Digitization of Lumped Models

Since lumped models are described by differential equations, they are digitized (brought into the digital-signal domain) by converting them to corresponding finite-difference equations (or simply ``difference equations''). General aspects of finite difference schemes are discussed in Appendix D. This chapter introduces a couple of elementary methods in common use:

1. Finite difference approximation: $sT= 1-z^{-1}$
2. Bilinear transform: $sT= 2\,(1-z^{-1})/(1+z^{-1})$

Note that digitization by the bilinear transform is closely related to the Wave Digital Filter (WDF) method introduced in Appendix F. Section 9.3.1 discusses a bilinearly transformed mass colliding with a digital waveguide string (an idealized struck-string example).