Genelec Optimisation of Active Loudspeakers, Optimisation of Active Loudspe User Manual
Automated In-situ Frequency Response
Optimisation of Active Loudspeakers
Andrew Goldberg1 and Aki Mäkivirta1
1
Genelec Oy, Olvitie 5, 74100 Iisalmi, Finland.
ABSTRACT
This paper presents a novel method for robust automatic selection of optimal in-situ acoustical frequency response
within a discrete-valued set of responses offered by room response controls on an active loudspeaker. A frequency
response measurement is used as the input data for the algorithm. The rationale of the room response control system
is described. The response controls are described for each supported loudspeaker type. The optimisation algorithm
is described. Examples of the optimisation process are given. The efficiency and performance of the algorithm are
discussed. The algorithm dramatically improves the speed of optimisation compared to an exhaustive search. It
improves the acoustical similarity between loudspeakers in one space and performs robustly and systematically in
widely varying acoustical environments. The algorithm is currently in active use by specialists who set up and tune
studios and listening rooms.
1. INTRODUCTION
This paper presents a system to optimally set the room
response controls currently found on full-range active
loudspeakers to achieve a desired in-room frequency
response.
The active loudspeakers [1] to be optimised are
designed and calibrated in anechoic conditions to have
a flat frequency response magnitude within the design
limits of ±2.5 dB. When a loudspeaker is placed into
the listening environment, response changes due to the
loudspeaker-room interaction. To help alleviate this,
these active loudspeakers incorporate a pragmatic set
of room response controls accounting for some
common acoustic issues found in professional
listening rooms.
Although many users have the facility to measure
loudspeaker in-situ frequency responses, they often do
not have the experience of calibrating active loudspeakers. Even with experienced system calibrators a
GOLDBERG AND MÄKIVIRTA AUTOMATED IN-SITU EQUALISATION
significant amount of variance between calibrations
can be seen. With a number of different people
calibrating loudspeaker systems there will be an
additional variance in results. For these reasons a
method to ensure consistency of calibrations is
required.
Presented first in this paper is the discrete-valued
room response equalizer employed in the active
loudspeakers. Then, the algorithm for automated value
selection is presented. This includes software structure, algorithm, features and operation. The performance of the optimisation algorithm is then investigated
with case studies. Finally, limitations of the acoustic
measurement system, room response controls and the
algorithm are discussed together with the case study
results.
2. IN-SITU EQUALISATION AND ROOM
RESPONSE CONTROLS
2.1. Equalisation Techniques
The purpose of room equalisation is to improve the
perceived quality of sound reproduction in a listening
environment. The goal of equalisation is usually not to
convert the listening room to anechoic. In fact,
listeners prefer to hear some room response in the
form of liveliness that can create a spatial impression
and some envelopment [2]. Electronic equalisation to
improve the subjective sound quality has been
widespread for at least 40 years; see Boner & Boner
[3] for an early example. Equalisation is particularly
prevalent in professional sound reproduction applications such as mixing rooms and sound reinforcement.
The room transfer function is position dependent,
which poses major problems for all equalisation
techniques. Perfect equalisation within a reasonably
large listening area appears not to be possible, and
even an acceptable equalisation is typically a compromise. Cox and D’Antonio [4] (Room Optimiser)
use a computer model of the room to find optimal
loudspeaker positions and acoustical treatment
location to give an optimally flat in-situ frequency
response magnitude. Positional areas for the loudspeaker and listening locations can be given as
constraints to limit the final solution. Despite
advances in psychoacoustics, it is difficult to quantify
how good the listener actually perceives the sound
quality to be, and to optimise equalisation based on
that evaluation [5-7]. Also, despite the widespread use
of equalisation, it is still difficult to provide exact
timbre matching between different environments.
In-situ response equalisation is typically implemented
using a separate equaliser. Some equalisers on the
market play a test signal and then alter their response
according to the in-situ transfer function measured in
this way [8] but the process can be so sensitive that a
simple ‘press the button and everything will be OK’
approach proves hard to achieve with reliability,
consistency and robustness.
