
Accession Number : ADP006603
Title : The Arithmetic Fourier Transform (AFT): Iterative Computation and Image Processing Applications,
Corporate Author : RHODE ISLAND UNIV KINGSTON DEPT OF ELECTRICAL ENGINEERING
Personal Author(s) : Tufts, Donald W. ; Chen, Haiguang
Report Date : MAR 1992
Pagination or Media Count : 24
Abstract : A Fourier analysis method using an iterative Arithmetic Fourier Transform (AFT) is presented. It overcomes the difficulty of dense, Fareyfraction sampling which is inherent in the original AFT algorithm. This disadvantage of the AFT is turned into an advantage and dense frequencydomain samples are obtained without any additional interpolation or zeropadding. The implementation of the iterative computations is designed to preserve the advantage of the AFT for VLSI implementation by using a permuted difference coefficient structure. This iterative AFT is intended for cases in which (a) the function to be analyzed can only be sampled uniformly and at a rate close to the Nyquist rate or (b) dense frequencydomain samples are needed. The one and two dimensional versions of the discrete cosine transform (1D DCT) and (2D DCT) can be simply computed using the 1D and 2D AFT, but dense, Fareyfraction sampling in the image domain is then required. And it also requires special computations for the marginal DCT values. These difficulties can be overcome by the iterative 1D or 2D AFT. Dense samples then occur in the transform domain where they can be advantageously used for parameter estimation or the determination of a few principal components.
Descriptors : *FOURIER TRANSFORMATION, *APPLIED MATHEMATICS, *ITERATIONS, ALGORITHMS, ARITHMETIC, COEFFICIENTS, COMPUTATIONS, DETERMINATION, FOURIER ANALYSIS, FREQUENCY, FREQUENCY DOMAIN, FUNCTIONS, IMAGES, INTERPOLATION, PARAMETERS, RATES, SAMPLING, STRUCTURES, TWO DIMENSIONAL, VALUE, VERY LARGE SCALE INTEGRATION, IMAGE PROCESSING.
Subject Categories : Numerical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE