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The classic digital filter architecture, often referred to as the Jackson-Kaiser-McDonald (JMK) filter, realizes a filter in terms of general purpose multipliers, adders, and shift-registers. In the mid-1970's, the memory-intensive linear shift invariant filter architectures, known as the distributed filter (or Peled and Liu PL filter) and Monkewich-Steenaart (or MS) fiter were introduced. By exploiting the parallel nature of the residue number system, and using high-speed table lookup operations, high speed JKM filters have been realized. In this paper, the fundamental structure of residue KJM, PL, and MS filters are developed and reported. Experimental results indicate that very high speed linear shift invariant filters can be designed in the residue number system. In additon, it is shown that the precision of the filter is gratly influenced by the chosen architecture.