It is possible that equalisation becomes skewed if it is
based only on a single point measurement. The
frequency response in nearby positions can actually
become worse after the equalisation designed using
only a single point measurement is applied. A
classical method to avoid this is to use a weighted
average of responses measured within the listening
area. Such spatial averaging is often required when
the listening area is large. Spatial averaging can
reduce local variance seen in the midrange to high
frequencies and can also reduce problems caused by
the fact that a listener perceives sound differently to a
microphone. Examples of spatial averaging have been
described in the automotive industry [9] and cinema in
the SMPTE Standard 202M [10].
When using one loudspeaker, no correction filter is
capable of reducing the difference between responses
measured at two separate receiver points. At high
frequencies a high-resolution correction can be very
position sensitive. Frequency dependent resolution
change becomes preferable and is typically applied
[11,12].
Traditionally, electronic equalisation uses arrangements of analogue low order minimum phase filters
[13-15]. Since the loudspeaker-room transfer function
is of substantially higher order than such equalisation
filters, the effect of filtering is to gently shape the
response. Several methods have been proposed for
more exact inversion of the frequency response to
achieve a close approximation of unity transfer
function (no change to magnitude or phase) within a
certain bandwidth of interest [16-23]. Some researchers have also shown an interest to control selectively
the temporal decay characteristics of a listening space
by active absorption or modification of the primary
sound [24-29]. If realisable, these are extremely
attractive ideas because they imply that the perceived
sound could be modified with precision, to different
target responses. One of the major problems is that
spatial variations in the frequency response can
become far more difficult to handle than with loworder methods because the correction depends
strongly on an exact match between the acoustic and
equalization transfer functions, and can therefore be
highly local in space [30].
2.2. Room Acoustic Considerations
In small to medium sized listening environments, the
sound field in the frequency range up to a critical
AES 114TH CONVENTION, AMSTERDAM, THE NETHERLANDS, 2003 MARCH 22-25 2
GOLDBERG AND MÄKIVIRTA AUTOMATED IN-SITU EQUALISATION
(
frequency f
(typically 70…200 Hz in small spaces) is
c
often dominated by room modes and comb filtering
caused by low-order discrete reflections from room
boundaries. Sound reproduction can be problematic
because of this. For a room with a reverberation time
of 0.3 s the room mode bandwidth is approxi-
T
60
mately 2.2/T
= 7.3 Hz [23]. However, this does not
60
predict accurately what the decay rate of an individual
mode is as reverberation time represents the total
decay rate in diffuse field whereas modal decay rate
may vary.
Above f
modal density becomes sufficiently high to
c
be described statistically. An unsmoothed room
transfer function shows a large number of high Q
notches. When frequency smoothing due to human
hearing is taken into account [31], the resulting
sensation is a rather smooth room transfer function
(Figure 3 and Figure 6).
In the time domain, early reflections before about 25
ms combine with the direct sound to produce tone
colouration (comb filtering effect). Reflections
arriving later than about 25 ms are less problematic as
they typically combine to produce the reverberation of
the room and are perceived as separate sound events
(echoes and reverberation) rather than tone colouration. This part of the time domain response contributes to the sensations of envelopment and spaciousness.
2.3. Room Response Controls
The loudspeakers to be optimised have room response
controls [1,32]. The smaller loudspeakers have
simpler controls than the larger systems but the
philosophy of filtering is consistent across the range
(Tables 1-4).
The treble tilt control is used to reduce the high
frequency energy. In the small two-way systems and
two way systems it is a level control of the treble
driver and has an effect down to about 4 kHz. In large
systems it has a noticeable effect only above 10 kHz
and has a roll-off character.
The driver level controls can be used to shape the
broadband response of a loudspeaker. They control
the output level of each driver with frequency ranges
that are determined by the crossover filters.
The bass tilt control compensates for a bass boost
seen when the loudspeaker is loaded by large nearby
boundaries [33-36]. This typically happens when a
loudspeaker is placed next to, or mounted into, an
acoustically hard wall. This filter is a first
order
shelving filter.
The bass roll-off control compensates for a bass
boost often seen at the very lowest frequencies the
loudspeaker can reproduce. This typically happens
when the loudspeaker is mounted in the corner of a
room where the loudspeaker is able to couple very
efficiently to the room thereby exacerbating room
mode effects that dominate this region of the frequency response. It is a notch filter with a centre
frequency set close to the low frequency cut-off of the
loudspeaker.
