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Proceedings Paper

Arithmetic Fourier Transform And Adaptive Delta Modulation: A Symbiosis For High Speed Computation
Author(s): D W Tufts; G Sadasiv
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Paper Abstract

We present preliminary results on the VLSI design and implementation of a novel and promising algorithm for accurate high-speed Fourier analysis and synthesis. The Arithmetic Fourier Transform (AFT) is based on the number -theoretic method of Mobius inversion. Its computations proceed in parallel and the individual operations are very simple. Except for a small number of scalings in one stage of the computation, only multiplications by 0, +1, and -1 are required. If the input samples were not quantized and if ideal real-number operations were used internally, then the results would be exact. The accuracy of the computation is limited only by the input A/D conversion process, any constraints on the word lengths of internal accumulating registers, and the implementation of the few scaling operations. Motivated by the goal of efficient, effective, high-speed realization of the algorithm in an integrated circuit, we introduce further simplicities by the use of delta modulation to represent the input function in digital form. The result is that only binary (or preferably, ternary) sequences need to be processed in the parallel computations. And the required accumulations can be replaced by up/down counters. The dynamic range of the resulting transformation can be increased by the use of adaptive delta modulation (ADM).

Paper Details

Date Published: 20 April 1988
PDF: 11 pages
Proc. SPIE 0880, High Speed Computing, (20 April 1988); doi: 10.1117/12.944048
Show Author Affiliations
D W Tufts, University of Rhode Island (United States)
G Sadasiv, University of Rhode Island (United States)

Published in SPIE Proceedings Vol. 0880:
High Speed Computing
David P. Casasent, Editor(s)

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