The alpha-approximation has stable range [0.5, 1], admits a 'hexagonal' integration interpretation, and the paper conjectures no single alpha minimizes both amplitude and phase distortion across all frequencies.
Figure 2(a) illustrates the Euler transformation (also known as the backward-difference approximation) geometrically
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Comprehensive Analysis and Exclusion Hypothesis of $\alpha$-Approximation Method for Discretizing Analog Systems
The alpha-approximation has stable range [0.5, 1], admits a 'hexagonal' integration interpretation, and the paper conjectures no single alpha minimizes both amplitude and phase distortion across all frequencies.