GOLDBERG AND MÄKIVIRTA
AUTOMATED IN-SITU EQUALISATION
AES 114TH CONVENTION, AMSTERDAM, THE NETHERLANDS, 2003 MARCH 22-25
5
type objective function to be minimised is given in
Equation 3,
df
f
x
f
x
f
a
E
f
f
f
m
m
2
0
2
1
)
(
)
(
)
(
min
∫
=
=
(3)
where
x
(
f
) is the smoothed magnitude of the in-situ
frequency response of the system,
a
m
(
f
) is the mid-
range and treble level control combination
m
currently
being tested,
x
0
(
f
) is the target response,
f
1
and
f
2
define the ‘midrange and treble driver band’
(Table
7). The lower frequency bound is fixed at 500 Hz but
a user selectable high frequency value is permitted.
The default value is 15 kHz.
The midrange-to-treble level ratio is saved for
performing the third stage of the optimisation process.
The reason for this is to reduce the number of room
response control combinations to be tested in the next
stage.
This stage of the optimisation algorithm takes 49
filtering steps and is not required for two-way models
or small two-way models.
3.2.3. Bass Tilt and Bass Level
This stage of the optimiser algorithm filters using all
possible combinations of bass tilt and bass level
controls for a given midrange/treble level difference.
By fixing this difference the total number of filter
combinations can be reduced substantially.
A constraint imposed in this stage is that only two of
the driver level controls can be set at any one time. If
three of the level controls are simultaneously set the
net effect is a loss of overall system sensitivity. Table
8 shows and example of incorrect and correct setting
of the driver level controls.
Table 8. Driver level control settings.
Control Incorrect
Setting
Correct
Setting
Bass level
–4 dB
–2 dB
Midrange level
–3 dB
–1 dB
Treble level
–2 dB
0 dB
Input sensitivity
–6 dBu
–4 dBu
The least squares type objective function to be
minimised is the same as shown in Equation 3.
However,
a
m
(
f
) is the bass tilt and bass level combina-
tion
m
currently being tested together with the fixed
midrange and treble level ratio setting found in the
previous stage. Also,
f
1
and
f
2
now define the ‘loud-
speaker pass band’
(Table 7). High and low user
selected frequency values are permitted. The default
values are the –3 dB lower cut-off frequency of the
loudspeaker and 15 kHz.
This part of the optimisation algorithm takes 35
filtering steps. There are no driver level controls in
two-way or small two way systems so these virtual
controls are set to 0 dB. The bass tilt control can then
be optimised using the same objective function. Only
five filtering steps are required for two-way and small
two-way systems.
3.2.4. Reset Bass Roll-off
Firstly, the bass roll-off control is reset to 0 dB. Then
the same method used to set the bass roll-off earlier is
repeated, but without modifying upwards the final
setting. The same objective function is used as
presented in Section 3.2.1.
3.2.5. Set Treble Tilt
The least squares type objective function to be
minimised is the same as shown in Equation 3.
However,
f
1
and
f
2
now define the ‘loudspeaker pass
band’
(Table 7). High and low user selected frequency
values are permitted. The default values are the –3 dB
lower cut-off frequency of the loudspeaker and 15
kHz.
This part of the algorithm requires five filtering steps
for two way and large models (three for small two
way models) and is skipped for three ways because
they do not have this control.
3.3. Reduction of Computational Load
The optimiser algorithm has been designed to reduce
the computational load by exploiting the heuristics of
experienced calibration engineers. The resulting
number of filtering steps has been dramatically
reduced for the larger systems (Table 9) and even the
relatively simple two-way systems show a substantial
improvement when compared to the number of
filtering steps needed by direct search method as
summarised in Table 5. There are two main reasons
for the improvement; the constraint of not allowing
the setting of all three of the driver level settings
simultaneously and the breaking up of the optimisa-
tion into stages.
The run time on a PII 366 MHz computer for a three-
way system is about 15 s (direct search 3 minutes).
Large systems now take about the same time as a
three-way system (predicted direct search time was 15
minutes). The processing time is directly proportional
to the processor speed as a PIII 1200 MHz based
computer takes about 4 s to perform the same
optimisation. Further changes in the software have
improved these run times by about 30%.
