Digital Signal Processing 101, 2nd Edition

Appendix D

Z-Transform

The z-transform is used for sampled signals. It is analogous to the s-transform used with continuous or analog signals. We shall use x_k and y_k to represent the input and output signals to a digital filter, respectively. Rather than using differentiators, as analog filters use, the delay function is used instead. The input and output of the IIR (recursive) digital filter is related by the following relationship.

yk=∑i=0toN−1Cixk−i+∑i=1toN−1Diyk−i

The first term is a sum of coefficient weighted delayed versions of the input (this is the familiar FIR filter expression). The second term is a coefficient weighted sum of the delayed ...