AN INTRODUCTION TO TRIGONOMETRIC SMOOTHING

We consider the method of trigonometric smoothing, which is a general technique based on the following two main steps: (1) expansion of a di screte function (1-D or 2-D) using trigonometric functions and (2) int roduction of a smoothness criterion. By tailoring the smoothness crite rion, a variety of problems can be solved. The method of trigonometric smoothing is conceptually simple and flexible with respect to smoothi ng and accuracy. Methodically, it can be considered to fall between th e polynomial least-squares fit and the spline technique. Possible appl ications of the method are demonstrated employing both experimental an d synthetic data.