On a matrix framework for the Teager-Kaiser energy operator

The non-linear, second-order, Teager-Kaiser energy operator (TKEO) finds applications in numerous areas such as speech processing, image processing, communications, biomedical problems, and abrupt event detection. In quantum mechanics, the Hamiltonian is considered the energy operator whose eigenvalue is the scalar energy. In this work, we provide a matrix framework for the Teager-Kaiser operator and several of its generalizations, interpreting the eigenvalues of the presented energy matrices as the square-root of the TKEO or its generalization.