Peaking Filter; Gain; Centre Frequency - Bang & Olufsen BeoLab 90 Technical Sound Manual

6
4
2
0
−2
−4
−6
10 100 1,000
Frequency (Hz)
Figure 15.3: Example of a high-shelving
filter with a positive gain. Frequencies
above approximately 8 kHz have been
a ected.
6
4
2
0
−2
−4
−6
10 100 1,000
Frequency (Hz)
Figure 15.4: Example of a high-shelving
filter with a negative gain. Frequencies
above approximately 8 kHz have been
a ected.
Note that the high-shelving filters used
in the BeoLab 90 define the centre
frequency as being the frequency
where the gain is one half the
maximum (or minimum) gain of the
filter. For example, in Figure 15.4, the
gain of the filter is -6 dB. The centre
frequency is the frequency where the
gain is one-half this value or -3 dB,
which can be found at 8 kHz.
Some care should be taken when using
high-shelving filters since their
a ected frequency bands can extend
beyond the audible frequency range.
This can cause a system to be pushed
beyond its limits in extremely high
frequency bands that are of little-to-no
consequence to the audio signal.

15.1.3 Peaking Filter

A peaking filter is used for a more local
adjustment of a frequency band. In this
case, the centre frequency of the filter
1
The "B" is a capital because it's named after Alexander Graham Bell.
2
This is literally the number of times a loudspeaker driver will move in and out of the loudspeaker cabinet per second.
3
Note that, although the term "Q" is used throughout this manual and the BeoLab 90 interface for both peaking and shelving filters, this is incorrect. To be technically correct,
the term "S" (or shelf slope) should be used for shelving filters.
is a ected most (it will have the Gain
of the filter applied to it) and adjacent
frequencies on either side are a ected
less and less as you move further
away. For example, Figure
the response of a peaking filter with a
centre frequency of 1 kHz and gains of
6 dB (the black curve) and -6 dB (the
10,000
red curve). As can be seen there, the
maximum e ect happens at 1 kHz and
frequency bands to either side are
a ected less.
6
4
2
0
−2
−4
−6
10
10,000
Figure 15.5: Example of two peaking fil-
ters. The black curve shows a filter with
a positive gain, the red curve shows the
reciprocal with a negative gain. The
centre frequency of this filter is 1 kHz.
You may notice in Figure
black and red curves are symmetrical –
in other words, they are identical
except in polarity of the gain. This is a
particular type of peaking filter called a
reciprocal peak/dip filter – so-called
because these two filters, placed in
series, can be used to cancel each
other's e ects on the signal.
Note that BeoLab 90 uses reciprocal
peak/dip filters.

15.2 Gain

If you need to make all frequencies in
your audio signal louder, then you just
need to increase the volume. However,
if you want to be a little more selective
and make some frequency bands
louder (or quieter) and leave other
bands unchanged, then you'll need an
equaliser. So, one of the important
questions to ask is "how much louder?"
or "how much quieter?" The answer to
15.5 shows
100 1,000 10,000
Frequency (Hz)
15.5 that the
50
this question is the gain of the filter –
this is the amount by which is signal is
increased or decreased in level.
The gain of an equaliser filter is almost
always given in decibels or dB
a scale based on logarithmic changes
in level. Luckily, it's not necessary to
understand logarithms in order to have
an intuitive feel for decibels. There are
really just three things to remember:
a gain of 0 dB is the same as
saying "no change"
positive decibel values are
louder, negative decibel values
are quieter
Adding approximately 6 dB to the
gain is the same as saying "two
times the level". (Therefore,
subtracting 6 dB is half the level.)

15.3 Centre Frequency

So, the next question to answer is
"which frequency bands do you want
to a ect?" This is partially defined by
the centre frequency or Fc of the filter.
This is a value that is measured in the
number of cycles per second
Hertz or Hz.
Generally, if you want to increase (or
reduce) the level of the bass, then you
should set the centre frequency to a
low value (roughly speaking, below
125 Hz). If you want to change the
level of the high frequencies, then you
should set the centre frequency to a
high value (say, above 8 kHz).
15.4 Q
In all of the above filter types, there
are transition bands – frequency areas
where the filter's gain is changing from
0 dB to the desired gain. Changing the
3
filter's Q allows you to alter the shape
of this transition. The lower the Q, the
smoother the transition. In both the
case of the shelving filters and the
peaking filter, this means that a wider
1
. This is
2
, labelled