High resolution signal processing
Abstract
Motivated by the goal of efficient, effective, high-speed integrated-circuit realization, we have discovered an algorithm for high speed Fourier analysis called the Arithmetic Fourier Transform (AFT). It is based on the number-theoretic method of Mobius inversion, a method that is well suited for integrated-circuit 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 switched-capacitor 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 rank-reduced data matrix to calculate its statistical properties. The improvements made have been demonstrated by computer simulation as well as by comparison with the Cramer-Rao 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