Computing discrete Fourier transforms on a rectangular array consisting of ordinary and crystallographic-invariant data.

Title: Computing discrete Fourier transforms on a rectangular array consisting of ordinary and crystallographic-invariant data.
Identifier: AAI9029986
identifier: 9029986
Creator: Tsai, Dwen-Ren.
Contributor: Adviser: Michael Vulis
Date: 1990
Language: English
Publisher: City University of New York.
Subject: Computer Science | Engineering, Electronics and Electrical
Abstract: The Weighted Redundancy Transform (WRT, (4)) algorithm for computing the multi-dimensional Discrete Fourier Transform (DFT) is generalized to the case in which the sample size (blocklength) is not the same on every axis. The proposed algorithm, similar to the WRT algorithm, is based on the one-dimensional Fast Fourier Transform (FFT) and, compared to traditional techniques of computing the multi-dimensional DFT, offers substantial savings in the number of one-dimensional FFT procedure calls. While the algorithm is applicable to transforms of any dimensions, only the two-dimensional case is explored in detail in this thesis. Then, a customized algorithm for computing crystallographic-invariant DFT was constructed based on the WRT algorithm. This new algorithm has a number of advantages over existing crystallographic transforms and is applicable toward a substantially larger set of problems.
Type: dissertation
Source: PQT Legacy CUNY.xlsx
degree: Ph.D.

Media: Computing discrete Fourier transforms on a rectangular array consisting of ordinary and crystallographic-invariant data.