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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b
2
w(n
-2)
w(n
-1)
b
1
x(n)
y(n)
b
0
z
-1
z
-1
- a
2
- a
1
w(n)
- a
M
b
L
-1
w(n
-L-1)
Figure 6.15 Direct-form II realization of general IIR filter, L M 1
and
yn
LÀ1
l0
b
l
wn À l:
6:4:10
The computed value of w(n) from the first equation is passed into the second equation to
compute the final output y(n).
6.4.2 Cascade Form
The cascade realization of an IIR filter assumes that the transfer function is the product
of first-order and/or second-order IIR sections. By factoring the numerator and the
denominator polynomials of the transfer function H(z) as a product of lower order
polynomials, an IIR filter can be realized as a cascade of low-order filter sections.
Consider the transfer function H(z) given in (6.3.4), it can be expressed as
Hz b
0
H
1
zH
2
z Á Á Á H
K
z b
0
K
k1
H
k
z,
6:4:11
where each H
k
z is a first-or second-order IIR filter and K is the total number of
sections. That is
H
k
z
z À z
i
z À p
j
1 b
1k
z
À1
1 a
1k
z
À1
,
6:4:12
or
266
DESIGN AND IMPLEMENTATION OF IIR FILTERS
Summary :
b 2 w(n -2) w(n -1) b 1 x(n) y(n) b 0 z -1 z -1 - a 2 - a 1 w(n) - a M b L -1 w(n -L-1) Figure 6.15 Direct-form II realization of general IIR filter, L M 1 and yn LÀ1 l0 b l wn À l: 6:4:10 The computed value of w(n) from the first equation is passed into the second equation to compute the final output y(n).
Tags :
iir,filter,transfer,function,sections,cascade,polynomials,realization,equation,product,secondorder,gien,642