Using the bilinear transform to derive digital low-pass filters from their analog prototypes introduces severe warping of the response once the cutoff frequency approaches the Nyquist limit. We show how to design pre- warped first and second order low-pass prototypes that, after application of the bilinear transform, provide a better match with the magnitude response of the analog original than applying the bilinear transform directly. Result plots are given and compared for different cutoff frequencies and Q factors.
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