A new generalization of the discrete Teager-Kaiser energy operator - application to biomedical signals

Abstract

The discrete Teager-Kaiser operator (TKO) was firstly introduced in [1]. Generalized versions of this operator (GTKO) were proposed later in [2]. Both the TKO and GTKO were able to detect instantaneous amplitude changes of signals and they significantly improved the signal to noise ratios (SNR). The TKO, as well as the GTKO, can be viewed as the determinant of an embedding square matrix of size 2 × 2 that is built using a window sliding over signals. In the present paper, we propose a new extension of these operators and we define the extended GTKO (EGTKO) as the determinant of an embedding matrix of size d × d with d ≥ 2. We discuss different structures of such an embedding matrix. The detection of instantaneous amplitude changes can be achieved by applying a threshold to the proposed EGTKO. To theoretically determine the optimal threshold that allows for the most accurate detection, we present a statistical characterization of the EGTKO based on the determinant theory of randommatrices. The receiver operating characteristic (ROC) curves obtained at different SNR show that the accuracy of the EGTKO outperforms that of the TKO and GTKO. An application to a real biomedical signal is also presented and illustrates the superiority of the proposed EGTKO.