Digital Signal Processing Reference
In-Depth Information
mat33.m
in Figure D.5 to obtain a 33-coefficient FIR bandpass filter centered at
1000 Hz. In lieu of the
remez
function for an FIR design, the MATLAB command
>>
[a
,
b]
=
yulewalk
(
n,nu,mag
)
returns the
a
and
b
coefficients in the general input-output equation in Chapter 5,
associated with an IIR filter. The filter's order n represents the number of second-
order sections. The C program in Example 5.1 implements an IIR filter with cas-
caded second-order sections, as is most commonly done. For example, if
n
=
6 in the
yulewalk
function, the general transfer function in Chapter 5 in terms of the
resulting
a
and
b
coefficients from MATLAB needs to be reduced to one in terms
of three cascaded sections.
D.5 BLT USING MATLAB AND SUPPORT PROGRAMS ON CD
This section expands on the discussion of BLT in Section 5.3.
Exercise D.1: First-Order IIR Lowpass Filter
Given a first-order lowpass analog transfer function
H
(
s
), a corresponding discrete-
time filter with transfer function
H
(
z
) can be obtained. Let the bandwidth or cutoff
frequency
B
=
1
r
/
s
and the sampling frequency
F
s
=
10 Hz.
1.
Choose an appropriate transfer function
1
()
=
Hs
s
+
1
which represents a lowpass filter with a bandwidth of 1
r
/
s
.
2.
Prewarp
w
D
using
w
D
T
1
20
1
20
Ê
Ë
ˆ
¯
@
w
=
tan
=
tan
A
2
1
/
10
.
where
w
D
=
B
=
1
r
/
s
and
T
=
3.
Scale
H
(
s
) to obtain
1
(
)
=
Hs
w
A
20
s
+
1
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