The most comprehensive treatment of FFTs to date. Van Loan captures the interplay between mathematics and the design of effective numerical algorithms--a critical connection as more advanced machines become available. A stylized Matlab notation, which is familiar to those engaged in high-performance computing, is used. The Fast Fourier Transform (FFT) family of algorithms has revolutionized many areas of scientific computation. The FFT is one of the most widely used algorithms in science and engineering, with applications in almost every discipline. This volume is essential for professionals interested in linear algebra as well as those working with numerical methods. The FFT is also a great vehicle for teaching key aspects of scientific computing.
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"This finely crafted work fills a gap in the library of books on the fast Fourier Transform (FFT). It provides a complete and elegant mathematical formulation of the family of algorithms that compute FFTs. It is written for students and professionals who already have a working knowledge of computational linear algebra. It leads the student directly into the current major fields of FFT research …This work is an excellent contribution to the modern FFT literature.’ J. R. Hubbard, Computing Reviews
‘This comprehensive book contains many examples, problems, notes and hints to the literature. It will be very useful for students as well as researchers who are interested in the application of the FFT.’ M. Tasche (Rostock), Zentralblatt fur Mathematik
"The fast Fourier transform (FFT) is one of the truly great computational developments. As the author emphasizes in the preface, the central feature of the FFT is essentially the factorization of the discrete Fourier transform (DFT) matrix. This point of view will not only unify the FFT and make it more understandable to outsiders, but also give key aspects for advanced scientific computing, e.g. vectorization or parallelization. . . This is only a brief glimpse of an excellent survey on the FFT, which will be valuable to all who wish to use it.’ S. Hitotumatu, Mathematical Reviews
‘ … the FFT has found application in almost every field of modern science, including fields as diverse as astronomy, acoustics, image processing, fluid dynamics, petroleum exploration, medicine and quantum physics, among many others. It is not an exercise in hyperbole to say that the world as we know it would be different without the FFT.’ David H. Bailey, SIAM Review
"It is generally accepted that `Life as we know it would be very different without the FFT.' The author adds to this `Life as we know it would be considerably different if, from the 1965 Cooley-Tukey paper onwards, the FFT community had made systematic and heavy use of the matrix-vector notation.' This book contains a very readable and up-to-date presentation of FFT techniques, their theory and application. Together with many explicit computational algorithms, the extensive annotated list of references add greatly to the scientific value of this reference text.’ Short Book Reviews
‘This comprehensive book contains many examples, problems, notes and hints to the literature. It will be very useful for students as well as researchers who are interested in the application of the FFT.’ M. Tasche (Rostock), Zentralblatt fur Mathematik
"The fast Fourier transform (FFT) is one of the truly great computational developments. As the author emphasizes in the preface, the central feature of the FFT is essentially the factorization of the discrete Fourier transform (DFT) matrix. This point of view will not only unify the FFT and make it more understandable to outsiders, but also give key aspects for advanced scientific computing, e.g. vectorization or parallelization. . . This is only a brief glimpse of an excellent survey on the FFT, which will be valuable to all who wish to use it.’ S. Hitotumatu, Mathematical Reviews
‘ … the FFT has found application in almost every field of modern science, including fields as diverse as astronomy, acoustics, image processing, fluid dynamics, petroleum exploration, medicine and quantum physics, among many others. It is not an exercise in hyperbole to say that the world as we know it would be different without the FFT.’ David H. Bailey, SIAM Review
"It is generally accepted that `Life as we know it would be very different without the FFT.' The author adds to this `Life as we know it would be considerably different if, from the 1965 Cooley-Tukey paper onwards, the FFT community had made systematic and heavy use of the matrix-vector notation.' This book contains a very readable and up-to-date presentation of FFT techniques, their theory and application. Together with many explicit computational algorithms, the extensive annotated list of references add greatly to the scientific value of this reference text.’ Short Book Reviews
Book Description
he Fast Fourier Transform family of algorithms has revolutionized many areas of scientific computation. The FFT is one of the most widely used algorithms in science and engineering, with applications in almost every discipline. Essential reading for professionals interested in linear algebra as well as those working with numerical methods.
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A fast Fourier transform (FFT) is a quick method for forming the matrix-vector product Fnx, where Fn is the discrete Fourier transform (DFT) matrix. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
algorithm overwrites, butterfly updates, vector workspace, qth step, transpose algorithm, prime factor algorithm, stride access, index reversal, unit stride, butterfly computations, bit reversal, discrete sine transform, following algorithm computes, butterfly operations, perfect shuffle, imaginary portions, sort permutation, matrix transposition, node program, array interpretation, weight computation, signal flow graph, local array Key Phrases - Capitalized Phrases (CAPs): (learn more)
Speech Signal Process, New York, Parallel Comput, Van Loan, Englewood Cliffs, Convolution Algorithms, John Wiley, Quantitative Approach, San Mateo, Self-Sorting Mixed Radix Fast Fourier Transforms, Academic Press, Boolean Cubes, Fast Cosine Transform, Harvard University, Implementing Fourier Transform Algorithms, Linear Algebra Appl, Various Architectures, Circuits Systems Signal Process, Cornell University, Johns Hopkins University Press, Modify Algorithm, Morgan Kaufmann Publishers, Supercomputer Applications New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
A fast Fourier transform (FFT) is a quick method for forming the matrix-vector product Fnx, where Fn is the discrete Fourier transform (DFT) matrix. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
algorithm overwrites, butterfly updates, vector workspace, qth step, transpose algorithm, prime factor algorithm, stride access, index reversal, unit stride, butterfly computations, bit reversal, discrete sine transform, following algorithm computes, butterfly operations, perfect shuffle, imaginary portions, sort permutation, matrix transposition, node program, array interpretation, weight computation, signal flow graph, local array Key Phrases - Capitalized Phrases (CAPs): (learn more)
Speech Signal Process, New York, Parallel Comput, Van Loan, Englewood Cliffs, Convolution Algorithms, John Wiley, Quantitative Approach, San Mateo, Self-Sorting Mixed Radix Fast Fourier Transforms, Academic Press, Boolean Cubes, Fast Cosine Transform, Harvard University, Implementing Fourier Transform Algorithms, Linear Algebra Appl, Various Architectures, Circuits Systems Signal Process, Cornell University, Johns Hopkins University Press, Modify Algorithm, Morgan Kaufmann Publishers, Supercomputer Applications New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
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61
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- Numerical Recipes in Fortran 90: Volume 2, Volume 2 of Fortran Numerical Recipes: The Art of Parallel Scientific Computing by William H. Press on page 2, page 49, and Back Matter
- Deblurring Images: Matrices, Spectra, and Filtering (Fundamentals of Algorithms 3) by Per Christian Hansen in Back Matter (1), and Back Matter (2)
- MATLAB Guide by Desmond J. Higham on page 170, and Back Matter
- Handbook of Writing for the Mathematical Sciences by Nicholas J. Higham on page 23, and Back Matter
- Parallel Scientific Computation: A Structured Approach using BSP and MPI by Rob H. Bisseling on page 144, and Back Matter
See all 61 books citing this book
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