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A procedure for the design of two-dimensional (2D) semicausal recursive digital filters is developed by employing the generalized class of PLSI (planar least square inverse) polynomials. For recursive filters, semicausal or half-plane filters are more general than causal or quarter-plane filters in approximating arbitrary magnitude characteristics. A stabilization procedure for 2D unstable filters based on the generalized class of PLSI polynomials is also discussed. It is shown that the generalized PLSI of a 2D polynomial has the capability to perform spectral factorization in an approximate way.