ECE 513 - DIGITAL SIGNAL PROCESSING
Cranos M. Williams
Assigned: October 16, 2017
HOMEWORK 7 Solution, DUE OCTOBER 23, 2017
1.IIR Lattice Filters: (25 Pts)The system transfer function for an IIR digital filter isgiven byH(z) =B(z)A(z)(1)whereB(z)=0.0609-0.3157z-1+ 0.8410z-2-1.4378z-3+ 1.7082z-4-1.4378z-5+ 0.8410z-6-0.3157z-7+ 0.0609z-8A(z)=1.0-0.8961z-1+ 2.6272z-2-0.9796z-3+ 2.1282z-4-0.0781z-5+ 0.9172z-6+ 0.0502z-7+ 0.2602z-8(2)(a) Use the MATLAB routinetf2sosto obtain the coefficients for the cascade im-plementation ofH(z) using second order sections
1
ECE 513 - Homework 7 Solution
2
(b) Calculate, by hand, the IIR lattice coefficients for the first second order section.Assume that the gain is distributed evenly through each second order section.
(9)
(c) Use MATLAB to determine the IIR lattice coefficients for each of the remainingsecond order sections. Provide your MATLAB code with your solution. Developblock diagrams for the IIR lattice implementation of all second order sections.
ECE 513 - Homework 7 Solution
(d) Develop appropriate difference equations for the implementation of the overallfilter using the second order IIR lattice sections.
ECE 513 - Homework 7 Solution
5
Z
-1
Z
-1
x(n)
f
3
(n)
f
2
(n)
f
1
(n)
K
2
-K
2
g
3
(n)
g
2
(n)
g
1
(n)
K
1
-K
1
V
3
V
2
V
1
Z
-1
Z
-1
f
6
(n)
f
5
(n)
f
4
(n)
K
4
-K
4
g
6
(n)
g
5
(n)
g
4
(n)
K
3
-K
3
V
6
V
5
V
4
Z
-1
Z
-1
f
9
(n)
f
8
(n)
f
7
(n)
K
6
-K
6
g
9
(n)
g
8
(n)
g
7
(n)
K
5
-K
5
V
9
V
8
V
7
Z
-1
Z
-1
f
12
(n)
f
11
(n)
f
10
(n)
K
8
-K
8
g
12
(n)
g
11
(n)
g
10
(n)
K
7
-K
7
V
12
V
11
V
10
s
1
(n)
s
2
(n)
s
3
(n)
s
4
(n)
y(n)
Figure 1: Block diagram of IIR filter in Problem. 1-(c)
Solution:
ECE 513 - Homework 7 Solution
