SAMPLED-DATA SYSTEMS 89 
Thus, it is clearly true that 
Ga6)-I1G1 GG ©) (5.14) 
for elements which are not separated by a sampler. To emphasize the 
condition, it is conventional to write the transform of two cascaded ele- 
ments with a continuous connection between them as G7,(s) : 
iw 
Cuca 7 » Gils + njwo)Go(s + njwo) (5.15) 
In terms of z-transform notation, (5.15) implies that the over-all pulse 
transfer function of two cascaded elements which are not separated by a 
sampler is given by 
Gio(z) = Z[Gi(s)G2(s)] (5.16) 
Stated in words, the pulse transfer function of two cascaded elements not 
separated by a sampler is the z transform corresponding to the product of 
G(z) 
G4 (z) i Go(z) 
Riz) 1 1 Cz) 
ae ley at oe 
Fic. 5.3. System used in example. 

their continuous transfer functions. Where different letters are used for 
the individual transfer functions, such as G(s) and H(s), the over-all pulse 
transfer function is written asGH(z). Referring back to (5.11) and using 
z-transform notation, the output z transform is given by 
C2(z) = Gio(z) R(z) (5.17) 
EXAMPLE 
It is desired to find the over-all pulse transfer function for two ele- 
ments separated by a sampler, as shown in Fig. 5.3. The pulse transfer 
functions of each of the elements are 
1 

Gi(z) =Z gdb a 
ic 1 
7 7 See 
7 a 
and G.(z) = bp 
1 
1 — e-*fz-1 
