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This paper proposes a novel method for the design of a recursive second-order (biquadratic) all-pass phase compensator with controllable stability margin. The design idea stems from the generalized stability triangle (GST) derived by the author for the second-order biquadratic digital filter. Based on the GST, a parameter-transformation method is proposed on the transformations of the denominator coefficients of the transfer function of the biquadratic phase compensator. The transformations convert the original denominator coefficients to other new parameters, and any values of those new parameters can guarantee that the GST condition is always satisfied. Optimizing the new parameters yields a biquadratic phase compensator that definitely meets a prespecified stability margin. That is, a biquadratic all-pass phase compensator can be designed to have an arbitrarily specified stability margin. This in turn avoids the occurrence that a recursive phase compensator may become unstable in the practical applications. Thus, the resulting biquadratic phase compensator has robust stability, which is extremely important during the practical filtering operations. A design example is given to show the stability margin guarantee as well as the approximation accuracy. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Guaranteeing the stability is one of the most critical issues in designing a variable recursive digital filter. In this paper, we first present an odd-order recursive variable model (transfer function) that is used for designing an odd-order variable-magnitude (VM) digital filter, and then we replace the original coefficients of the denominator of the odd-order transfer function with a set of new parameters. These new parameters can ensure that they can take arbitrary values without incurring instability of the designed odd-order VM filter. To make the VM filter coefficients variable, we find all the VM filter coefficients as polynomial functions of the tuning parameter, which includes two phases. The first phase designs a set of recursive digital filters with fixed coefficients (constant filters), and the second phase utilizes a curve-fitting scheme to represent each coefficient as a polynomial function. As a result, the VM filter coefficients become variable, and the proposed parameter-substitution-based denominator coefficients ensure the filter stability. This is the most important contribution of the parameter-substitution-based design scheme. This paper uses the fifth-order demonstrative example to verify the stability guarantee as well as the design accuracy of the obtained the fifth-order VM filter. [ABSTRACT FROM AUTHOR]