Specifications

tf
16-223
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 transfer 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')
uses the DSP convention and creates
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 the
polynomial (coefficients in
ascending powers of or ).
z
2
z
2
2z 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
hz
1–
()
1 z
1–
+
12z
1–
3z
2–
++
----------------------------------------
zg z()==