Numerical Integration and Orthogonal Expansion

In MATLAB, numerical integration of an arbitrary function can be done by using the so-called Riemann sum. This chapter shows an m-file example that calculates the definite integral using the simplest version of Riemann sum. The integrals are calculated by using symbolic math. The results obtained by using symbolic math are compared with numerical integration result. Normalized error is used to compute the difference of these results. The chapter illustrates an arbitrary function as a linear combination of orthogonal basis functions. It also illustrates three examples of the time-limited functions, and provides step-by-step code exercises and instructions to implement execution sequences. The chapter is designed to help teach and understand communication systems using a classroom-tested, active learning approach.