DSP Lecture 23
of 10
Transcript of DSP Lecture 23
-
7/30/2019 DSP Lecture 23
1/10
Lectures 23-24EE-802 ADSP SEECS-NUST
EE 802-Advanced Digital SignalProcessing
Dr. Amir A. Khan
Office : A-218, SEECS
9085-2162; [email protected]
1
-
7/30/2019 DSP Lecture 23
2/10
Lectures 23-24EE-802 ADSP SEECS-NUST
Lecture Outline
All-pole Lattice Structure Lattice-Ladder IIR Structures
(Chapter 9 Proakis)
2
-
7/30/2019 DSP Lecture 23
3/10
Lectures 23-24EE-802 ADSP SEECS-NUST
All-Pole Lattice Structures
Consider an all-pole IIR systemDirect-form realization
Interchanging the roles of input and ouput (x[n] to y[n]) in above system
FIR
IIR
We can thus build upon FIR Lattice to obtain the All-pole Lattice
structure
3
-
7/30/2019 DSP Lecture 23
4/10
Lectures 23-24EE-802 ADSP SEECS-NUST
All-Pole Lattice Structures
Recall the all-zero (FIR) lattice
Redefine
Opposite formulation as that of FIR Lattice
Would require computation offm(n) in descending order
Reformulating the top branch equation
The bottom branch gm(n) remains the same
New set of Eqs.
4
-
7/30/2019 DSP Lecture 23
5/10
Lectures 23-24EE-802 ADSP SEECS-NUST
All-Pole Lattice Structures
5
-
7/30/2019 DSP Lecture 23
6/10
Lectures 23-24EE-802 ADSP SEECS-NUST
Example:2-pole Lattice Structure
Two-pole Lattice
Two-pole IIR
Two-zero FIR
Coefficients are same but in reverse order
Forward Path
Backward Path
Lattice parameters (K1, K2) same for all-pole/all-zero systemsbut different interconnections
6
-
7/30/2019 DSP Lecture 23
7/10
Lectures 23-24EE-802 ADSP SEECS-NUST
Lattice Structure for IIR systems
Direct Form II structure
I/O of all-pole system
I/O of all-zero system
7
-
7/30/2019 DSP Lecture 23
8/10Lectures 23-24
EE-802 ADSP SEECS-NUST
Lattice Structure for IIR systems
I/O of all-pole system
I/O of all-zero system
8
-
7/30/2019 DSP Lecture 23
9/10Lectures 23-24
EE-802 ADSP SEECS-NUST
Lattice-Ladder structure for IIR systems
I/O of all-pole system
I/O of all-zero system
9
-
7/30/2019 DSP Lecture 23
10/10Lectures 23 24
EE-802 ADSP SEECS-NUST
Popularity of Lattice Structures
Require minimum amount of memory of all the structures
but not minimum number of multipliers
The modularity provided by these structures is their
biggest plus point
In addition they offer built-in stability characteristics aswell as robustness to round-off effects (to be discussed
in a later session)
A stable system requires the lattice (reflection)
coefficients magnitudes to be less than unity
10
