Least-Squares Design of Linear-Phase FIR Half-Band Filters

Abstract

Two approaches are described which can be used to design half-band filters for multirate applications. The approaches are based on the method of formulating the weighted mean-square error between the amplitude responses of the practical and ideal filters as a quadratic function. The filter coefficients are obtained by solving a set of linear equations. This method yields filters that are optimal in the least-squares sense. Design examples are provided.

Indexing terms:

• FIR half band filter
• Least square design