User`s guide

Table Of Contents

2 LTI Models

2-22

Similarly,

z = zpk('z', 0.1);

H = [z/(z+0.1)/(z+0.2) ; (z^2+0.2*z+0.1)/(z^2+0.2*z+0.01)]

produces the single-input, two-output ZPK model

Zero/pole/gain from input to output...

#1: ---------------

(z+0.1) (z+0.2)

(z^2 + 0.2z + 0.1)

#2: ------------------

(z+0.1)^2

Sampling time: 0.1

Note that:

• The synta x

z = tf('z') is equivalent to z = tf('z',–1) and leaves the

sample time unspecified. The same applies to

z = zpk('z').

• Once you have defined

z as indicated above, any rational expressions in z

createsadiscrete-timemodelofthesametypeandwiththesamesample

time as

Discrete Transfer Functions in DSP Format

In digital signal processing (DSP), it is customary to write discrete transfer

functions as rational expressions in and to order the numerator and

denominator coefficients in ascending powers of . For example, the

numerator and denominator of

would be specified as the row vectors

[1 0.5] and [1 2 3], respectively. When

the numerator and denominator have different degrees, this convention

clashes with the “descending powers of ” convention assumed by

tf (see

“Transfer Function Models” on page 2-8, or

tf on page 11-224). For example,

h = tf([1 0.5],[1 2 3])

–

1–

()

10.5z

–

12z

1–

2–

----------------------------------------=