On The Statistical Properties Of The Generalized Discrete Teager-Kaiser Energy Operator Applied To Uniformly Distributed Random Signals

The discrete Teager-Kaiser operator and its generalized versions (GTKO) have found many applications in various fields of signal processing. However, few studies have focused on their statistical properties and most of them were limited to the mean and variance expressed under Gaussian assumptions. We aim at filling the lack of distribution laws of these operators in the case of uniformly distributed random signals. To that end, the GTKO definition is reformulated as the determinant of a 2×2 embedding square matrix. Based on the determinant theory of independent uniform random matrix, we first introduce the probability density function (pdf) of the GTKO under the assumption of identically distributed matrix entries. We then derive the GTKO pdf under the assumption of nonidentically distributed matrix entries. The former assumption is motivated by the case where the matrix entries are the raw signal samples whereas the latter assumption is motivated by the case where the matrix entries are the signal samples multiplied by a window function, Hanning or Hamming widow for example. We also derive for the first time the explicit expressions of the high order moments of the considered operators. An application to a real signal is then presented.