Using least‐mean‐square‐approximation technique in filter design

Abstract

Abstract The applications of the least‐mean‐square‐approximation technique to filter synthesis are discussed, and explicit expressions for the characteristic function of all‐pole lowpass filters are derived using a weighted least mean‐square error norm. The weight function depends on one variable parameter which controls the shape of the magnitude response both in the passband and in the stopband. It is shown that most of the filter functions in common use are special cases of this approximation procedure, including Legendre monotonic passband filters as a limiting, degenerate case. Also, a useful generalization of Legendre filter functions is proposed.