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# Algorithms for Discrete Fourier Transform and Convolution by Richard Tolimieri

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## Summary

This graduate-level text provides a language for understanding, unifying, and implementing a wide variety of algorithms for digital signal processing - in particular, to provide rules and procedures that can simplify or even automate the task of writing code for the newest parallel and vector machines.

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## Algorithms for Discrete Fourier Transform and Convolution Summary

### Algorithms for Discrete Fourier Transform and Convolution by Richard Tolimieri

This graduate-level text provides a language for understanding, unifying, and implementing a wide variety of algorithms for digital signal processing - in particular, to provide rules and procedures that can simplify or even automate the task of writing code for the newest parallel and vector machines. It thus bridges the gap between digital signal processing algorithms and their implementation on a variety of computing platforms. The mathematical concept of tensor product is a recurring theme throughout the book, since these formulations highlight the data flow, which is especially important on supercomputers. Because of their importance in many applications, much of the discussion centres on algorithms related to the finite Fourier transform and to multiplicative FFT algorithms.

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.

NLS9781441931153
9781441931153
1441931155
Algorithms for Discrete Fourier Transform and Convolution by Richard Tolimieri
New
Paperback
Springer-Verlag New York Inc.
2010-12-06
268
N/A
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
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