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It has recently been shown that high-speed fixed-point digital filtering can be realized using modular arithmetic (viz., residue arithmetic). In these studies modular arithmetic is performed using table lookup methods. Here, precomputed modular operations are accessed from high-speed ROM's and/or RAM's. However, when large dynamic ranges are required, table size requirements can become unrealistically large. In this work we present a memory compression scheme which reduces the memory requirements imposed on modular arithmetic systems by as much as a factor of four. This dramatic memory savings is accomplished through the uncovering of some intrinsic symmetry properties found in modular arithmetic matrices.