On tensor products formulations of additive fast Fourier transform algorithms and their implementations.
Item
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Title
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On tensor products formulations of additive fast Fourier transform algorithms and their implementations.
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Identifier
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AAI8820894
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identifier
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8820894
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Creator
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Rodriguez, Domingo Antonio.
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Contributor
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Adviser: Richard Tolimieri
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Date
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1988
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Language
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English
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Publisher
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City University of New York.
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Subject
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Engineering, Electronics and Electrical
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Abstract
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One of the objectives of this work is to present a mathematical language or structure in which to analyze in a unified format similarities and differences among the commonly known fast Fourier transform (FFT) algorithms. This language is the language of tensor products, a branch of finite dimensional multilinear algebra. We concentrate on algorithms which take advantage of the additive structure of the indexing sets of input and output data during an algorithmic computation. One of the advantages of using tensor products language to describe FFT algorithms is that this mathematical language may be used as an analytic tool for the study of algorithmic structures for machine hardware and software implementations as well as the identification of new algorithms. For instance, an inherent part of the study of computer implementation of FFT algorithms is the analysis of the data communications aspects of the algorithms which manifest themselves during implementation procedures. These data communication aspects can be best studied, in turn, through the analysis of permutation matrices which appear in our tensor products formulations of the FFT algorithms.;Another objective of this work is to present a mathematical characterization of linear shift invariant, finite impulse response (LSI-FIR) filters, and describe how to use the tensor products language as tool to aid in the implementation of these filters using FFT algorithms.
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Type
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dissertation
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Source
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PQT Legacy CUNY.xlsx
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degree
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Ph.D.
