Haar wavelet operational matrix based numerical inversion of Laplace transform for irrational and transcendental transfer functions

Abstract

Irrational and transcendental functions can often be seen in signal processing or physical phenomena analysis as consequences of fractional-order and distributed order models that result in fractional or partial differential equations. In cases when finding solution in analytical form tends to be difficult or impossible, numerical calculations such as Haar wavelet operational matrix method can be used. Haar wavelet establishes a direct procedure for transfer function inversion using the wavelet operational matrix for orthogonal function set integration. In this paper an inverse Laplace transform of irrational and transcendental transfer functions using Haar wavelet operational matrix is proposed. Results for a number inverse Laplace transforms are numerically solved and compared with the analytical solutions and solutions provided by commonly used Invlap and NILT algorithms. This approach is useful when the original cannot be represented by an analytical formula and validity of the obtained result needs to be crosschecked and error estimated.