The problem of approximating the response of the ideal frequency-selective transfer-function in both the time and frequency domain represents a fundamental limitation in linear systems theory. In this paper, we propose the uniformly-damped binomial filter (UDBF) transfer-function as a better and balanced compromise to this approximation problem in the time and frequency domain, than both the butterworth filter and the binomial filter. This class of filter can be viewed as a general approach to realize, in any integer order, a damped binomial filter transfer-function with a maximum complementary-sensitivity and transient response similar to the standard second-order butterworth filter. We further demonstrate that this uniformly-damped binomial response overcomes both the excessive ringing phenomena associated with the butterworth response, and the sluggish response associated with the binomial response for higher order transfer-functions. Finally, we conclude that in applications of interest, where both strong filtering and a smooth transient-response are desired, this uniformly-damped binomial standard form response is a viable replacement for both the butterworth and binomial forms.

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关于均匀阻尼二项式滤波器

在时域和频域中逼近理想频率选择性传递函数的响应的问题代表了线性系统理论的基本限制。在本文中，我们提出了均匀阻尼二项式滤波器 (UDBF) 传递函数，作为在时域和频域中对这个近似问题的更好和平衡的折衷方案，比 Butterworth 滤波器和二项式滤波器都好。此类滤波器可被视为以任何整数阶实现具有最大互补灵敏度和瞬态响应的阻尼二项式滤波器传递函数的通用方法，类似于标准二阶巴特沃斯滤波器。我们进一步证明，这种均匀阻尼二项式响应克服了与巴特沃斯响应相关的过度振铃现象，以及与高阶传递函数的二项式响应相关的缓慢响应。最后，我们得出结论，在需要强滤波和平滑瞬态响应的相关应用中，这种均匀阻尼二项式标准形式响应是巴特沃斯和二项式形式的可行替代品。