Algorithms for Discrete Fourier Transform and Convolution

2. Auflage 1997
ISBN: 978-0-387-98261-8
Verlag: Springer

Buch, Englisch, 268 Seiten, HC runder Rücken kaschiert, Format (B × H): 160 mm x 241 mm, Gewicht: 1270 g

Reihe: Signal Processing and Digital Filtering

This book is based on several courses taught during the years 1985-1989 at the City College of the City University of New York and at Fudan Univer­ sity, Shanghai, China, in the summer of 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 that would serve to represent the vast array of algorithms designed over the last twenty years for computing 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 concepts 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 that can serve both of these needs. In fact, it is our belief that certain mathematical ideas provide a natural language and culture for understanding, unifying and implementing a wide range of digital signal processing (DSP) algo­ rithms. This belief is reinforced by the complex and time-consuming effort required to write code for recently available parallel and vector machines. A significant part of this text is devoted to establishing rules and procedures that reduce and at times automate this task.

Zielgruppe

Research

Autoren/Hrsg.

Tolimieri, Richard

Lu, Chao

An, Myoung

Fachgebiete

• Mathematik | Informatik EDV | Informatik Informatik Bildsignalverarbeitung
• Mathematik | Informatik EDV | Informatik Informatik Mathematik für Informatiker
• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
• Technische Wissenschaften Sonstige Technologien | Angewandte Technik Signalverarbeitung, Bildverarbeitung, Scanning
• Technische Wissenschaften Technik Allgemein Technik: Allgemeines
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis

Inhaltsverzeichnis

1 Review of Applied Algebra.- 2 Tensor Product and Stride Permutation.- 3 Cooley-Tukey FFT Algorithms.- 4 Variants of FT Algorithms and Implementations.- 5 Good-Thomas PFA.- 6 Linear and Cyclic Convolutions.- 7 Agarwal-Cooley Convolution Algorithm.- 8 Multiplicative Fourier Transform Algorithm.- 9 MFTA: The Prime Case.- 10 MFTA: Product of Two Distinct Primes.- 11 MFTA: Composite Size.- 12 MFTA: p2.- 13 Periodization and Decimation.- 14 Multiplicative Characters and the FT.- 15 Rationality.