Curve Fitting

One of the most common ‘post-measurement’ data processing operations is curve fitting, i.e., fitting samples to a predicted expression. This is usually derived by least-square calculations, but this chapter will use the orthogonality principle to derive the curve fitting expressions. The advantage of this is that it offers a graphical argument for its legitimacy. The pseudo inverse of a non-square matrix is defined and some common pitfalls due to error propagation in matrix operations are highlighted. Once curve fitting is understood, it can be used to understand how sampling instruments, such as digital oscilloscopes, retrieve the original signal from only a few samples; in Sect. 17.6 the sampling theorem is revisited, and this section explains the difference between linear interpolation and sinx/x interpolation.