A first course in fourier analysis / (Record no. 519410)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 06066nam a22003498i 4500 |
| 001 - CONTROL NUMBER | |
| control field | CR9780511619700 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | UkCbUP |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20200124160250.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS--GENERAL INFORMATION | |
| fixed length control field | m|||||o||d|||||||| |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr|||||||||||| |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 090915s2007||||enk o ||1 0|eng|d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9780511619700 (ebook) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Cancelled/invalid ISBN | 9780521883405 (hardback) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Cancelled/invalid ISBN | 9780521709798 (paperback) |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | UkCbUP |
| Language of cataloging | eng |
| Description conventions | rda |
| Transcribing agency | UkCbUP |
| 050 00 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA403.5 |
| Item number | .K36 2007 |
| 082 00 - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 515/.2433 |
| Edition number | 22 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Kammler, David W., |
| Dates associated with a name | 1940- |
| Relator term | author. |
| 245 12 - TITLE STATEMENT | |
| Title | A first course in fourier analysis / |
| Statement of responsibility, etc | David W. Kammler. |
| 250 ## - EDITION STATEMENT | |
| Edition statement | Second edition. |
| 264 #1 - Production, Publication, Distribution, Manufacture, and Copyright Notice (R) | |
| Place of production, publication, distribution, manufacture (R) | Cambridge : |
| Name of producer, publisher, distributor, manufacturer (R) | Cambridge University Press, |
| Date of production, publication, distribution, manufacture, or copyright notice | 2007. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource (1 volume (various pagings)) : |
| Other physical details | digital, PDF file(s). |
| 336 ## - Content Type (R) | |
| Content type term (R) | text |
| Content type code (R) | txt |
| Source (NR) | rdacontent |
| 337 ## - Media Type (R) | |
| Media type term (R) | computer |
| Media type code (R) | c |
| Source (NR) | rdamedia |
| 338 ## - Carrier Type (R) | |
| Carrier type term (R) | online resource |
| Carrier type code (R) | cr |
| Source (NR) | rdacarrier |
| 500 ## - GENERAL NOTE | |
| General note | Title from publisher's bibliographic system (viewed on 05 Oct 2015). |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 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. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc | 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 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Fourier analysis. |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Display text | Print version: |
| International Standard Book Number | 9780521883405 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://doi.org/10.1017/CBO9780511619700">https://doi.org/10.1017/CBO9780511619700</a> |
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