Convolution filtering at ends of data sets

Abstract

Convolution filters are normally applied to data sets in one of two modes. The first is to terminate the operation, at a distance equal to half the filter length from the ends of the data. This results in loss of information. The second is to run the filter off the end of the data set, by adding sufficient zeros to the ends of the data. The effects of this second method are shown to be serious, in cases where there is significant information in the ends of the data set. An alternative method is proposed in which the convolution operator is modified when operating on the end portion of the data.