Noise Sensitivity of Teager-Kaiser Energy Operators and Their Ratios

TL;DR

This paper investigates the impact of additive Gaussian noise on Teager-Kaiser energy operators and their ratios, analyzing noise limits, sample requirements, and statistical properties to improve AM-FM demodulation robustness.

Contribution

It provides a detailed analysis of noise effects on TKO outputs, including statistical characterization and limits, which was not thoroughly addressed before.

Findings

Noise degrades positivity of TKO outputs under small signals.

Derived probability density functions for TKO quadratic forms and ratios.

Identified noise power thresholds for reliable TKO-based demodulation.

Abstract

The Teager-Kaiser energy operator (TKO) belongs to a class of autocorrelators and their linear combination that can track the instantaneous energy of a nonstationary sinusoidal signal source. TKO-based monocomponent AM-FM demodulation algorithms work under the basic assumption that the operator outputs are always positive. In the absence of noise, this is assured for pure sinusoidal inputs and the instantaneous property is also guaranteed. Noise invalidates both of these, particularly under small signal conditions. Post-detection filtering and thresholding are of use to reestablish these at the cost of some time to acquire. Key questions are: (a) how many samples must one use and (b) how much noise power at the detector input can one tolerate. Results of study of the role of delay and the limits imposed by additive Gaussian noise are presented along with the computation of the cumulants and probability density functions of the individual quadratic forms and their ratios.