User`s guide

Biquadratic Filter
5-37
5Biquadratic Filter
Purpose Apply a cascade of biquadratic (second-order section) filters to the input.
Library Filtering / Filter Designs
Description The Biquadratic Filter block applies a cascade of biquadratic filters
independently to each input channel. Biquadratic filters are useful for reduced
precision implementations because the coefficients are bounded between ±2 for
typical minimum-phase designs. This may reduce scaling and coefficient
sensitivity problems.
The filter is constructed from L second-order sections, each having a quadratic
numerator and denominator.
The figure below illustrates the structure of a 4th-order biquadratic filter (L=2)
with states v
ik
, where k is the section number.
An M-by-N sample-based matrix input is treated as M
∗N independent
channels, and an M-by-N frame-based matrix input is treated as N
independent channels. In both cases, the block filters each channel
independently over time, and the output has the same size and frame status as
the input.
Hz() H
k
z()
k 1=
L
∏
b
1k
b
2k
z
1–
b
3k
z
2–
++
a
1k
a
2k
z
1–
a
3k
z
2–
++
----------------------------------------------------------
k 1=
L
∏
==
u(nT
s
)
z
-1
Σ
a
31
a
21
b
11
b
21
b
31
y(nT
s
)
Section 1, H
1
(z) Section 2, H
2
(z)
Σ
Σ
z
-1
z
-1
Σ
a
32
a
22
b
22
b
32
Σ
Σ
z
-1
v
11
v
21
v
12
v
22
b
12