Basis Selection - Derivative Order

In order to choose the derivative orders to be used in this basis set, we first note that all Gaussian derivative spectra are bandpass with the sole exception of the original Gaussian which is low-pass.
We can define the spectral location as the peak of the curve in the frequency domain.

Here we see that the spectral location is dependent on both the Gaussian variance and the derivative order. Solving for n yields a real number representing the derivative order necessary to locate a pass band peak at a desired _n. This value is rounded to obtain an integral derivative order.