Genelec Proceedings of the Institute of Acoustics, Proceedings of Institute of Ac Introduction Manual
Proceedings of the Institute of Acoustics
AN AUTOMATED IN-SITU FREQUENCY RESPONSE OPTIMISATION ALGORITHM FOR ACTIVE LOUDSPEAKERS,
INCLUDING A STATISTICAL ANALYSIS OF ITS PERFORMANCE
Andrew Goldberg Genelec Oy, Olvitie 5, 74100 Iisalmi, Finland.
Aki Mäkivirta Genelec Oy, Olvitie 5, 74100 Iisalmi, Finland.
1 INTRODUCTION
This paper presents a system to optimally set the room response controls currently found on fullrange active loudspeakers to achieve a desired in-room frequency response. The active loudspeak-
1
ers
to be optimised are individually calibrated in anechoic conditions to have a flat frequency response magnitude within design limits of ±2.5 dB.
When a loudspeaker is placed into the listening environment, the frequency response changes due
to loudspeaker-room interaction. To help alleviate this, the active loudspeakers incorporate a pragmatic set of room response controls, which account for 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 loudspeakers. Significant variance between calibrations can be seen even with experienced system calibrators. Additional variance will occur with different people calibrating loudspeaker systems. An automated calibration method was developed to
ensure consistency of calibrations because of these reasons.
Presented first in this paper is the discrete-valued room response equaliser employed in the active
loudspeakers. Then, the algorithm for automated value selection is explained including the software
structure, algorithm, features and operation. The performance of the optimisation algorithm is then
investigated by studying the statistical properties of frequency responses before and after equalisation.
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, not to convert the listening room anechoic. In fact, listeners prefer to hear some
room response in the form of liveliness creating a spatial impression and some envelopment
An approach to improve the loudspeaker performance in a room is to choose an optimal location for
the loudspeaker. Cox and D’Antonio
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. Problems with this approach are that optimisation may
not be practically possible in all cases.
Electronic equalisation to improve the subjective sound quality has been widespread for at least 40
years; see Boner & Boner
sional applications such as recording studios, mixing rooms and sound reinforcement, typically using a separate equaliser, although equalisers are increasingly built into active loudspeakers. Some
equalisers play a test signal and alter their response according to the in-situ transfer function meas-
5
ured
. This process can be sensitive and simple ‘press the button and everything will be OK’ approach proves hard to achieve with reliability, consistency and robustness.
Equalisation may become skewed if based only on a single point measurement. The frequency response in nearby positions can actually become worse after equalisation designed using only a sin-
Vol. 25. Pt 4. 2003
2
.
3
(Room Optimiser) use a computer model of the room to find
4
for an early example. Equalisation is particularly prevalent in profes-
Proceedings of the Institute of Acoustics
gle point measurement. A classical method to avoid this is to use a weighted average of responses
measured within a listening area. Such spatial averaging is often required when the listening area is
large; see examples described in the automotive industry
7
202M
. Spatial averaging can reduce local variance in mid to high frequencies and can reduce prob-
6
and cinema in the SMPTE Standard
lems caused by the fact that a listener perceives sound differently to a microphone, but typically reduces the accuracy of equalisation obtained at the primary listening location.
The room transfer function is position dependent, and this poses major problems for all equalisation
techniques. For a single loudspeaker in diffuse field no correction filter is capable of removing differences between responses measured at two separate receiver points. At high frequencies a required high-resolution correction can become very position sensitive. Frequency dependent resolution change is then preferable and is typically applied
8,9
but with the expense of reduced equalisation accuracy. Perfect equalisation able to achieve precisely flat frequency response in a listening
room, even within a reasonably small listening area, appears not possible. An acceptable equalisation is typically a compromise to minimise the subjective coloration in audio due to room effects.
Typically electronic equalisation in active loudspeakers uses low order analogue minimum phase fil-
10-12
ters
. Since the loudspeaker-room transfer function is of substantially higher order than such
equaliser, the effect of filtering is to gently shape the response. Even with this limitation, in-situ
equalisers have the potential to significantly improve perceived sound quality. The practical challenge is the selection of the best settings for the low-order in-situ equaliser.
Despite advances in psychoacoustics, it is difficult to quantify what the listener actually perceives
the sound quality to be, or to optimise equalisation based on that evaluation
13-15
. Because of this, insitu equalisation typically attempts to obtain the best fit to some objectively measurable target, such
as a flat third-octave smoothed response, known to link to the perception of sound free from coloration. Also, despite the widespread use of equalisation, it is still hard to provide exact timbre matching between different environments.
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
tively the temporal decay characteristics of a listening space by active absorption or modification of
the primary sound
25-30
16-24
. Some researchers have also shown an interest to control selec-
. If realisable, these are extremely attractive ideas because they imply that the
perceived sound could be modified with precision, to different target responses. Then, spatial variations in the frequency response can become far more difficult to handle than with low-order methods because the correction depends strongly on an exact match between the acoustic and equalisation transfer functions, and can therefore be highly local in space
25
.
2.2 Room Response Controls
1,32
The loudspeakers to be optimised have room response controls
. 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
nearby boundaries
compensates for a bass boost seen when the loudspeaker is loaded by large
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.
