Obtaining a rational all-pass filter that matches a target phase response is a common problem in signal processing. Typical approaches have generally focused on optimizing filter coefficients while minimizing the deviation from the target phase response. However, these approaches typically do not offer a guarantee of exact match of the phase or any conditions on group delay. In this letter, we propose a Blaschke interpolation based all-pass filter design, wherein, if the phase response is known at $n$ distinct frequencies, an all-pass filter that exactly satisfies the target values can be obtained. Moreover, the group delay at the interpolating points can be optimized or tuned to control the phase response for remaining frequencies. Simulations reveal that the design method is able to produce filters that closely match the target phase response accurately with much lower complexity than prior approaches.

中文翻译：

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使用 Blaschke 插值的全通滤波器设计

获得匹配目标相位响应的合理全通滤波器是信号处理中的常见问题。典型的方法通常侧重于优化滤波器系数，同时最小化与目标相位响应的偏差。然而，这些方法通常不提供相位精确匹配或群延迟的任何条件的保证。在这封信中，我们提出了一种基于 Blaschke 插值的全通滤波器设计，其中，如果在 $n$ 个不同频率下已知相位响应，则可以获得完全满足目标值的全通滤波器。此外，可以优化或调整内插点的群延迟以控制剩余频率的相位响应。