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- Title
The -Norm-Minimization Design of Stable Variable-Bandwidth Digital Filters.
- Authors
Deng, Tian-Bo
- Abstract
This paper proposes a two-step strategy for designing a variable-bandwidth (VBW) digital filter through minimizing the -norm of the magnitude-response error. This -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 -norm-minimization design for . 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 -norm-minimization-based design and verifying the stability guarantee.
- Subjects
RECURSIVE filters; DIGITAL signal processing; LEAST squares; TRANSFER functions; BANDPASS filters
- Publication
Journal of Circuits, Systems & Computers, 2018, Vol 27, Issue 7, p-1
- ISSN
0218-1266
- Publication type
Article
- DOI
10.1142/S0218126618501025