hmwk7.pdf - ECE 513 DIGITAL SIGNAL PROCESSING Cranos M...

ECE 513 - DIGITAL SIGNAL PROCESSING
Cranos M. Williams
Assigned: October 21, 2019
HOMEWORK 7, DUE OCTOBER 28, 2019
1. IIR Lattice Filters: (25 Pts) The system transfer function for an IIR digital filter is
given by
H ( z ) =
B ( z )
A ( z )
(1)
where
B ( z ) = 0 . 0609 - 0 . 3157 z
- 1
+ 0 . 8410 z
- 2
- 1 . 4378 z
- 3
+ 1 . 7082 z
- 4
- 1 . 4378 z
- 5
+ 0 . 8410 z
- 6
- 0 . 3157 z
- 7
+ 0 . 0609 z
- 8
A ( z ) = 1 . 0 - 0 . 8961 z
- 1
+ 2 . 6272 z
- 2
- 0 . 9796 z
- 3
+ 2 . 1282 z
- 4
- 0 . 0781 z
- 5
+ 0 . 9172 z
- 6
+ 0 . 0502 z
- 7
+ 0 . 2602 z
- 8
(2)
(a) Use the MATLAB routine tf2sos to obtain the coefficients for the cascade im-
plementation of H ( z ) using second order sections
(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.
(c) Use MATLAB to determine the IIR lattice coefficients for each of the remaining
second order sections. Provide your MATLAB code with your solution. Develop
block diagrams for the IIR lattice implementation of all second order sections.
(d) Develop appropriate difference equations for the implementation of the overall
filter using the second order IIR lattice sections.
2. IIR Lattice Filters: (25 Pts) This problem involves the implementation of a sixth order
IIR filter using second order lattice sections. The lattice parameters for section 1 are