PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

550 Practical MATLAB® Applications for Engineers

The partial fraction expansion is:

Fz =

(5/6-1/426*i*3723311^(1/2))/(z-7/20-1/20*i*71^(1/2))+

(5/6+1/426*i*3723311^(1/2))/(z-7/20+1/20*i*71^(1/2))+10/3

The impulse response h(n) is:

hn =

127/9*charfcn[0](n)-97/18*(-6/(i*71^(1/2)-7))^n-979/1278*i*(-6/(i*71^

(1/2)-7))^n*71^(1/2)97/18*6^n*(1/(7+i*71^(1/2)))^n+979/1278*i*6^n*(1/(7+i*71^

(1/2)))^n*71^(1/2)

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Pole and zero plot of H(z)

1

0.8

0.6

0.4

0.2

0

−0.2

−0.4

−0.6

−0.8

− 1

− 1 −0.5 0

Real Part

Imaginary Part

0.5 1

FIGURE 5.63
Pole/zero plot of H(ejW) of Example 5.15.

FIGURE 5.64
Plot of abs{H(ejW)} and angle {H(ejW)} of Example 5.15.

− 4 − 3 − 2 − (^1) 01 23 4
12
10
8
6
Magnitude 4
2
− 4 − 3 − 2 − (^10)
frequency W in rad
1234
2
Phase in rad.
1
0
− 1
− 2
abs[H(exp(-jW))] versus W
angle[H(exp(-jW))] versus W