Novel scheme for compact orthogonal modified-prony representation of signals

Abstract

In this paper, an algorithm is developed to construct a set of M orthogonal basis along which signals, whether noisy or noise-free, can be decomposed. Combining a modified Prony signal approximation and Gram-Schmidt orthogonalization schemes (to obtain the orthogonal bases), the proposed method represents the processed signal as the sum of M damped exponentials. It is shown that the employed bases are closely related to the roots of an M^th order forward linear prediction polynomial, satisfying the system. In addition, an optimization procedure is described to optimally adjust these bases to accurately represent the signal under consideration. The proposed procedure finds applications in signal compression and signal de-noising, where it is only necessary to specify the orthogonal basis, as well as the decomposition weights rather than sending the complete signal batch. Illustrative examples are given