Download e-book for kindle: Algorithms for Discrete Fourier Transform and Convolution by Richard Tolimieri

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By Richard Tolimieri

ISBN-10: 0387982612

ISBN-13: 9780387982618

This graduate-level textual content presents a language for figuring out, unifying, and imposing a large choice of algorithms for electronic sign processing - particularly, to supply ideas and approaches which could simplify or maybe automate the duty of writing code for the latest parallel and vector machines. It hence bridges the space among electronic sign processing algorithms and their implementation on various computing structures. The mathematical inspiration of tensor product is a routine subject matter in the course of the booklet, due to the fact those formulations spotlight the knowledge movement, that is in particular vital on supercomputers. due to their value in lots of functions, a lot of the dialogue centres on algorithms with regards to the finite Fourier rework and to multiplicative FFT algorithms.

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Additional resources for Algorithms for Discrete Fourier Transform and Convolution (Signal Processing and Digital Filtering)

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A Nk-1-2 into aNi aNk_i interchanging the k-th and k Since aN IC aNk+1 0 aNk+i ell< aNk 1-th positions. ININk ANk = P(N, NINk)(ANk IN/NJP(N, NINk)-1 , we obtain the vector factorization analogs of the preceding two theorems. 13 (Vector II) ANi ANK = H (A NI, ININJRk, k=1 where Rk = P(N,Nk)QkiCh+iP(N,NINk+1). If ANk, < k < K, is symmetric, then applying the transpose operation to both sizes of the factorizations in the preceding theorems produces additional factorizations which, although similar in form, can have significant data flow differences.

Tensor product identities can be used in the process of automating the implementation of the algorithms on these architectures. The formalism of tensor product notation can be used to keep track of the complicated index calculation needed in implementing FT algorithms. In [1], the implementation of tensor product actions on the CRAY X-MP was carried out in detail. 28 2. 2 Tensor Product In this section, we present some of the basic properties of tensor products which are encountered in the algorithms that we will describe in future chapters of this work.

The n-th processor acts by this code on the components X(2n), X(2n + 1) of the input vector X and places the results in memory as the components Y(2n), Y(2n + 1) in the output vector Y. In the same fashion, A 0 IN is computed by having the n-th processor act on the components X (n), X (n N). The results are placed in memory as the components Y(n), Y(n + N) in the output vector Y. If the number M of processors is less than N , then the problem is more complicated. Suppose that N = M L. Using the identity IN 0 A = /Ai (/"L 0 A), we assign the code //, 0 A to each processor to perform the computation as above with M replacing N in the discussion.

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Algorithms for Discrete Fourier Transform and Convolution (Signal Processing and Digital Filtering) by Richard Tolimieri

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