User`s guide

Continuous/Discrete Conversions of LTI Models
3-23
Similarly, the d2c conversion relies on the inverse correspondence
Tustin with Frequency Prewarping
This variation of the Tustin approximation uses the correspondence
This change of variable ensures the matching of the continuous- and
discrete-time frequency responses at the frequency .
Matched Poles and Zeros
The ma tched pole-zero method applies only to SISO systems. The continuous
and discretized systems have matching DC gains and their poles and zeros
correspond in the transformation
See [ 2], p. 14 7 for more details.
H
d
z() Hs'(),where= s'
2
T
s
------
z 1
–
z 1+
------------
=
Hs() H
d
z'(),where= z'
1 sT
s
2
⁄+
1 sT
s
2⁄–
--------------------------=
H
d
z() Hs'(),= s'
ω
ωT
s
2⁄()tan
---------------------------------
z 1
–
z 1+
------------
=
ω
Hjω() H
d
e
j
ω
T
s
()=
ze
sT
s
=