4.7z-Domain Transfer Function

We have seen how the transfer function of a linear continuous-time system is used to find the system’s response to elementary inputs. Stability and frequency response characteristics of the system can be inferred from the transfer function as well. A discrete-time system transfer function does the same for linear discrete-time systems. We begin with the nth-order, linear, constant coefficient difference equation

yk+a1yk−1+⋯+anyk−n=b0uk−1+⋯+bmuk−m, n≥m

(4.456)

z-Transforming both sides and applying the linearity property gives

z{yk}+a1z{yk−1}+⋯+anz{yk−n}=b0z{uk}+b1z{uk−1}+⋯+bmz{uk−m}

(4.457)

Assuming the input is applied at k = 0 and the initial values y–1, y–2, …, y–n are zero, we can use the delay property ...

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