Abstract This paper presents an overview on advancement made in designing of a digital infinite impulse response (IIR) filter. The design problem of an IIR filter was found to be challenging due to presence of poles in its transfer function. This makes the phase response of an IIR transfer function nonlinear and its magnitude response is also drifted due to quantization of coefficient values of denominator polynomials, which leads towards instability. Therefore, numerous efforts were made in order to acquire an optimal filter response using several optimization methods. Design problem of an IIR filter with various constraints was developed and solved using gradient based techniques, which resulted in optimal passband response with nearly linear phase or in some cases, absolute linearity was also achieved. However, the obtained solutions were sub-optimal in many cases due to transferring the multimodal design problem of an IIR filter into convex optimization. The solution was also affected due to the quantization of filter coefficients and in case of absolute linear phase response; a strong hick in magnitude response at beginning of transition edge frequency was obtained. To overcome the sub-optimality, researchers used evolutionary algorithms (EAs) for designing of an IIR filter. In time domain, system identification (SI) was adopted, whereas various error functions were developed in frequency domain for obtained magnitude responses close to desired response. This approach resulted in an optimal IIR filter response, however phase response linearity was not improved. Thus, EA approach was appropriated for lower order IIR filters. The design of various IIR filters like lowpass filter (LPF), highpass filter (HPF), bandpass filter (BPF) and bandstop filter (BSP) using an all-pass infinite impulse response (APF-IIR) was also reported. This approach is most appropriate, because the filter response is stable, nearly linear and magnitude response was also accurate. However, there is high error at the band edges of passband. Therefore, literature reveals that an APF based approach is most appropriate for various magnitude response filters.

中文翻译：

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数字 IIR 滤波器的设计：一项研究调查

摘要 本文概述了数字无限脉冲响应 (IIR) 滤波器的设计进展。发现 IIR 滤波器的设计问题具有挑战性，因为其传递函数中存在极点。这使得 IIR 传递函数的相位响应呈非线性，并且其幅度响应也因分母多项式的系数值的量化而漂移，从而导致不稳定。因此，为了使用多种优化方法获得最佳滤波器响应，进行了大量努力。使用基于梯度的技术开发和解决了具有各种约束的 IIR 滤波器的设计问题，这导致具有接近线性相位的最佳通带响应，或者在某些情况下还实现了绝对线性。然而，由于将 IIR 滤波器的多模态设计问题转化为凸优化，所获得的解在许多情况下是次优的。由于滤波器系数的量化和绝对线性相位响应的情况，该解决方案也受到影响；在过渡边缘频率开始时获得了强烈的幅度响应。为了克服次优问题，研究人员使用进化算法 (EA) 来设计 IIR 滤波器。在时域中，采用了系统识别 (SI)，而在频域中开发了各种误差函数，以获得接近所需响应的幅度响应。这种方法产生了最佳的 IIR 滤波器响应，但是相位响应线性度没有得到改善。因此，EA 方法适用于低阶 IIR 滤波器。还报告了使用全通无限脉冲响应 (APF-IIR) 设计各种 IIR 滤波器，如低通滤波器 (LPF)、高通滤波器 (HPF)、带通滤波器 (BPF) 和带阻滤波器 (BSP)。这种方法是最合适的，因为滤波器响应稳定，接近线性并且幅度响应也很准确。然而，在通带的频带边缘有很高的误差。因此，文献表明基于 APF 的方法最适合各种幅度响应滤波器。通带的带边有很大的误差。因此，文献表明基于 APF 的方法最适合各种幅度响应滤波器。通带的带边有很大的误差。因此，文献表明基于 APF 的方法最适合各种幅度响应滤波器。