THE Z-TRANSFORM ANALYSIS OF LINEAR SAMPLED-DATA SYSTEMS 69 
function can be found by applying an impulse to the input of a system 
whose continuous transfer function is G(s) and sampling the output. The 
z transform of the resulting sequence is G(z), the pulse transfer function 
of the system. It 1s emphasized that the pulse transfer function relates 
only the output pulse sequence to the input pulse sequence. It does not 
relate the continuous output c(¢) to the pulse sequence at the input. 
No information concerning the behavior of the output c(t) between 
sampling instants is available from the pulse transfer function, although 
in its modified form indirect information can be obtained, as will be 
shown in a later chapter. 
EXAMPLE 
A step function is applied to a system, as shown in Fig. 4.6. The 
continuous transfer function G(s) is 
1 
Cy eeeata 
The pulse transfer function G(z) is 
IL 
sta 
which is, from the table in Appendix I, 
GEDA 
1 — e-27Fz71 
G(z) = Z—— 
Ge 
The input z transform R(z) is also obtained from the table and is 
1 
RO) ee 
The z transform of the output C(z) is the product of R(z) and G(z), 
1 1 
1 — e-@?fz-1 1] — 2g 

C(z) = 
which, upon multiplication, becomes 
1 
— (1 a GE) + e eT z—2 
If the pulse sequence in the time domain is desired, the z transform 
C(z) may be inverted either by long division or by the residue method.. 
Cz) = 

It is seen from the foregoing example that the application of the pulse 
transfer function to sampled-data-system problems is no more complex 
than the application of the continuous transfer function i is to continuous 
linear systems. 
