ABSTRACT
This chapter shows how to smooth data with the simplest of models that are not based on physical laws but on experience and judgment. The concepts used in smoothing range from the simplest least squares approach to digital filtering, Fourier series, and spline fitting. The smoothing of data is an intuitive process based on the assumption that most physical parameters are generally continuous and have continuous derivatives. The chapter aims to illustrate the general framework of dynamic programming and generalized cross validation as it applies to smoothing and differentiation of data. The use of generalized cross validation will play a vital role in our application in that it injects some objectivity into the smoothing process. The chapter analyzes a mathematical extension of what an experimenter might do to analyze a black box — which is to simply apply a sine wave of fixed amplitude and frequency to the input and observe the output.
