SMOOTHING PERIODIC DATA.

In certain cases of smoothing and filtering, the data are known to be periodic. For example, the creep measurement of a revolving disk. Or the shaft of a motor position is being monitored. Many times the data collected is corrupted by noise and ought to be smoothed. It is valuable to set the problem in probability setting. However, a difficulty occurs in the vector case. Normally, when the periodicity occurs, the entire vector has not yet begun repeating, therefore, a recursive formulation is useful. It will be shown that if the number of observations is a multiple of the number in one revolution the result is simple and practical. In fact, if the data is enlarged by repeating itself over and over, the Weiner Smoother results. Thus one may say that the Weiner Smoother is a special case where the period of the data is infinite.