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<p>The paper investigates a newly developed iterative linear programming (LP) tactic for producing an allpass filter with tunable fractional-delay (FD). This design targets at minimizing the peak of filter’s spectrum errors (frequency-response errors) while constraining the peak value of the FD errors. Although the allpass tunable-FD filter relates its FD response and its filter coefficients in a highly nonlinear fashion, this paper exploits an approximate FD expression whose numerator reduces to a linearized function of the tunable-FD filter’s coefficients to develop a novel design strategy. The linearized numerator facilitates the design formulation, enabling the tunable-FD filter design to be reduced to the LP minimization. Exploiting this approximate FD expression, we formulate the implementation of an allpass tunable FD-filter as an iterative minimization problem. This problem can be simply solved by employing LP so as to minimize the peak of filter’s spectrum errors while simultaneously constraining the overshoot of the FD errors. Executing the LP repeatedly yields an allpass tunable-FD filter with FD-error peak suppressed, while the peak of the spectrum errors is minimized. This paper exemplifies a demonstrative design to validate the usefulness of the iterative LP strategy.</p>

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Iterative Linear-Prgogramming Tactic for Implementing Allpass Tunable Fractional-Delay Filters with Delay-Error Suppression

  • 期刊论文

  • 发表日期：

    2025年7月4日

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  • Tian-Bo Deng

摘要

The paper investigates a newly developed iterative linear programming (LP) tactic for producing an allpass filter with tunable fractional-delay (FD). This design targets at minimizing the peak of filter’s spectrum errors (frequency-response errors) while constraining the peak value of the FD errors. Although the allpass tunable-FD filter relates its FD response and its filter coefficients in a highly nonlinear fashion, this paper exploits an approximate FD expression whose numerator reduces to a linearized function of the tunable-FD filter’s coefficients to develop a novel design strategy. The linearized numerator facilitates the design formulation, enabling the tunable-FD filter design to be reduced to the LP minimization. Exploiting this approximate FD expression, we formulate the implementation of an allpass tunable FD-filter as an iterative minimization problem. This problem can be simply solved by employing LP so as to minimize the peak of filter’s spectrum errors while simultaneously constraining the overshoot of the FD errors. Executing the LP repeatedly yields an allpass tunable-FD filter with FD-error peak suppressed, while the peak of the spectrum errors is minimized. This paper exemplifies a demonstrative design to validate the usefulness of the iterative LP strategy.