Real-time digital signal processing: implementations, ... changes in the input signal is limited by its internal clock rate, so that it may be slow to
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for(j 1; j < nbÀ1; ++j)
{
yn2 yn2 y[maxbÀj]*b[j];
/*FIR filtering of y(n)to get y2(n) */
}
yn yn1Àyn2;
/*y(n) y1(n)Ày2(n)
*/
return(yn);
/*Return y(n)to the main function */
}
6.6.4 Practical Applications
Consider a simple second-order resonator filter whose frequency response is dominated
by a single peak at frequency !
0
. To make a peak at ! !
0
, we place a pair of complex-
conjugate poles at
p
i
r
p
e
Æj!
0
,
6:6:14
where 0 < r
p
< 1. The transfer function can be expressed as
Hz
A
1 À r
p
e
j!
0
z
À1
1 À r
p
e
Àj!
0
z
À1
A
1 À 2r
p
cos!
0
z
À1
r
2
p
z
À2
A
1 a
1
z
À1
a
2
z
À2
,
6:6:15
where A is a fixed gain used to normalize the filter to unity at !
0
. That is, jH!
0
j 1.
The direct-form realization is shown in Figure 6.22.
The magnitude response of this normalized filter is given by
jH!
0
j
ze
Àj!0
A
1 À r
p
e
j!
0
e
Àj!
0
À
Á
1 À r
p
e
Àj!
0
e
Àj!
0
À
Á
1:
6:6:16
This condition can be solved to obtain the gain
A 1 À r
p
Á
1 À r
p
e
À2j!
0
À
Á 1 À r
p
À
Á
1 À 2r
p
cos2!
0
r
2
p
q
:
6:6:17
x(n)
A
2r
p
cos w
0
y(n)
-r
p
z
-1
z
-1
2
Figure 6.22 Signal flow graph of second-order resonator filter
280
DESIGN AND IMPLEMENTATION OF IIR FILTERS
Summary :
0 À Á 1: 6:6:16 This condition can be solved to obtain the gain A 1 À r p Á 1 À r p e À2j! 0 À Á 1 À r p À Á 1 À 2r p cos2! 0 r 2 p q : 6:6:17 x(n) A 2r p cos w 0 y(n) -r p z -1 z -1 2 Figure 6.22 Signal flow graph of second-order resonator filter 280 DESIGN AND IMPLEMENTATION OF IIR FILTERS
Tags :
filter,figure,yn2,frequency,peak,gain,function,ynto,secondorder,cos,resonator,response,622