Lateral derivatives

First, k_x will range over $\pm \pi / \Delta x$.If the x-axis is going to be handled by finite differencing then we will need equation (39):

$$\left( \ { \hat k \, \Delta x \over 2 }\ \right)^2 \eq {\si... ...Delta x\over 2} \over 1\ -\ b\,4\ \sin^2\ {k\,\Delta x\over 2}}$$

So if the x-axis is going to be handled by finite differencing then subsequent reference to k_x should be replaced by ${\hat k}_x$.The finite differencing introduces the free parameter b. Likewise, you could also scale the whole expression by an adjustable parameter near unity. Also, $\Delta x$ isn't necessarily fixed by the data collection. You could always interpolate the data before processing. A finite-difference method using interpolated data could be mandated by enough lateral velocity variation.