Convergent method for designing high-accuracy bi-equiripple variable-delay filters using new delay-error expression
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This paper proposes a fast non-iterative approach to the design of an odd-order bi-equiripple variable-delay (VD) digital filter whose mathematical model is a multi-variable (MV) transfer function. The objective of the bi-equiripple design is to minimize the maximum frequency-response deviation of this MV transfer function while mitigating the large overshoots of the VD response at the same time. Since the group-delay function is nonlinear with respect to the MV transfer-function coefficients, it is first linearized through using an approximate approach. This linearization enables the bi-equiripple VD filter to be designed with linear constraints, and the bi-equiripple design is then formulated as a convex minimization problem. The convex minimization does not require any iterations and thus it is fast and yields a convergent optimal solution. Solving the convex minimization problem produces a bi-equiripple VD filter with minimized worst-case frequency-response error and mitigated VD-deviation overshoots (jumps). An illustrating example is presented to demonstrate the above simultaneous deviation suppressions.
KeywordsMulti-variable (MV) Transfer function Group-delay Variable-delay (VD) filter Odd-order VD filter Linearized group-delay error Bi-equiripple design
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