The stab argument in lamb.

There really is no need for a stability factor, unless you are running itype=8 which takes the derivative right at the source point, R=0. With all other itype values, you can set stab=0. The derivative operator used in lamb is a bilinear transform realization of the derivative with respect to time. In terms of the Z-transform,

$\displaystyle Y(z)=\frac{2}{\Delta t}\cdot\frac{\left(1-z\right)}
{\left(\left(1+stab\right)+z\right)}\cdot X(z),$ (45)

where Y(z) is the output signal Z-transform, and X(z) is the input signal Z-transform. The stab factor nudges the pole at the Nyquist frequency slightly off the unit circle to prevent extreme blow up of any Nyquist amplitudes in the input signal. The derivative is realized by an ARMA operator. The formula which realizes equation (45) is

$\displaystyle y_{j}=\frac{\frac{2}{\Delta t}\left(x_{j}-x_{j-1}\right)-y_{j-1}}
{\left(1+stab\right)},$ (46)

where $y_{j}$ is the j-th sample corresponding to the temporal derivative of $x_{j}$ , the j-th sample of the input signal being differentiated.