Digital Signal Processing Reference
In-Depth Information
26 Digital Filters and SignalProcessing
Maximum Passband Ripple
A
p
0.1
[dB]
Minimum Stopband Loss
A
a
40
[dB]
Lower Stopband-Edge Normalized Frequency
ω
a
1
0.31
π
[Rad]
Lower Passband-Edge Normalized Frequency
ω
p
1
0.33
π
[Rad]
Upper Passband-Edge Normalized Frequency
ω
p
2
0.60
π
[Rad]
Upper Stopband-Edge Normalized Frequency
ω
a
2
0.61
π
[Rad]
Normalized Sampling Period
T
1
[s]
Lowpass Filter Interpolation Factor
M
l p
6
Highpass Filter Interpolation Factor
M
h p
5
TABLE3.
DesignSpecificationsfor BandpassFRMIIR DigitalFilter
v
min
v
max
K
w
c
1
c
2
L
f
L
h
−5
700
0.4
2
2
5
10
10
TABLE4.
PSODesignParametersfor BandpassFRMIIR DigitalFilter
L
0
l
0
f
0
L
1
l
1
f
1
11
3
10
12
3
7
TABLE5.
CSD Parametersfor BandpassFRMIIR DigitalFilter
10. Application examples
10.1. Bandpass FRM IIR digital filter design example
Consider the design of a bandpass FRM IIR digital filter satisfying the magnitude response design
specifications given in Table
3
over the CSD multiplier coefficient space.
The parameters for the PSO of bandpass FRM IIR digital filter is shown in Table
4
and the CSD
parameters are presented in Table
5
.
Given the design specification in Table
3
, The order of the digital allpass networks
G
0
l p
(
z
)
,
G
1
l p
(
z
)
,
G
0
h p
(
z
)
and
G
1
h p
(
z
)
are found to be
3
,
4
,
3
and
4
, respectively. In addition, the digital masking subfilters
F
0
l p
(
z
)
,
F
1
l p
(
z
)
,
F
0
h p
(
z
)
and
F
1
h p
(
z
)
have the same length as the previous example, i.e.
24
,
42
,
25
and
35
respectively, resulting in
N
=
140
. In this example a set of fifteen CSD LUTs are required, fourteen
LUTs for the multiplier coefficients
m
C
0,1
,
m
C
0,2
,
m
C
0,3
,
m
L
0,2
,
m
L
0,3
,
m
C
1,1
,
m
L
1,1
,
m
C
1,2
and
m
L
1,2
constituent in the digital allpass networks
G
0
l p
(
z
)
,
G
1
l p
(
z
)
,
G
0
h p
(
z
)
and
G
1
h p
(
z
)
, and one template
LUT for all the multiplier coefficients constituent in the masking digital subfilters
F
0
l p
(
z
)
,
F
1
l p
(
z
)
,
F
0
h p
(
z
)
and
F
1
h p
(
z
)
.
Finally, by using Parks McClellan approach, the subfilters
F
0
l p
(
z
)
,
F
1
l p
(
z
)
,
F
0
h p
(
z
)
and
F
1
h p
(
z
)
can be
designed. Also, by using the EMQF technique, the digital allpass networks
G
0
l p
(
z
)
,
G
1
l p
(
z
)
,
G
0
h p
(
z
)
and
G
1
h p
(
z
)
can be designed. Consequently, the magnitude and group delay frequency responses of the
overall infinite-precision bandpass FRM IIR digital filter
H
(
z
)
is obtained as shown in Figs.
13
and
14
.
