How to Specify Basis Systems for Building Functions

Abstract

This chapter is primarily about setting up a basis system. The next chapter will discuss the second step of bundling a set of coefficient values with the chosen basis system.

The functions that we wish to model tend to fall into two main categories: periodic and nonperiodic. The Fourier basis system is the usual choice for periodic functions, and the spline basis system (and bsplines in particular) tends to serve well for nonperiodic functions. We go into these two systems in some detail, and the spline basis especially requires considerable discussion. These two systems are often supplemented by the constant and monomial basis systems, and other systems are described more briefly.

A set of functions in both languages are presented for displaying, evaluating and plotting basis systems as well as for other common tasks.