Conformal Maps for the Discretization of Analog Filters Near the Nyquist Limit

We propose a new analog filter discretization method that is useful for discretizing systems with features near or above the Nyquist limit. A conformal mapping approach is taken, and we introduce the peaking conformal map and shelving conformal map. The proposed method provides a close match to the original analog frequency response below half the sampling rate and is parameterizable, order preserving, and agnostic to the original filter's order or type. The proposed method should have applications to dis-cretizing filters that have time-varying parameters or need to be implemented across many different sampling rates.