. The diffraction equation ; 9.5. Fast computation of frames for movies ; Further reading ; Exercises ; Chapter 10. Wavelets. 10.1. The Haar wavelets ; 10.2. Support-limited wavelets ; 10.3. Analysis and synthesis with Daubechies wavelets ; 10.4. Filter banks ; Further reading ; Exercises ; Chapter 11. Musical tones. 11.1. Basic concepts ; 11.2. Spectrograms ; 11.3. Additive synthesis of tones ; 11.4. FM synthesis of tones ; 11.5. Synthesis of tones from noise ; 11.6. Music with mathematical structure ; Further reading ; Exercises ; Chapter 12. Probability. 12.1. Probability density functions of R ; 12.2. Some mathematical tools ; 12.3. The characteristic function ; 12.4. Random variables ; 12.5. The central limit theorem ; Further reading ; Exercises -- Appendices. Appendix 1. The impact of Fourier analysis ; Appendix 2. Functions and their Fourier transforms ; Appendix 3. The Fourier transform calculus ; Appendix 4. Operators and their Fourier transforms ; Appendix 5. The Whittaker-Robinson flow chart for harmonic analysis ; Appendix 6. FORTRAN code for a randix 2 FFT ; Appendix 7. The standard normal probability distribution ; Appendix 8. Frequencies of the piano keyboard This book provides a meaningful resource for applied mathematics through Fourier analysis. It develops a unified theory of discrete and continuous (univariate) Fourier analysis, the fast Fourier transform, and a powerful elementary theory of generalized functions and shows how these mathematical ideas can be used to study sampling theory, PDEs, probability, diffraction, musical tones, and wavelets. The book contains an unusually complete presentation of the Fourier transform calculus. It uses concepts from calculus to present an elementary theory of generalized functions. FT calculus and generalized functions are then used to study the wave equation, diffusion equation, and diffraction equation. Real-world applications of Fourier analysis are described in the chapter on musical tones. A valuable reference on Fourier analysis for a variety of students and scientific professionals, including mathematicians, physicists, chemists, geologists, electrical engineers, mechanical engineers, and others Fourier analysis Harmonische Analyse (DE-588)4023453-8 gnd rswk-swf 1\p (DE-588)4123623-3 Lehrbuch gnd-content Harmonische Analyse (DE-588)4023453-8 s 2\p DE-604 Erscheint auch als Druckausgabe 978-0-521-70979-8 Erscheint auch als Druckausgabe 978-0-521-88340-5 https://doi.org/10.1017/CBO9780511619700 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Kammler, David W. 1940- A first course in Fourier analysis part 1. The mathematical core. Chapter 1. Fourier's representation for functions on R, Tp, Z, and PN. 1.1. Synthesis and analysis equations ; 1.2. Examples of Fourier's representation ; 1.3. The Parseval identities and related results ; 1.4. The Fourier-Poisson cube ; 1.5. The validity of Fourier's representation ; Chapter 2. Convolution of functions on R, Tp, Z, and PN. 2.1. Formal definitions of f * g, F x g ; 2.2. Computation of f * g ; 2.3. Mathematical properties of the convolution product ; 2.4. Examples of convolution and correlation ; Further reading ; Exercises ; Chapter 3. The calculus for finding Fourier transformations of functions on R. 3.1. Using the definition to find Fourier transformations ; 3.2. Rules for finding Fourier transformations ; 3.3. Selected applications of the Fourier transform calculus ; Further reading ; Exercises ; Chapter 4. The calculus for finding Fourier transforms of functions of Tp, Z, and PN. 4.1. Fourier series ; 4.2. Selected applications of Fourier series ; 4.3. Discrete Fourier transformations ; 4.4. Selected applications of the DFT calculus ; Further reading ; Exercises ; Chapter 5. Operator identities associated with Fourier analysis ; 5.1. the concept of an operator identity ; 5.2. Operators generated by powers of F ; 5.3. Operators related to complex conjugation ; 5.4. Fourier transforms of operators ; 5.5. Rules for Hartley transforms ; 5.6. Hilbert transforms ; Further reading ; Exercises ; Chapter 6. The fact Fourier transform. 6.1. Pre-FFT computation of the DFT ; 6.2. Deprivation of the FFT via DFT rules ; 6.3. The bit reversal permutation ; 6.4. Sparse matric factorization of F when N = 2m ; 6.5. Sparse matric factorization of H when N = 2m ; 6.6. Sparse matric factorization of F when N = P1P2...Pm ; 6.7. Kronecker product factorization of F ; Further reading ; Exercises ; Chapter 7. Generalized functions on R. 7.1. The concept of a generalized function ; 7.2. Common generalized functions ; 7.3. Manipulation of generalized functions ; 7.4. Derivatives and simple differential equations ; 7.5. The Fourier transform calculus for generalized functions ; 7.6. Limits of generalized functions ; 7.7. Periodic generalized functions ; 7.8. Alternative definitions for generalized functions ; Further reading ; Exercises -- Part 2. Selected applications. Chapter 8. Sampling. 8.1. Sampling and interpolation ; 8.2. Reconstruction of f from its samples ; 8.3. Reconstruction of f from samples of a1 * f, a2 * f, ... ; 8.4. Approximation of almost bandlimited functions ; Further reading ; Exercises ; Chapter 9. Partial differential equations. 9.1. Introduction ; 9.2. The wave equation ; 9.3. The diffusion equation ; 9.4. The diffraction equation ; 9.5. Fast computation of frames for movies ; Further reading ; Exercises ; Chapter 10. Wavelets. 10.1. The Haar wavelets ; 10.2. Support-limited wavelets ; 10.3. Analysis and synthesis with Daubechies wavelets ; 10.4. Filter banks ; Further reading ; Exercises ; Chapter 11. Musical tones. 11.1. Basic concepts ; 11.2. Spectrograms ; 11.3. Additive synthesis of tones ; 11.4. FM synthesis of tones ; 11.5. Synthesis of tones from noise ; 11.6. Music with mathematical structure ; Further reading ; Exercises ; Chapter 12. Probability. 12.1. Probability density functions of R ; 12.2. Some mathematical tools ; 12.3. The characteristic function ; 12.4. Random variables ; 12.5. The central limit theorem ; Further reading ; Exercises -- Appendices. Appendix 1. The impact of Fourier analysis ; Appendix 2. Functions and their Fourier transforms ; Appendix 3. The Fourier transform calculus ; Appendix 4. Operators and their Fourier transforms ; Appendix 5. The Whittaker-Robinson flow chart for harmonic analysis ; Appendix 6. FORTRAN code for a randix 2 FFT ; Appendix 7. The standard normal probability distribution ; Appendix 8. Frequencies of the piano keyboard Fourier analysis Harmonische Analyse (DE-588)4023453-8 gnd |
| subject_GND | (DE-588)4023453-8 (DE-588)4123623-3 |
| title | A first course in Fourier analysis |
| title_auth | A first course in Fourier analysis |
| title_exact_search | A first course in Fourier analysis |
| title_full | A first course in Fourier analysis David W. Kammler |
| title_fullStr | A first course in Fourier analysis David W. Kammler |
| title_full_unstemmed | A first course in Fourier analysis David W. Kammler |
| title_short | A first course in Fourier analysis |
| title_sort | a first course in fourier analysis |
| topic | Fourier analysis Harmonische Analyse (DE-588)4023453-8 gnd |
| topic_facet | Fourier analysis Harmonische Analyse Lehrbuch |
| url | https://doi.org/10.1017/CBO9780511619700 |
| work_keys_str_mv | AT kammlerdavidw afirstcourseinfourieranalysis |