Designing filters with perfect frequency responses (i.e., flat passbands, sharp transition bands, highly suppressed stopbands, and linear phase responses) is always the ultimate goal of any digital signal processing (DSP) practitioner. High-order finite impulse response (FIR) filters may meet these requirements when we put no constraint on implementation complexity. In contrast to FIR filters, infinite impulse response (IIR) filters, owing to their recursive structures, provide an efficient way for high-performance filtering at reduced complexity. However, also due to their recursive structure, IIR filters inherently have nonlinear phase responses, and this does restrain their applicability. In this article, we propose two tricks regarding cascading a prototype IIR filter with a few shaping all-pass filters (APFs) for an almost linear phase response over its passband. After performing a delicate design on the prototype and shaping filters, we approach perfect filtering with reduced complexity.

中文翻译：

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设计具有几乎线性相位响应的级联无限脉冲响应滤波器的技巧 [提示与技巧]

设计具有完美频率响应（即平坦的通带、尖锐的过渡带、高度抑制的阻带和线性相位响应）的滤波器始终是任何数字信号处理 (DSP) 从业者的最终目标。当我们不限制实现复杂性时，高阶有限脉冲响应 (FIR) 滤波器可以满足这些要求。与 FIR 滤波器相比，无限脉冲响应 (IIR) 滤波器由于其递归结构，提供了一种以降低复杂性实现高性能滤波的有效方法。然而，同样由于其递归结构，IIR滤波器本质上具有非线性相位响应，这确实限制了它们的适用性。在本文中，我们提出了两个技巧，将原型 IIR 滤波器与一些整形全通滤波器 (APF) 级联，以在其通带上实现几乎线性的相位响应。在对原型和整形滤波器进行精细设计后，我们以降低的复杂性实现了完美的滤波。