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 discretizing filters that have time-varying parameters or need to be
implemented across many different sampling rates.