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, Farey-fraction sampling which is inherent in the original AFT algorithm. This disadvantage of the AFT is turned into an advantage and dense frequency-domain samples are obtained without any additional interpolation or zero-padding. 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 frequency-domain samples are needed. The one and two dimensional versions of the discrete cosine transform (1-D DCT) and (2-D DCT) can be simply computed using the 1-D and 2-D AFT, but dense, Farey-fraction 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 1-D or 2-D 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