User`s guide

tf
11-229
engineers use the variable a nd order the numerator and denominator terms
in descending powers of , for example,
The polynomials and are then specified by the row vectors
[1 0 0] and [1 2 3], respectively. By contrast, DSP engineers prefer to write
this trans fer function as
and specify its numerator as
1 (instead of [1 0 0]) and its denominator as
[1 2 3].
tf switches convention based on your choice of variable (value of the
'Variable' property).
For example,
g = tf([1 1],[1 2 3],0.1)
specifies the discrete transfer function
because is the default variable. In contrast,
h = tf([1 1],[1 2 3],0.1,'variable','z^–1')
Variable Convention
'z'
(default) Use the row vector [ak ... a1 a0] to specify the
polynomial (coefficients ordered in
descending powers of ).
'z^–1', 'q' Use the row vector [b0 b1 ... bk] to specify t he
polynomial (coefficients in
ascending powers of or ).
z
z
hz()
z
2
z
2
2z 3++
----------------------------=
z
2
z
2
2 z 3++
hz
1–
()
1
12z
1–
3z
2–
++
----------------------------------------=
a
k
z
k
... a
1
za
0
++ +
z
b
0
b
1
z
1
–
... b
k
z
k
–
+++
z
1
–
q
gz()
z 1
+
z
2
2z 3++
----------------------------=
z