GOLDBERG AND MÄKIVIRTA
AUTOMATED IN-SITU EQUALISATION
AES 114TH CONVENTION, AMSTERDAM, THE NETHERLANDS, 2003 MARCH 22-25
4
3.1. Efficiency of Direct Search
The room response controls of an active loudspeaker
form a discrete-valued set of frequency responses. If
the optimum is found by trying every possible
combination of room response controls then the
number of processing steps becomes prohibitively
high (Table 5).
Table 5. Number of setting combinations.
Type of loudspeaker
Room Response
Control
Large 3-way 2-way
Small
2-way
Treble tilt
5
-
4
2
Treble level
7
7
-
-
Midrange level
7
7
-
-
Bass level
7
7
-
-
Bass
tilt
5 5 4 4
Bass
roll-off
5 5 5 2
Total
42875
8575
80
16
3.2. The
Algorithm
The algorithm exploits the heuristics of experienced
system calibration engineers by dividing the optimisa-
tion into five main stages (Table 6), which will be
described in detail. The optimiser considers certain
frequency ranges in each stage (Table 7). Figure 9 in
Appendix A shows a flow chart of the software. A
screenshot of the software graphic user interface can
be seen in Appendix B.
Table 6. Optimisation stages.
Type of loudspeaker
Optimisation
stage Large 3-way 2-way Small
2-way
Preset bass roll-off
9
9
9
9
Find midrange/
treble ratio
9
9
- -
Set bass tilt and
level
9
9
- -
Reset bass roll-off
9
9
9
9
Set treble tilt
9
-
9
9
Table 7. Optimiser frequency ranges;
f
HF
= 15 kHz;
f
LF
is the frequency of the lower –3 dB limit of the
frequency range.
Frequency Range
Limit
Low
High
Loudspeaker pass band
f
LF
f
HF
Midrange and treble driver band
500 Hz
f
HF
Bass roll-off region
f
LF
1.5
f
LF
Bass region
1.5
f
LF
6
f
LF
3.2.1. Pre-set Bass Roll-off
In this stage, the bass roll-off control is set to keep the
maximum level found in the ‘bass roll-off region’ as
close to the maximum level found in the ‘bass region’.
Once found the bass roll-off control is reset to one
position higher, for example, –4 dB is changed to –2
dB. The reason for this is to leave some very low bass
energy for the bass tilt to filter. It is possible that the
bass tilt alone is sufficient to optimise the response
and less or no bass roll-off is eventually required. The
min-max type objective function to be minimized is
given by Equation 2,
[
]
[
]
3
2
2
1
0
0
,
,
,
,
)
(
)
(
)
(
max
)
(
)
(
)
(
max
min
f
f
f
f
f
f
f
x
f
x
f
a
f
x
f
x
f
a
E
b
a
m
b
f
m
f
m
a
=
=
=
(2)
where
x
(
f
) is the smoothed magnitude of the in-situ
frequency response of the system,
a
m
(
f
) is the bass
roll-off setting
m
currently being tested,
x
0
(
f
) is the
target response,
f
a
defines the ‘bass roll-off region’
(Table 7) and
f
b
defines the ‘bass region’ (Table 7).
User selected frequency ranges are not permitted.
The reason for this arrangement rather than using a
least squares type objective function is that the bass
roll-off tends to assume maximum attenuation to
minimise the rms deviation. This type of objective
function does not yield the best setting, as subjectively
a loss of bass extension is perceived.
This stage of the optimiser algorithm takes six
filtering steps (three for small two-way models).
3.2.2. Midrange Level to Treble Level Ratio
The aim of this stage is to find the relative levels of
the midrange level and treble level controls required
to get closest to the target response. The least squares
