Infinite Impulse Response Filter Design - Digital Signal Processing: Fundamentals and Applications - page 338

8.4 HIGHER-ORDER INFINITE IMPULSE RESPONSE FILTER DESIGN USING
THE CASCADE METHOD
For higher order IIR filter design, use of a cascade transfer function is preferred. The factored forms for
the lowpass prototype transfer functions for Butterworth and Chebyshev filters are given in Tables 8.7,
8.8 and 8.9 . A Butterworth filter design example will be provided and a similar procedure can be
adopted for the Chebyshev filters.

Table 8.7 3-dB Butterworth Prototype Functions in Cascade Form
n

H P ðsÞ

1
ðs þ 1Þðs

3

2

þ s þ 1Þ

1

4

2 2

ðs þ 0:7654s þ 1Þðs þ 1:8478s þ 1Þ

1

5

2 2

ðs þ 1 Þðs þ 0 : 6180 s þ 1 Þðs þ 1 : 6180 s þ 1 Þ

1

6

ðs

2

þ 0 : 5176 s þ 1 Þðs

2

þ 1 : 4142 s þ 1 Þðs

2

þ 1 : 9319 s þ 1 Þ

Table 8.8 Chebyshev Prototype Functions in Cascade Form with 0.5-dB Ripple ( ε ¼ 0 : 3493 )
n H P ðsÞ 0.5-dB Ripple ( 0 : 3493)

ε[

0 : 7157

3

ðs þ 0 : 6265 Þðs

2

þ 0 : 6265 s þ 1 : 1425 Þ

0 : 3579

4

ðs

2

þ 0 : 3507 s þ 1 : 0635 Þðs

2

þ 0 : 8467 s þ 0 : 3564 Þ

0 : 1789

5

ðs þ 0 : 3623 Þðs

2

þ 0 : 2239 s þ 1 : 0358 Þðs

2

þ 0 : 5862 s þ 0 : 4768 Þ

0 : 0895

6

ðs

2

þ 0:1553s þ 1:0230Þðs

2

þ 0:4243s þ 0:5900Þðs

2

þ 0:5796s þ 0:1570Þ

EXAMPLE 8.14
a. Design a fourth-order digital lowpass Butterworth filter with a cutoff frequency of 2.5 kHz at a sampling
frequency of 8,000 Hz.
b. Use MATLAB to plot the magnitude and phase responses.