Locally Parabolic Approximation

Consider the Taylor expansion of the main lobe at its midpoint:

$$W(\omega) = W(0) + \frac{1}{2}W''(0)\omega^2 + \frac{1}{4!}W''''(0)\omega^4 + \cdots$$

• Parabolic interpolation effectively neglects terms higher than second order
• Parabolic interpolation on a dB scale = Gaussian interpolation on a linear magnitude scale
• All main lobes can be approximated arbitrarily well using quadratic interpolation in conjunction with sufficient zero padding