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A method for incorporating the requirement of smoothness into the estimation procedure for speech parameters is described. The traditional method of estimating a speech parameter, such as the fundamental period or a formant, is to determine the speech parameter separately for each time frame, usually by optimizing a suitable function of the speech signal. However, it is known a priori that adjacent speech parameters are strongly correlated, and that the overall contour of the parameter versus time must be a relatively smooth curve. An overall criterion of optimality for the contour of the speech parameter is introduced; the optimization problem is solved by means of dynamic programming. A recursive algorithm is obtained which does without statistical assumptions and is purely deterministic. The algorithm, although computationally expensive, can easily be implemented and has a tracking capability for on-line estimation.