Digital Signal Processing 101, 2nd Edition

Appendix C

Laplace Transform

The Laplace transform is used for continuous or analog signals. We shall use x(t) and y(t) to represent the input and output signals to an analog filter, respectively. Rather than use delays, as digital filters use, the differentiator is used instead. The input and output of the analog filter is related by the following relationship.

y(t)=∑i=0toNAi·dix(t)/dti+∑i=0toMBi·diy(t)/dti

The first term is a sum of coefficient weighted derivatives of the input, which is analogous to the FIR filter being a sum of weighted delayed inputs. The second term is a coefficient weighted sum of the derivatives of the output, which implies ...