Table 1. Small two way room response controls.
Control type Room response control settings, dB
Treble tilt 0, –2
Bass tilt 0, –2, –4, –6
Bass roll-off 0, –2
Table 2. Two way room response controls.
Control type Room response control settings, dB
Treble tilt +2, 0, –2, –4, driver mute
Bass tilt 0, –2, –4, –6, driver mute
Bass roll-off 0, –2, –4, –6, –8
Table 3. Three way room response controls.
Control type Room response control settings, dB
Treble level 0, –1, –2, –3, –4, –5, –6, driver mute
Midrange level 0, –1, –2, –3, –4, –5, –6, driver mute
Bass level 0, –1, –2, –3, –4, –5, –6, driver mute
Bass tilt 0, –2, –4, –6, –8
Bass roll-off 0, –2, –4, –6, –8
Table 4. Large system room response controls.
Control type Room response control settings, dB
Treble tilt +1, 0, –1, –2, –3
Treble level 0, –1, –2, –3, –4, –5, –6, driver mute
Midrange level 0, –1, –2, –3, –4, –5, –6, driver mute
Bass level 0, –1, –2, –3, –4, –5, –6, driver mute
Bass tilt 0, –2, –4, –6, –8
Bass roll-off 0, –2, –4, –6, –8
3. ROOM EQUALISATION OPTIMISER
Optimisation involves the minimisation or maximisation of a scalar-valued objective function E(x),
where, x is the vector of design parameters, x
)
xEmin (1)
n
∈ℜ
.
Multi-objective optimisation is concerned with the
minimisation of a vector of objectives E(x) that may
be subject to constraints or bounds. Several robust
methods exist for optimising functions with design
parameters x having a continuous value range [37].
AES 114TH CONVENTION, AMSTERDAM, THE NETHERLANDS, 2003 MARCH 22-25 3
GOLDBERG AND MÄKIVIRTA AUTOMATED IN-SITU EQUALISATION
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
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
Large 3-way 2-way
Small
2-way
3.2. The Algorithm
The algorithm exploits the heuristics of experienced
system calibration engineers by dividing the optimisation 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
Find midrange/
treble ratio
Set bass tilt and
level
Reset bass roll-off
Set treble tilt
9 9 9 9
9 9
9 9
- -
- -
9 9 9 9
9
-
9 9
Table 7. Optimiser frequency ranges; fHF = 15 kHz; fLF
is the frequency of the lower –3 dB limit of the
frequency range.
Low High
Loudspeaker pass band
Midrange and treble driver band 500 Hz
Bass roll-off region
Bass region
Frequency Range
Limit
f
fHF
LF
f
1.5 fLF
LF
1.5
f
6 fLF
LF
f
HF
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,
m
max
f
min
m
a
=
E
max
f
b
0
m
0
[] []
==
ba
)()(
fxfa
)(
fx
,
)()(
fxfa
)(
fx
(2)
,,,
ffffff
3221
where x(f) is the smoothed magnitude of the in-situ
frequency response of the system, a
roll-off setting m currently being tested, x
target response, f
(Table 7) and f
defines the ‘bass roll-off region’
a
defines the ‘bass region’ (Table 7).
b
(f) is the bass
m
(f) is the
0
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
AES 114TH CONVENTION, AMSTERDAM, THE NETHERLANDS, 2003 MARCH 22-25 4
GOLDBERG AND MÄKIVIRTA AUTOMATED IN-SITU EQUALISATION
type objective function to be minimised is given in
Equation 3,
f
2
min
m
E
= (3)
m
∫
ff
=
1
fx
0
2
fxfa
)()(
df
)(
where x(f) is the smoothed magnitude of the in-situ
frequency response of the system, a
(f) is the mid-
m
range and treble level control combination m currently
being tested, x
define the ‘midrange and treble driver band’
(f) is the target response, f1 and f2
0
(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
(f) is the bass tilt and bass level combina-
m
tion m currently being tested together with the fixed
midrange and treble level ratio setting found in the
previous stage. Also, f
speaker pass band’
and f2 now define the ‘loud-
1
(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
band’
and f2 now define the ‘loudspeaker pass
1
(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 optimisation into stages.
