Book contents
- Frontmatter
- Contents
- Preface
- Acknowledgments
- 1 Introduction
- 2 Introduction to abstract algebra
- 3 Fast algorithms for the discrete Fourier transform
- 4 Fast algorithms based on doubling strategies
- 5 Fast algorithms for short convolutions
- 6 Architecture of filters and transforms
- 7 Fast algorithms for solving Toeplitz systems
- 8 Fast algorithms for trellis search
- 9 Numbers and fields
- 10 Computation in finite fields and rings
- 11 Fast algorithms and multidimensional convolutions
- 12 Fast algorithms and multidimensional transforms
- A A collection of cyclic convolution algorithms
- B A collection of Winograd small FFT algorithms
- Bibliography
- Index
Preface
Published online by Cambridge University Press: 03 May 2011
- Frontmatter
- Contents
- Preface
- Acknowledgments
- 1 Introduction
- 2 Introduction to abstract algebra
- 3 Fast algorithms for the discrete Fourier transform
- 4 Fast algorithms based on doubling strategies
- 5 Fast algorithms for short convolutions
- 6 Architecture of filters and transforms
- 7 Fast algorithms for solving Toeplitz systems
- 8 Fast algorithms for trellis search
- 9 Numbers and fields
- 10 Computation in finite fields and rings
- 11 Fast algorithms and multidimensional convolutions
- 12 Fast algorithms and multidimensional transforms
- A A collection of cyclic convolution algorithms
- B A collection of Winograd small FFT algorithms
- Bibliography
- Index
Summary
A quarter of a century has passed since the previous version of this book was published, and signal processing continues to be a very important part of electrical engineering. It forms an essential part of systems for telecommunications, radar and sonar, image formation systems such as medical imaging, and other large computational problems, such as in electromagnetics or fluid dynamics, geophysical exploration, and so on. Fast computational algorithms are necessary in large problems of signal processing, and the study of such algorithms is the subject of this book. Over those several decades, however, the nature of the need for fast algorithms has shifted both to much larger systems on the one hand and to embedded power-limited applications on the other.
Because many processors and many problems are much larger now than they were when the original version of this book was written, and the relative cost of addition and multiplication now may appear to be less dramatic, some of the topics of twenty years ago may be seen by some to be of less importance today. I take exactly the opposite point of view for several reasons. Very large three-dimensional or four-dimensional problems now under consideration require massive amounts of computation and this computation can be reduced by orders of magnitude in many cases by the choice of algorithm. Indeed, these very large problems can be especially suitable for the benefits of fast algorithms.
- Type
- Chapter
- Information
- Fast Algorithms for Signal Processing , pp. xi - xiiPublisher: Cambridge University PressPrint publication year: 2010