LEAST SQUARED ERROR FIR FILTER DESIGN WITH TRANSITION BANDS

This paper proposes the use of transition bands and transition functions in the ideal amplitude frequency response to allow the analytical design of optimal least squared error FIR digital filters with an explicit control of the transition band edges. The paper derives design formulas for approximations to ideal frequency responses which use pth order spline transition functions. It also derives a mixed analytical and numerical method for zero-error weight in the transition bands, and pass and stopband error weighting functions with an integral squared error approximation. A variable order spline transition function is developed and a method given for choosing the optimal order to minimize the integral squared approximation error.