E-Book, Englisch, 350 Seiten, eBook
Tolimieri / An / Lu Algorithms for Discrete Fourier Transform and Convolution
Erscheinungsjahr 2013
ISBN: 978-1-4757-3854-4
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark
E-Book, Englisch, 350 Seiten, eBook
Reihe: Signal Processing and Digital Filtering
ISBN: 978-1-4757-3854-4
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark
This book is based on several courses taught during the last five years at the City College of the City University of New York and at Fudan University, Shanghai, China in the Summer, 1986. It was originally our intention to present to a mixed audience of electrical engineers, mathematicians and computer scientists at the graduate level, a collection of algorithms which would serve to represent the vast array of algorithms designed over the last twenty years for com puting the finite Fourier transform (FFT) and finite convolution. However, it was soon apparent that the scope of the course had to be greatly expanded. For researchers interested in the design of new algorithms, a deeper understanding of the basic mathematical con cepts underlying algorithm design was essential. At the same time, a large gap remained between the statement of an algorithm and the implementation of the algorithm. The main goal of this text is to describe tools which can serve both of these needs. In fact, it is our belief that certain mathematical ideas provide a natural lan guage and culture for understanding, unifying and implementing a wide range of digital signal processing (DSP) algorithms. This belief is reenforced by the complex and time-consumming effort required to write code for recently available parallel and vector machines. A significant part of this text is devoted to establishing rules and precedures which reduce and at times automate this task. In Chapter 1, a survey is given of basic algebra.
Zielgruppe
Research
Weitere Infos & Material
1. Introduction to Abstract Algebra.- 2. Tensor Product and Stride Permutation.- 3. Cooley-Tukey FFF Algorithms.- 4. Variants of FFT Algorithms and Their Implementations.- 5. Good-Thomas PFA.- 6. Linear and Cyclic Convolution.- 7. Agarwal-Cooley Convolution Algorithm.- 8. Introduction to Multiplicative Fourier Transform Algorithms (MFTA).- 9. MFTA: The Prime Case.- 10. MFTA: Product of Two Distinct Primes.- 11. MFTA: Transform Size N = Mr M-Composite Integer and r-Prime.- 12. MFTA: Transform Size N = p2.- 13. Periodization and Decimation.- 14. Multiplicative Character and the FFT.- 15. Rationality.
