Review of Five Sets of Piecewise Constant Orthogonal Functions for Function Approximation, Integration and Solution of First Order Differential Equation Using These Function Sets

This paper reviews five types of piecewise constant orthogonal functions namely Walsh, block-pulse, sample-and-hold, triangular and hybrid functions. Approximation, integration of the functions are performed and compared with the actual result. By performing integration we get the operational matrix for each individual function set. With the help of integration operational matrices we can solve an nth order differential equation which is of importance for solving control engineering problems although a first order ordinary differential equation has been dealt with in this paper.