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Statistical Behavior of Teager-Kaiser Energy Operator in Presence of White Gaussian Noise

In this work we are interested in the behavior of Teager-Kaiser energy operator (TKEO) applied to a zero-mean white Gaussian noise. For this purpose, we analyze the statistical distribution of the outputs of the TKEO under this noise. We show that the probability density function (pdf) characterizing the output of TKEO, is asymmetric and highly skewed pdf with a stronger peak near the mean, and can be fitted by a shifted Log-Laplace distribution. Some useful moments charactering key aspects of the pdf of TKEO are calculated. We prove that the coefficient of variation, skewness and kurtosis are independent on the variance of the noise, while mean and standard deviation are proportional to this variance. Results of simulations show the interest of TKEO moments for signal detection.