
8.2.3 TRANSFER FUNCTION ERRORS
A second class of dynamic error involv es the frequency response functions of the continuous-time
system and the discrete-time system used to simulate it. The fractional error in the (discrete-time
system) transfer function is
e
H
¼
H(e
jvT
) H( jv)
H( jv)
(8:59)
where it is important to remember that
H( jv) ¼ H(s)
j
s jv
, H(z ) ¼ H(s)
j
s 1=H
I
(z)
, H(e
jvT
) ¼ H(z)
j
z e
jvT
(8:60)
The fractional error in transfer function is a complex-valued, frequency-dependent function, which
can be expressed in terms of a real and imaginary compon ent, that is,
e
H
¼
H(e
jvT
)
H( jv)
1 ¼ e
M
þ j e
A
(8:61)
In polar form, the frequency response functions are ...