350 Practical MATLAB® Applications for Engineers
R.4.91 Similarly, a noncausal system can be defi ned as the one with the ROC located to the
left of the pole having the smallest real part.
R.4.92 Mix systems are the ones that have poles in the left-half plane (causal), as well as,
poles in the right-half plane (noncausal). The ROC then lies between the pole hav-
ing the smallest real part, of the causal subsystem, and the pole having the smallest
real part of the noncausal subsystem.
R.4.93 The stability of a system is given by the location of its system’s poles. Stable causal
systems must have all the poles to the left of the imaginary axis, and the axis itself
may be considered part of the ROC.
R.4.94 The MATLAB function pzmap (Y, X) returns the plot of the poles and zeros specifi ed
by the coeffi cients of the polynomials of Y and X, the numerator and denominator
of H(s), expressed as vectors arranged in descending powers of s. It is customary to
indicate the location of the system’s poles by xs, and the system’s zeros by os, on the
s-plane (complex plane).
The command pzmap uses those characters and returns the pole and zero
constellation.
R.4.95 For example, create the script fi le map_pz that returns the constellation plot of the
poles and zeros of the transfer function H(s) given by
Hs
ss
sss()
5530
342
2(^32)
their respective values (poles and zeros), and indicate the ROC (Figure 4.8).
MATLAB Solution
% Script file: map pz
num = [5 5 -30];
den = [1 3 4 2];
pzmap(num,den);
disp(‘’)
disp(‘The zeroes and poles of H(s) are:’)
disp(‘’)
zeroes = roots(num)
poles = roots(den)
real s = min(real(poles));
disp(‘’)
disp(‘The ROC lie in the region given by : real part greater than ‘)
roc
disp(‘’)
The script fi le map_pz is executed and the results are indicated as follows:
map _ pz
The zeroes and poles of H(s) are:
zeroes =
-3
2