A dynamic programming technique for nonlinear smoothing

This paper describes an optimization approach to the nonlinear smoothing problem. Linear techniques of smoothing do not yield satisfactory results for curves which exhibit both sharp discontinuities to be preserved and incorrect samples to be filtered out. The presented nonlinear approach employs the concept of a cost function which penalizes for large variations between two consecutive samples and rewards for close vicinity between them. The overall cost is used as a criterion of optimality. The optimization is carried out by a dynamic programming strategy. The resulting algorithm requires only very moderate computational costs. Examples of the application of the non-linear smoothing to pitch period contours are presented.