The Gaussian Window in Spectral Modeling

Special Property: On a dB scale, the Gaussian is quadratic $\Rightarrow$ parabolic interpolation of a sampled Gaussian transform is exact.

Conjecture: Quadratic interpolation of spectral peaks is generally more accurate on a log-magnitude scale (e.g., dB) than on a linear magnitude scale. This has been verified in a number of cases, and no counter-examples are yet known. Exercise: Prove this is true for the rectangular window.