A common sub-expression elimination method for simplifying hardware logic of a hardware filter circuit by eliminating a common sub-expression included in a plurality of sub-expressions is provided. Each of the sub-expressions includes a corresponding two or more of inputs constituting a plurality of coefficients used by the hardware filter circuit. The method is implemented on a computing device and includes: identifying for each coefficient of the plurality of coefficients, a combination of the inputs constituting the coefficient; counting occurrences of the sub-expressions in each of the coefficients; identifying one or more of the sub-expressions having a maximum one of the counts and including the corresponding two or more of the inputs; selecting one of the one or more of the sub-expressions as the common sub-expression; eliminating the common sub-expression; and repeating these steps to eliminate more of the sub-expressions common to multiple ones of the coefficients.