Digital Filters - Digital Signal Processing: A Practitioner's Approach - page 62

60

Varying r from 0.65 to 0.95

50

40

30

20

10

0

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Normalised frequency

Figure 3.21 Filter response for varying values of r

3.8.2 Varying p
Another parameter which can be varied in the filter is p. So we increase the value of
p while keeping r constant. From Figure 3.22 we find that the curve shifts towards
the right as p increases. The value of p is varied from p ¼ 1 6180 ð ¼ 36 Þ : to

6180 ð ¼ 144 Þ keeping the value of r constant at 0.9. Thus we can
conclude from the above curves that we can vary the filter characteristics by
changing r or by changing p. But if we change the values of r continuously, then the

p ¼ 1 :

Varying p from +1.6180 to −1.6180

12

10

8

6

4

2

0

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Normalised frequency

Figure 3.22 Filter response for varying values of p

value of r may exceed one. Under these conditions the system will become
unstable, which is not desirable. To keep the system in a stable condition, we
vary p. By varying

we perform a non-linear variation. Hence we choose to vary

the value of p ¼ 2 cos . Thus frequency tracking can be done without changing the

value of r and by varying p from 2 to 2 and fixing r at an optimum value.