Common subexpression elimination involving multiple variables for linear DSP synthesis

Common subexpression elimination is commonly employed to reduce the number of operations in DSP algorithms after decomposing constant multiplications into shifts and additions. Conventional optimization techniques for finding common subexpressions can optimize constant multiplications with only a single variable at a time, and hence cannot fully optimize the computations with multiple variables found in matrix form of linear systems like DCT, DFT etc. In this paper we transform these computations such that all common subexpressions involving any number of variables can be detected. We then present heuristic algorithms to select the best set of common subexpressions. Experimental results show the superiority of our technique over conventional techniques for common subexpression elimination.