Low sensitivity realization of FIR filters with 2-stage cascade structure

In this paper, the authors propose a low sensitivity realization of linear phase FIR filters with a 2-stage cascade form. The authors obtain the upper limit of the error in the magnitude of the frequency response of the resulting filter realized with the quantized coefficients. They use the coefficient sensitivity of the magnitude of the frequency response and obtain the optimum condition for the magnitudes of the frequency response for each of the stages in the cascade. Based on this result, they propose a method for the least sensitive decomposition of the given zero locations of the original filter in a direct form. They also illustrate the effectiveness of this method with the help of a few examples and show that the realization based on the proposed method indeed results in very low sensitivity structures. Finally, they also discuss the optimum realization of a 2-stage cascade form with arbitrary order in each section