A first course in fourier analysis /
"A modern introduction to Fourier analysis and selected applications which shows how these mathematical ideas can be used to study sampling theory, PDEs, probability, diffraction, musical tones, and wavelets. Aimed at students from the physical, engineering, and mathematical sciences who have m...
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| Format: | Book |
| Language: | English |
| Published: |
Cambridge ; New York :
Cambridge University Press,
©2007.
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| Edition: | Rev. ed. |
| Series: | MyiLibrary.
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| Subjects: |
MARC
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| 100 | 1 | |a Kammler, David W., |d 1940- | |
| 245 | 1 | 2 | |a A first course in fourier analysis / |c David W. Kammler. |
| 250 | |a Rev. ed. | ||
| 260 | |a Cambridge ; |a New York : |b Cambridge University Press, |c ©2007. | ||
| 300 | |a 1 volume (various pagings) : |b illustrations ; |c 25 cm | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a unmediated |b n |2 rdamedia | ||
| 338 | |a volume |b nc |2 rdacarrier | ||
| 504 | |a Includes bibliographical references and index. | ||
| 505 | 0 | |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. 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. | |
| 506 | |a Electronic version is restricted to subscribing institutions. | ||
| 520 | 1 | |a "A modern introduction to Fourier analysis and selected applications which shows how these mathematical ideas can be used to study sampling theory, PDEs, probability, diffraction, musical tones, and wavelets. Aimed at students from the physical, engineering, and mathematical sciences who have mastered the college level courses in calculus and linear algebra."--Jacket | |
| 650 | 0 | |a Fourier analysis. | |
| 650 | 7 | |a Fourier analysis. |2 fast |0 (OCoLC)fst00933401 | |
| 650 | 7 | |a Fourier analysis. |2 nli | |
| 650 | 7 | |a Fourieranalys. |2 sao | |
| 830 | 0 | |a MyiLibrary. | |
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