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A class of digital filters having rational transfer functions, optimum magnitude in the Chebyshev sense, and minimum phase is discussed. These filters are required to have all zeros on the unit circle, as do the classic elliptic filters. An algorithm for design of these filters is presented which allows the order of numerator and denominator polynomials to differ. Several properties of low pass filters of this type are discussed such as the minimum attainable pass-band ripple for a given denominator order, and the effect of an extra ripple. Several examples are presented and compared with the elliptic filter. Filters are described which meet the same tolerance scheme as an elliptic filter with fewer coefficients than the elliptic filter.