Evaluation of Impulse Response of Linear Systems by using Legendre Polynomials

TLDR: In this paper, the authors proposed an experimental procedure to evaluate the coefficients of these polynomials to find the best approximation to the impulse response of a linear time invariant system.

Abstract: Impulse response of linear time invariant systems is partitioned by dividing time axis into equal intervals of time. Then impulse response is expressed as a sum of partitioned portions of impulse response. Each individual portion of impulse response is approximated by a finite sum of Legendre polynomials, satisfying integral squared error criterion. In this investigation an experimental procedure is suggested to evaluate the coefficients of these polynomials to cahieve the best approximation. Knowing these coefficients the best approximation to impulse response is obtained us illustrated by the examples considered. If the coefficients of the input signal are also known then it is shown that the values of the output response at the partitioning instants can be computed.