Discrete orthogonal polynomial deconvolution for time-varying systems

Abstract

Discrete orthogonal polynomial deconvolution (DOPD) has been demonstrated to be a robust method for obtaining the inverse solution for time-invariant systems. In this communication, extension of the method to time-varying linear systems is explored. The operator-based nature of DOPD lends itself to application to linear time-varying systems expressible as an operator matrix. The stability and noise tolerance characteristics of time-invariant DOPD are demonstrated to apply to tine-varying systems. A priori estimation of the quality of the inverse solution is possible if the characteristics of noise in the forward solution can be estimated. For time-varying linear systems having a region of basis function support approximately congruent to the support region of the transfer function, and for which there is sufficient a priori knowledge of the system, DOPD provides an efficient and noise tolerant method of inverse solution. >