The Lp-Norm-Minimization Design of Stable Variable-Bandwidth Digital Filters

Abstract

This paper proposes a two-step strategy for designing a variable-bandwidth (VBW) digital filter through minimizing the [Formula: see text]-norm of the magnitude-response error. This [Formula: see text]-norm design can be regarded as a generalized version of the existing weighted-least-squares (WLS) design. Equivalently, the WLS design is a special case of the [Formula: see text]-norm-minimization design for [Formula: see text]. This paper discusses the design of the recursive VBW filter with the transfer function whose denominator is expressed as the product of the second-order sections. As long as all the second-order sections are stable, the recursive VBW filter is also stable. To ensure that the designed recursive VBW filter is stable, we adopt the coefficient-conversion strategy that constrains all the denominator-parameter pairs of the second-order sections within the stability triangle. This paper also proposes a novel conversion function for performing the coefficient conversion. As a consequence, the designed VBW filter is definitely stable. A bandpass VBW filter is designed for showing the feasibility of the [Formula: see text]-norm-minimization-based design and verifying the stability guarantee.