The direct integer factorization approach to the Crochiere and Rabiner multistage FIR designs for multirate systems

The parameters of designing a multistage, multirate narrow-band FIR system are the total storage requirements (TSR) for the coefficients or the number of multiplications per second (MPS). Crochiere and Rabiner had developed an approximated optimization problem for the choice of parameters. The minimum solution can be found by any suitable multidimensional optimization technique. However, the dimension (number of stages) can only be determined after a full investment of the minimum solutions, and then a heuristic procedure should also be employed to choose the integer factors. An equivalent constrained optimization problem is solved by the direct factorization of positive integer. The proposed algorithm provides a direct factorization to find the true minimum solution of the constrained integer optimization problem. With this approach, the true integer solution of the constrained is obtained. A typical design curve is present by the proposed approach.