Digital Filters - Digital Signal Processing: A Practitioner's Approach - page 59

y -axis

90

0.8

120 60

Second- order pole trace

0.6

150 30

0.4

0.2

180 0

x- axis

210 330

240 300

270

Figure 3.18 A Butterworth autoregressive filter

the type given in (3.17) with minor variations to meet the overall specifications.
Consider a filter with the following specifications (the same as in Figure 3.1):

1. Cut-off frequency as 0 2Hz;

2. Sixth-order filter giving a roll-off of 6 20 ¼ 120 dB/decade
3. A permitted passband ripple of 0.4 dB

:

With these specifications, using the MATLAB package, we get the Chebyshev
filter as

x k ¼ 2 : 5579x k 1 3 : 9518x k 2 þ 3 : 8694x k 3 2 : 5378x k 4

þ 1 : 0415x k 5 0 : 2144x k 6 þ 0 : 0035u k þ 0 : 021u k 1

ð 3 : 23 Þ

þ 0 : 0526u k 2 þ 0 : 0702u k 3 þ 0 : 0526u k 4 þ 0 : 0210u k 5

þ 0 : 0035u k 6