Waveform information from quantum mechanical entropy

Abstract

Although the entropy of a given signal-type waveform is technically zero, it is nonetheless desirable to use entropic measures to quantify the associated information. Several such prescriptions have been advanced in the literature but none are generally successful. Here, we report that the Fourier-conjugated 'total entropy' associated with quantum-mechanical probabilistic amplitude functions (PAFs) is a meaningful measure of information in non-probabilistic real waveforms, with either the waveform itself or its (normalized) analytic representation acting in the role of the PAF. Detailed numerical calculations are presented for both adaptations, showing the expected informatic behaviours in a variety of rudimentary scenarios. Particularly noteworthy are the sensitivity to the degree of randomness in a sequence of pulses and potential for detection of weak signals.

Order Through Disorder: The Characteristic Variability of Systems

“…Fourier-conjugated "total entropy" has been linked to quantummechanical probabilistic amplitude functions, as a measure of the information in non-probabilistic real waveforms. This entropy is sensitive to the degree of randomness in a sequence of pulses and can distinguish weak signals (Funkhouser et al, 2016).…”