Methods of Converting Weight Sequences in Digital Subtraction Filtration

Abstract

The speed limit for non-recursive digital filtering is determined by the length of the weight sequence (pulse characteristic) of the filter and of the bit depth representations of coefficients. We reduce the bit depth when switching to subtraction methods of signal representation (e.g., differential pulse-code modulation) however, the number of non-zero values of the coefficients is significant. In this paper, we consider the method of effective transformation of weight sequence in general and specific weight coefficients to the form at which the number of bit depth is shortened, and the number of zero values is increased. The proposed methods of selecting and calculating the auxiliary sequence to reduce the number of units in the representation of these coefficients, which leads to the transition from inefficient non-recursive implementation to economic recursive. An example of such a transformation is given.