New digit-serial implementations of stack filters

We propose several new ways to find the tradeoff between throughput and complexity of stack filter implementations using digit-serial processing. First, we consider the problem in general for lexicographic representations of input data and suggest a digit-serial procedure to calculate the stack filter output. This procedure is a generalization of the bit-serial algorithm for stack filters (Chen, 1989) and we show also that this digit-serial procedure can be used for stack filters if and only if the data representation is lexicographic. Next, we consider the digit-serial case based on multiple-value representations with radix r. We show that stack filters can be realized with an arbitrary number r of positive Boolean function units varying from one in the bit-serial case (Chen, 1989) to M - 1 in the parallel threshold decomposition structure (Wendt et al., 1986). This class of parallel implementations parametrized by r allows us to choose the fastest possible architecture when the complexity is bounded by application requirements. These parallel architectures reduce both the delay and the cycle time of the circuit, a property that cannot be achieved systematically by the other methods. (C) 1997 Elsevier Science B.V.