The run time on a PII 366 MHz computer for a threeway 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%.
AES 114TH CONVENTION, AMSTERDAM, THE NETHERLANDS, 2003 MARCH 22-25 5
GOLDBERG AND MÄKIVIRTA AUTOMATED IN-SITU EQUALISATION
x
y
x
Table 9. Number of filter evaluations needed by the
optimisation algorithm.
Type of loudspeaker
Optimisation
stage
Preset bass roll-
off
Find midrange/
treble ratio
Set bass tilt and
level
Reset bass roll-off 6 6 6 3
Set treble tilt 5 - 4 2
Total 101 96 21 13
Total re. direct
search
Large 3-way 2-way
6 6 6 3
49 49 - -
35 35 5 5
0.2% 1.1% 26% 81%
Small
2-way
3.4. Algorithm Features
3.4.1. Frequency Range of Equalisation
The default frequency range of equalisation is from
the low frequency
–3 dB cut-off of the loudspeaker f
LF
to 15 kHz. If there is a wide band cancellation in the
frequency response around f
, or the high frequency
LF
level is decreased strongly due to an off-axis location
or the loudspeaker is positioned behind a screen or
due to very long measuring distance, manual readjustment of the design frequency range (indicated on
the graphical output by the blue crosses, Figure 1) is
needed. Naturally it is preferable to remove the causes
of such problems, if possible.
(f)
(f)
Figure 1. Typical graphical output of the optimiser
software. Original response x(f), target response x
and final response y(f). Also, –3 dB cut-off frequencies (triangles), optimisation range (crosses) and target
tolerance (dotted).
3.4.2. Target for Optimisation
There are five target curves from which to select:
1. ‘Flat’ is the default setting for a studio monitor.
The tolerance lines are set to +/–2.5 dB.
(f)
0
(f)
0
2. ‘Slope’ gives a user defined sloping target
response. There are two user defined knee frequencies and a dB drop/lift value. A positive slope
can also be set but is generally not desirable. The
tolerance lines are set to ±2.5 dB. Some relevant
slope settings include:
• –2 dB slope from low frequency –3 dB cut-off
to 15 kHz for the large systems to reduce the
aggressiveness of sound at very high output
levels
• –2 dB slope from 4 kHz to 15 kHz to reduce
long-term usage listening fatigue
• –3 dB slope from 100 Hz to 200 Hz for Home
Theatre installations to increase low frequency
impact without affecting midrange intelligibility
3. ‘Another Measurement’ allows the user to
optimise a loudspeaker’s frequency response magnitude to that of another loudspeaker. For example,
measure the left loudspeaker and optimise it, then
measure the right speaker and optimise this to the
optimised left speaker response. The result will be
the closest match possible between the left and
right speaker pair ensuring a good stereo pair
match and phantom imaging. Tolerance lines are
set at ±2.5 dB.
4. ‘X Curve – Small Room’ will give the closest
approximation to the X Curve for a small room as
defined in ANSI/SMPTE 202M-1998 [10]. This is
a target response commonly used in the movie
industry. A small room is defined as having a
volume less than 5300 cubic feet or 150 cubic
meters. The curve is flat up to 2 kHz and rolls off
1.5 dB per octave above 2 kHz. Tolerance lines are
set to ±3 dB.
1
5. ‘X Curve – Large Room’ will give the closest
approximation to the X Curve for a large room as
defined in ANSI/SMPTE 202M-1998 [10]. The
curve is flat from 63 Hz to 2 kHz and then rolls off
at 3 dB per octave above 2 kHz. Below 63 Hz
there is also a 3 dB roll off, with 50 Hz being
down by 1 dB and 40 Hz by 2 dB. Tolerance lines
are set to ±3 dB with additional leeway at low and
high frequencies.
1
An example of the room equaliser settings output for
the large system optimised in Figure 1 is shown in
Figure 2. The optimised result is displayed in green
and dark grey boxes. The green boxes are room
1
The room response controls do not directly support
the X Curves but it may be possible to achieve X
Curves in a room due to particular acoustic circumstances. This is also a good way to check how close
the response is to the selected X Curve.
AES 114TH CONVENTION, AMSTERDAM, THE NETHERLANDS, 2003 MARCH 22-25 6
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