High resolution signal processing
Abstract
Motivated by the goal of efficient, effective, highspeed integratedcircuit realization, we have discovered an algorithm for high speed Fourier analysis called the Arithmetic Fourier Transform (AFT). It is based on the numbertheoretic method of Mobius inversion, a method that is well suited for integratedcircuit realization. The computation of the AFT can be carried out in parallel, pipelined channels, and the individual operations are very simple to execute and control. Except for a single scaling in each channel, all the operations are additions or subtractions. Thus, it can reduce the required power, volume, and cost. Also, analog switchedcapacitor realizations of the AFT have been studied. We have also analyzed the performance of a broad and useful class of data adaptive signal estimation algorithms. This in turn has led to our proposed improvements in the methods. We have used perturbation analysis of the rankreduced data matrix to calculate its statistical properties. The improvements made have been demonstrated by computer simulation as well as by comparison with the CramerRao Bound.
 Publication:

Final Report
 Pub Date:
 August 1993
 Bibcode:
 1993uri..rept.....T
 Keywords:

 Computerized Simulation;
 Electric Networks;
 Fourier Analysis;
 Fourier Transformation;
 High Resolution;
 Integrated Circuits;
 Inversions;
 Network Analysis;
 Parallel Processing (Computers);
 Signal Processing;
 Spectrum Analysis;
 Statistical Distributions;
 Algorithms;
 Estimating;
 High Speed;
 Communications and Radar