A measure of the randomness of signals and suggested applications
Abstract
The solution to an optimization or estimation problem depends on some criterion of optimality. Typically, all prospective solutions have an associated measure of goodness, and the optimum solution is that with maximum (or minimum) measure. The choice of measure incorporates whatever is known about the physics of the problem as well as other assumptions. This presentation suggests two closely related measures of the randomness of signals. Each of these measures is related to the uncertainty principle of quantum mechanics. It is further suggested that minimizing either of these measures is an appropriate criterion for the solution of a variety of problems, including spectral estimation, signal extrapolation and/or interpolation, nonparametric signal detection, and phase retrieval. The criterion may be appropriate when the unknown signal is postulated to be simple rather than complex and it is necessary to minimize the number of arbitrary assumptions made about the signal and noise characteristics.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 March 1986
 Bibcode:
 1986STIN...8711925R
 Keywords:

 Random Processes;
 Signal Processing;
 Signal To Noise Ratios;
 Spectra;
 Entropy;
 Extrapolation;
 Interpolation;
 Optimization;
 Quantum Theory;
 Communications and Radar