Author | Tolimieri, Richard. author |
---|---|
Title | Mathematics of Multidimensional Fourier Transform Algorithms [electronic resource] / by Richard Tolimieri, Myoung An, Chao Lu |
Imprint | New York, NY : Springer US, 1993 |
Connect to | http://dx.doi.org/10.1007/978-1-4684-0205-6 |
Descript | XIV, 233 p. online resource |
1 Tensor Product -- 1.1 Introduction -- 1.2 Tensor Product -- 1.3 Stride Permutations -- 1.4 Algebra of Stride Permutations -- 1.5 Tensor Product Factorization -- 1.6 Fast Fourier Transform Algorithms I -- 1.7 General 1-Dimensional FFT -- Problems -- 2 Multidimensional Tensor Product and FFT -- 2.1 Introduction -- 2.2 Multidimensional Fourier Transform -- 2.3 2-Dimensional Operations -- 2.4 2-Dimensional Cooley-Tukey FFT -- Problems -- 3 Finite Abelian Groups -- 3.1 Introduction -- 3.2 Character Group -- 3.3 Duality -- 3.4 Chinese Remainder Theorem -- 3.5 Vector Space L(A) -- Problems -- 4 Fourier Transform of Finite Abelian Groups -- 4.1 Introduction -- 4.2 Fourier Transform of A -- 4.3 Induced Fourier Transform -- 4.4 Periodic and Decimated Data -- 4.5 Periodization and Decimation -- 5 CooleyโTukey and GoodโThomas -- 5.1 Introduction -- 5.2 Good-Thomas FFT -- 5.3 Abstract Cooley-Tukey FFT -- 6 Lines -- 6.1 Introduction -- 6.2 Examples -- 6.3 Prime Case -- 6.4 Prime Power Case -- 6.5 Square Case -- 6.6 Rectangular Case -- Problems -- 7 Duality of Lines and Planes -- 7.1 Automorphism Group -- 7.2 Dual of Lines -- 7.3 Planes and Duality -- Problems -- 8 Reduced Transform Algorithms -- 8.1 Introduction -- 8.2 General Structure -- 8.3 Periodizations -- 8.4 Examples -- 8.5 RTA Permutations -- Bibliograpgy -- Problems -- 9 Field Algorithm -- 9.1 Introduction -- 9.2 Rader Field Algorithm -- 9.3 Finite Fields -- 9.4 Fourier Transform of Finite Fields -- 9.5 Factorization of Core Matrices -- 9.6 Auslander-Feig-Winograd DFT -- Bibliograpgy -- Problems -- 10 Implementation on RISC Architectures -- 10.1 Introduction -- 10.2 Algorithm Design for RISC Architectures -- 10.3 Implementation on the IBM RS/6000 -- 10.4 Implementation on the Intel i860 -- 11 Implementation on Parallel Architectures -- 11.1 Introduction -- 11.2 Parallel Implementation of FFT -- 11.3 Parallel Implementation of the RTA -- 11.4 New Strategy for the Parallel Implementation of FFT -- 11.5 Hybrid Algorithm -- 11.6 A Program Example on iPSC/860