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This paper examines constrained optimization designs of infinite impulse response (I.I.R.) digital filters and introduces two new design methods, including one based upon discrete prolate spheroidal wave functions. The designs employ a recently introduced model for the magnitude squared function of an all pole filter, the coefficients of which can be obtained using optimization techniques subject to either linear or quadratic constraints. The generalized design methods introduced in this paper allow the design of low pass and high pass filters and since the filters can be implemented as lattice filters they should have low finite word length errors. The design methods introduced for 1 Dimensional filters can be extended to 2 Dimensions and preliminary results are included.