High Resolution Signal Processing
D.W. Tufts · Defense Technical Information Center (DTIC) · 1993
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.