Some properties of prediction and interpolation errors

Linear prediction and interpolation are widely used in signal processing. Usually they are obtained by linear filters of finite memory, and the prediction and interpolation errors decrease when this memory increases. If the asymptotic values of these errors are null, the signal is singular. Some theoretical aspects of finite and infinite prediction and interpolation are discussed, and a numerical method to compute the prediction and interpolation errors for signals with a given power spectrum is presented. A large number of results obtained with this method are discussed, especially the difference between regular and singular signals. This method also allows the behavior of prediction and interpolation errors when the memory of the filter increases to be studied