NUMERICAL SMOOTHING - THE BASIC THEORY AND APPLICATIONS FOR SIGNAL PROCESSING.

Some new ideas for signal processing using numerical smoothing are proposed in this report. The first idea consists in the representation of the input mixture as a series of sinc-functions. The advantages of such expansion become clear because we can consider that the samples of input mixture are given. This representation permits us to calculate the energy by simple means. Besides that, we can establish some important properties of the accepted algorithm of smoothing and examine it for convergence. The second idea consists in the transition to adaptive smoothing, i. e. , the smoothing with a varying step which must be calculated together with the processing; this procedure causes a delay in the output signal. The next idea is related to both above mentioned ones: instead of a probability approach for the study of the operations of smoothing, we use a deterministic one.