where the "h"[•] sequence is the impulse response, and "K" is the largest value of "k" for which "h"["j" + "kL"] is non-zero. In the case "L" = 2, "h"[•] can be designed as a half-band filter, where almost half of the coefficients are zero and need not be included in the dot products. Impulse response coefficients taken at intervals of "L" form a subsequence, and there are "L" such subsequences (called phases) multiplexed together. Each of "L" phases of the impulse response is filtering the same sequential values of the "x"[•] data stream and producing one of "L" sequential output values. In some multi-processor architectures, these dot products are performed simultaneously, in which case it is called a polyphase filter.