Discretizing the ODE

• Typical choices: Euler methods, bilinear transformation, Impulse Response invariance.
• Our choice: the 1-step Weighted Sample method.

k-step WS methods

• Designed for linear differential systems $\mbox{\boldmath${\dot{w}}$}= \mbox{\boldmath${Aw}$}+\mbox{\boldmath${Bu}$}$.
• Based on a $k$-order polynomial interpolation of the input $\mbox{\boldmath${u}$}$.
• The Impulse Response invariance is equivalent to the 0-step Weighted Sample method.

Efficiency

• A $n$-order continuous filter is mapped by the $k$-step WS method into a $(n+k-1)$-order digital filter.
• : the reed filter $H_c(s)$ is mapped into a $2$nd order digital filter.