Biomedical Engineering Reference
In-Depth Information
Ideal Band-pass
A
0
0.707
A
0
w
w
L
w
0
w
U
Practical filter
FIGURE 11.5
:
Band-pass filter transfer function characteristic curves. The ideal band-pass filter
is shown as the dashed-line trace, and the normal practical response trace is shown as dotted-line
trace
or higher order, since the filters require two slopes (high and low). Note that band-pass
filters are not All-Pole filters, since the equation shows a zero in the numerator.
A
BP
ω
0
s
H
(
s
)
=
(11.9)
+
ω
Q
s
2
0
s
2
+
ω
11.1.6 Band-Reject or “Notch” Filters
Band-reject filters may be of the Butterworth or of the Chebyshev class. Band-reject
filters are designed to attenuate or reject a band of frequencies of bandwidth,
B
, with
the center of the band around a center frequency (
Hz. As
with the band-pass filter, it is necessary to designate the two cutoff frequencies for a
band-reject filter; the lower cutoff,
ω
0
rad/sec) or
f
0
=
ω
0
/
2
π
U
. The frequencies that
are passed by the filter are those for which the transfer function,
H
(
s
), gain is greater
than or equal to 0.707
A
0
as shown in Fig. 11.6.
ω
L
, and the upper cutoff,
ω
H(s)
Ideal Notch
A
0
0.707
A
0
Practical filter
w
L
w
0
w
U
FIGURE 11.6
:
Band-reject filter transfer function characteristic curves. The ideal band-reject
or notch filter is shown as the dashed-line trace, and the normal practical response trace is shown
in dotted-line trace
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