On the Uniformly-Damped Binomial Filter
Oluwasegun Ayokunle Somefun, Kayode Francis Akingbade, Folasade Mojisola Dahunsi · arXiv (Cornell University) · 2020
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.