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Overlap-save (OLS) and overlap-add (OLA) are two techniques widely used in digital filtering. In traditional OLS and OLA implementations, the system is compelled to be time-invariant and conventional filter synthesis techniques are used for designing the block filter. In this paper, based on the OLS and the OLA structures, we develop a fast algorithm for designing the optimal OLS and OLA block filters using a quadratic criterion. Comparing OLA to OLS optimal design, we demonstrate that, as in classical design approaches, they show no difference when the filters are time-invariant. However, when aliasing is not zero, although the global aliasing is the same, its components with respect to frequency are different. This conclusion is supported by simulation results, and a comparison between the optimal approach and some other standard approaches is also provided. [ABSTRACT FROM AUTHOR]