How to Build Functional Data Objects

Abstract

We saw in the last chapter that functions are built up from basis systems\r$$\phi_1 (t),..., \phi_K (t) $$\rby defining the linear combination\r\r\r\r\r\r$$x(t) = \sum \limits_{k=1}^k ck \phi k (t) = {\bf c'} \phi (t).$$\r\r\r\r\r\r\r\r\rThat chapter described how to build a basis system. Now we take the next step, defining a functional data object by combining\ra set of coefficients c\rk (and other useful information) with a previously specified basis system. Once we have selected a basis, we have only to supply\rcoefficients in order to define an object of the functional data class (with class name fd).