EFFECTIVE BANDWIDTH
The total integrated random white noise power passed by the practical
filters
is
equal
to
that
which would be passed by
an
ideal 1/3 octave filter.
The white noise power passed by such a filter
is
given by:
(21
/6-
2-1
/6)
fm
Pm
or 0.2316
Fm
Pm
where
Pm
is
the
noise power per unit frequency
of
the
filter midband
frequency fm.
Due
to
tolerances
in
filter production,
the
tolerance
of
the
effective band-
width
of
a practical filter
is
±
10%
(approx. ± 0.4 dB). The effective band-
width
concept
is
illustrated
in
Fig.6.1.
Since
the
noise power
is
proportional
to
the
square of
the
noise voltage,
the
amplitude response
of
the
filter
is
squared and then
the
area under this
curve (shaded)
is
equal
to
the
area of
the
rectangle which represents
the
ideal filter frequency characteristic.
OCTAVE
An octave
is
the
interval between two pure tones having a frequency ratio
of 2.
Other frequency intervals can also be expressed as a number of octaves n,
where n can be
any
value. Then
the
interval between
the
frequencies
f"
and
f'
is
given by
f II
fll
f
' -
2n
or
n =
log2-
fl
When n
is
negative,
f''
is
said
to
be
n octaves below f', and when n
is
positive, f"
is
said
to
be n octaves above f
'·
OCTAVE
Frequency ratio
up
down
1/12
0.0833
1.0594 0.9439
1/8
0.1250
1.0905 0.9170
1/6
0.1667 1.1225
0.8909
1/4
0.2500
1.1892
0.8409
1/3
0.3333
1.2591
0.7937
1/2
0.5000
1.4142
0.7071
2/3
0.6667
1.5871 0.6303
3/4
0.7500
1.6817 0.5946
1
1.0000
2.0000
0.5000
n
2n
2-n
42
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