Analytical guess of error for nonlinear FIR filters to approximate linear phase response

This paper presents a method to analytically guess output errors for a type of nonlinear FIR filter to approximate linear phase response. The optimal nonlinear FIR filters generate much smaller output errors than conventional linear FIR filters under the condition of the specified amount of multiplications and additions and are obtained by using an iterative optimization. Using the analytical guess, we can not only estimate the error of the optimal nonlinear filter but also speed up the optimization. We confirm that the analytical guess is accurate in many design examples and the effectiveness of the nonlinear filters in various design specifications