文档介绍：Outline of chapter 6
Digital Filter Structures
数字滤波器结构
Basic Elements
Adder: add two inputs into one output
y =x1+x2
Multiplier: scale an input to an output;
y = ax
Delay element: delays an input for one sample to form the output;
y(n) = x(n-1)
Signal-Flow Graph
Each signal in the system is expressed as the output of a node.
ponent in the system is expressed as an arrowed line labeled by its model function qij.
The output of each node equals to the summation of all inputs to this node.
Four Structure Forms of the IIR Filter
IIR Filter Structures
Direct Form
Direct Form I and Direct Form II
Coefficient b and a get from Transfer Function:
H(z-1)=b(z-1)/a(z-1)
Cascade Form
Coefficients get from:
[b0,B,A] = dir2cas(b,a) in the textbook or
[sos,G] = tf2sos(b,a) in Signal Toolbox
where sos=[B,A]
IIR Filter Structures (continue)
Parallel Form
Coefficients get from:
[C,B,A] = dir2par(b,a) in the textbook
To implement the filtering, use
y = parfiltr(C,B,A,x)
Notify structure plots and the coefficients meaning of the four forms
MATLAB implement dir2cas
For cascade structures
1. Find roots(a) and roots(b);
2. Find conjugate pairs of the roots
Using cplxpair in MATLAB
3. Concatenate the pairs in to sos sections
Using poly, conv
MATLAB implement dir2par
For parallel structures
1. Separate it into single partial fraction sections;
Using residue
2. Find conjugate pairs of the roots ;
3. Find the corresponding residue pairs;
Using function p
4. Concatenate the pairs in to sos sections;
FIR Filter Structures
Direct Form:
Cascade Form:
Linear-phase Form:
h(n)=h(M-1-n);(symmetry) β=0, 0≤n≤M-1
h(n)=-h(M-1-n);(symmetry) β=±π/2, 0≤n≤M-1
Examples
determine cascade structure form;
determine parallel structure form;
of cas and par forms;
Three structure forms of a FIR filter;
cascaded linear-phase structure form;