Proceedings of the Institute of Acoustics
Table 1. Small two way controls.
Control type Room response control settings, dB
Treble tilt 0, –2
Bass tilt 0, –2, –4, –6
Bass roll-off 0, –2
Table 3. Two way 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 2. Three way 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 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
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
37
range
.
3.1 Efficiency of Direct Search
)(min xE
(1)
∈ℜ
n. Multi-objective optimisation is concerned with
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
38
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). A screenshot of the software graphic user interface can be seen in Appendix A and a flow chart of the software can be seen in Appendix B.
Vol. 25. Pt 4. 2003
Proceedings of the Institute of Acoustics
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.
Frequency Range Limit
Low High
Loudspeaker pass band fLF fHF
Midrange and treble driver band 500 Hz fHF
Bass roll-off region fLF 1.5 fLF
Bass region 1.5 fLF 6 fLF
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 minimised is given by Equation 2,
m
max
f
a
=
min ffffff
E
m
max
f
b
0
m
0
)()(
fxfa
)(
fx
)()(
fxfa
)(
fx
[] []
ba
,,,,
==
3221
(2)
where x(f) is the smoothed magnitude of the in-situ frequency response of the system, a
bass roll-off setting m currently being tested, x
region’ (Table 7) and f
defines the ‘bass region’ (Table 7). User selected frequency ranges are not
b
(f) is the target response, fa defines the ‘bass roll-off
0
(f) is the
m
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 type objective function to be minimised is given in Equation 3,
f
2
E
min
=
m
m
∫
=
ff
1
2
fxfa
)()(
fx
0
df
)(
(3)
Proceedings of the Institute of Acoustics
where x(f) is the smoothed magnitude of the in-situ frequency response of the system, a
midrange and treble level control combination m currently being tested, x
f
and f2 define the ‘midrange and treble driver band’ (Table 7). The lower frequency bound is fixed
1
(f) is the target response,
0
(f) is the
m
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 an 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
fixed midrange and treble level ratio setting found in the previous stage. Also, f
(f) is the bass tilt and bass level combination m currently being tested together with the
m
and f2 now define
1
the ‘loudspeaker pass band’ (Table 7). The user can select both values. 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 twoway 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 method used to set the bass roll-off earlier
is repeated, but without modifying upwards the final setting. The same objective function as presented in Section 3.2.1 is used.
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
and f2 now define the ‘loudspeaker pass band’ (Table 7). The user can select both val-
1
ues. The defaults 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 it is skipped for three ways because having no such control.
3.3 Reduction of Computational Load
The optimiser algorithm reduces the computational load by exploiting the heuristics of experienced
calibration engineers. As a result, the number of filtering steps has dramatically reduced for larger
Proceedings of the Institute of Acoustics
systems (Table 9) and even relatively simple two-way systems show a substantial improvement
compared to the number of steps needed by direct search method (Table 5). There are two main
reasons for this improvement: the constraint of not allowing modification of all three driver level settings simultaneously and breaking-up of optimisation into stages.
Table 9. Number of filter evaluations by the optimisation algorithm.
Type of loudspeaker
Optimisation stage Large 3-way 2-way Small 2-way
Preset bass roll-off 6 6 6 3
Find midrange/ treble ratio 49 49 - -
Set bass tilt and level 35 35 5 5
Reset bass roll-off 6 6 6 3
Set treble tilt 5 - 4 2
Total 101 96 21 13
Total re. direct search 0.2% 1.1% 26% 81%
The run time on a PII 366 MHz computer for three-way and large systems is about 15 s (direct
search for three-way systems 3 minutes, large systems 15 minutes). The processing time is directly
proportional to the processor speed. A modern PIII 1200 MHz based computer takes about 4 s to
perform the same optimisation. Further improvements in the software have improved run times by
about 30%.
3.4 Algorithm Features
3.4.1 Frequency Range of Equalisation
The default equalisation frequency range is from the loudspeaker low frequency –3 dB cut-off f
to
LF
15 kHz. Manual readjustment of the design frequency range (indicated on the graphical output by
blue crosses, Figure 1) is needed in some special cases. Examples of these include a strong cancellation notch in the frequency response around f
, when off-axis loudspeaker location reduces
LF
significantly the high frequency level, when a loudspeaker is positioned behind a screen, or when
the measuring distance is very long. It is naturally preferable to remove such causes of problems, if
possible.
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.
2. ‘Slope’ allows the user to define a sloping target response. There are two user defined knee fre-
quencies and a dB drop/lift value. A positive slope can also be set but is normally not acoustically desirable. The tolerance lines are set to ±2.5 dB. Some relevant slope settings include:
• for large systems a –2 dB slope across the passband up to 15 kHz to reduce the aggressive-
ness 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 magni-
tude to that of another loudspeaker. For example, measure the left loudspeaker and optimise it,
then measure the right loudspeaker and optimise this to the optimised left loudspeaker response. This results in the closest match possible between the left-right loudspeaker pair ensuring good stereo pair match and phantom imaging. Tolerance lines are set at ±2.5 dB.
4. ‘X Curve – Small Room’ approximates the X Curve for a small room (volume less than 5300 cu-
bic feet or 150 cubic meters) as defined in ANSI/SMPTE 202M-1998
7
. The curve is flat up to 2