Normalized peak ripple magnitude as an objective function in discrete coefficient FIR filter design

Normalized peak ripple magnitude (NPRM) has been a convenient design criterion for discrete coefficient FIR filters. "Filter gain" is the major concern for NPRM. This paper presents an exact closed form expression of the filter gain for a given set of filter coefficients. Based on this expression the characteristics of NPRM cost function are discussed. The selection of the initial value of the filter gain for suboptimal design methods is considered. Deficiency of the previously proposed methods is pointed out and a way to overcome the problem is presented. Proposed solution provides additional information that has been proved to be useful in determining the initial point when using a suboptimal optimization method.