GOLDBERG AND MÄKIVIRTA
OPTIMISED EQUALISATION COMPARISON
AES 116TH CONVENTION, BERLIN, GERMANY, 2004 MAY 8-11
3
3.2. Graphic Equaliser Optimiser
With
Q
and centre frequency
f
0
fixed for each third-
octave band, the remaining variable available for ad-
justment is the gain
G
. This is bound between 0 and –
12 dB. A least squares method, Matlab’s
“
lsqnonlin
” function [18], minimises the objective
function,
df
f
x
f
x
f
a
E
f
f
f
m
m
2
0
2
1
)
(
)
(
)
(
min
∫
=
=
(5)
where
x
(
f
) is the third-octave smoothed [19] magni-
tude of the loudspeaker in-situ frequency response,
a
m
(
f
) is the graphic equaliser magnitude response,
x
0
(
f
)
is the target response and frequencies
f
1
and
f
2
define
the optimisation band, i.e. –3 dB lower cut-off fre-
quency for the loudspeaker in question and the high
frequency limit for the optimisation at 15 kHz.
The optimised filter values are rounded after optimisa-
tion to the nearest 0.1dB, as this is the typical gain
resolution found in commercially available DSP
graphic equalisers [20]. These values are used to filter
the in-situ loudspeaker response prior to statistical
analysis.
Visual inspection of the optimised responses shows
that the algorithm is robust to finding the global mini-
mum.
3.3. Computational Load
Optimisation speed was tested on a Pentium M 1.6
GHz based computer. The room response equaliser
optimisation algorithm runs in about 1.5–3 s depend-
ing on the loudspeaker model, whereas the graphical
equaliser optimisation algorithm takes 30–60 s, i.e.
10…20 times longer. The longer run time is explained
by the higher degrees of freedom in a graphical equal-
iser. The large optimisation time variation is due to
differing in-situ responses causing variations in the
run time because the optimisation continues until the
required fitting tolerance is achieved.
4. METHODS
4.1. Statistical Data Analysis
To assess the performance of the combination of
optimisation algorithm and equalisation in the
loudspeakers, the analysis compares the unequalised
in-situ magnitude response to the equalised response.
The third-octave smoothed magnitude response was
calculated. The optimal room response control settings
were calculated for each loudspeaker response. Statis-
tical data was recorded for each magnitude response
measurement before and after equalisation to study
how the objective quality was improved. Further sta-
tistical analysis is conducted on all measurements in
three frequency bands (Table 1) “
LF
”, “
MF
” and
“
HF
”, collectively called “
subbands
” and correspond-
ing roughly to the bandwidths for each driver in a
three-way system.
Table 1. Frequency band definitions the statistical data
analysis:
f
LF
is the frequency of the lower –3 dB limit
of the frequency range.
Frequency Range Limit
Bandwidth Name
Low
High
Broadband
f
LF
15
kHz
LF
f
LF
400
Hz
MF
400 Hz
3.5 kHz
HF
3.5 kHz
15 kHz
For each loudspeaker, the broadband median pressure
is calculated. Pressure deviations from this median are
recorded within each subband and for the broadband.
These deviations are then used to describe the proper-
ties and extent of deviations from a flat response. Me-
dians calculated for subbands, defined above, are re-
corded. The differences from the broadband median to
subband medians are calculated and then used as an
indicator for broadband balance of the frequency re-
sponse. Both statistical descriptors are recorded before
and after equalisation for each frequency band and
each equalisation method.
The quartile difference and RMS deviation are calcu-
lated for the four loudspeaker categories determined
by the type of built-in room response controls in the
loudspeakers. Both the quartile difference and RMS
deviation values represent two slightly different ways
to look at the deviation from the median value of the
distribution. The quartile values are more robust to
outlier values while the RMS values include these ef-
fects.
4.2. Data Analysis Case Study
Figure 5 in Appendix C shows the third-octave
smoothed and unsmoothed in-situ response of a large
soffit mounted system [5]. The measurement tech-
nique is detailed in [12,14].
4.2.1. Room Response Control Equalisation
Appendix A shows a case example where the room
response control settings are calculated according to
the optimisation algorithm [12-14]. The equalisation
target is a flat magnitude response, i.e. a straight line
at 0 dB level. The loudspeaker’s passband (triangles)
and the frequency band of equalisation (crosses) are
