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
Aki Mäkivirta

1

Genelec Oy, Olvitie 5, 74100 Iisalmi, Finland.
Genelec Oy, Olvitie 5, 74100 Iisalmi, Finland.

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 loudspeakers1 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 toensure 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 theninvestigated 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 someroom response in the form of liveliness creating a spatial impression and some envelopment2.
An approach to improve the loudspeaker performance in a room is to choose an optimal location forthe loudspeaker. Cox and D’Antonio3 (Room Optimiser) use a computer model of the room to findoptimal 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 begiven 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 & Boner4 for an early example. Equalisation is particularly prevalent in professional applications such as recording studios, mixing rooms and sound reinforcement, typically using a separate equaliser, although equalisers are increasingly built into active loudspeakers. Someequalisers play a test signal and alter their response according to the in-situ transfer function measured5. 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 sinVol. 25. Pt 4. 2003

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 islarge; see examples described in the automotive industry6 and cinema in the SMPTE Standard
202M7. Spatial averaging can reduce local variance in mid to high frequencies and can reduce problems 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 applied8,9 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 filters10-12. 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 evaluation13-15. Because of this, insitu equalisation typically attempts to obtain the best fit to some objectively measurable target, suchas 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 toachieve a close approximation of unity transfer function (no change to magnitude or phase) within acertain bandwidth of interest16-24. 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 sound25-30. If realisable, these are extremely attractive ideas because they imply that theperceived 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 space25.
2.2

Room Response Controls

The loudspeakers to be optimised have room response controls1,32. 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 boundaries33-36. 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 thecorner 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.

Table 3. Two way controls.

Control type
Treble tilt
Bass tilt
Bass roll-off

Control type
Treble tilt
Bass tilt
Bass roll-off

Room response control settings, dB0, –20, –2, –4, –6
0, –2

Room response control settings, dB+2, 0, –2, –4, driver mute0, –2, –4, –6, driver mute0, –2, –4, –6, –8

Table 2. Three way controls.
Control type
Treble level
Midrange level
Bass level
Bass tilt
Bass roll-off

3

Room response control settings, dB
0, –1, –2, –3, –4, –5, –6, driver mute0, –1, –2, –3, –4, –5, –6, driver mute0, –1, –2, –3, –4, –5, –6, driver mute0, –2, –4, –6, –8
0, –2, –4, –6, –8

Table 4. Large system controls.
Control type
Treble tilt
Treble level
Midrange level
Bass level
Bass tilt
Bass roll-off

Room response control settings, dB+1, 0, –1, –2, –3
0, –1, –2, –3, –4, –5, –6, driver mute0, –1, –2, –3, –4, –5, –6, driver mute0, –1, –2, –3, –4, –5, –6, driver mute0, –2, –4, –6, –8
0, –2, –4, –6, –8

ROOM EQUALISATION OPTIMISER

Optimisation involves the minimisation or maximisation of a scalar-valued objective function E(x),min E ( x)(1)where, x is the vector of design parameters, x∈ℜn. Multi-objective optimisation is concerned withthe 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
range37.
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.
Room Response Control
Treble tilt
Treble level
Midrange level
Bass level
Bass tilt
Bass roll-off
Total

3.2

Large
5
7
7
7
5
5
42875

Type of loudspeaker
3-way
2-way
4
7
7
7
5
4
5
5
8575
80

Small 2-way
2
4
2
16

The Algorithm

The algorithm38 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.
Optimisation stage
Preset bass roll-off
Find midrange/ treble ratio
Set bass tilt and level
Reset bass roll-off
Set treble tilt

Large
9
9
9
9
9

Type of loudspeaker
3-way
2-way
9
9
9
9
9
9
9
-

Small 2-way
999

Table 7. Optimiser frequency ranges; fHF = 15 kHz; fLF is the frequency of the lower –3 dB limit of
the frequency range.

Loudspeaker pass band
Midrange and treble driver bandBass roll-off region
Bass region

3.2.1

Frequency Range Limit
Low
High
fLF
fHF
500 HzfHF
fLF
1.5 fLF
1.5 fLF
6 fLF

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 toleave 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 typeobjective function to be minimised is given by Equation 2,

 a ( f ) x( f ) max mfa x0 ( f ) 

min E =

 a ( f ) x( f ) max mfb x0 ( f ) m,

f a = [ f1 , f 2 ], f b = [ f 2 , f 3 ](2)

where x(f) is the smoothed magnitude of the in-situ frequency response of the system, am(f) is thebass roll-off setting m currently being tested, x0(f) is the target response, fa defines the ‘bass roll-off
region’ (Table 7) and fb defines the ‘bass region’ (Table 7). User selected frequency ranges are notpermitted.
The reason for this arrangement rather than using a least squares type objective function is that thebass 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,
f2

min E = ∫mf = f1am ( f ) x ( f ) 2
dfx0 ( f )(3)

Proceedings of the Institute of Acoustics

where x(f) is the smoothed magnitude of the in-situ frequency response of the system, am(f) is the
midrange and treble level control combination m currently being tested, x0(f) is the target response,
f1 and f2 define the ‘midrange and treble driver band’ (Table 7). The lower frequency bound is fixedat 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 betested 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 numberof 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 systemsensitivity. Table 8 shows an example of incorrect and correct setting of the driver level controls.
Table 8. Driver level control settings.
Control
Bass level
Midrange level
Treble level
Input sensitivity

Incorrect Setting
–4 dB
–3 dB
–2 dB
–6 dBuCorrect Setting
–2 dB
–1 dB
0 dB
–4 dBuThe least squares type objective function to be minimised is the same as shown in Equation 3.
However, am(f) is the bass tilt and bass level combination m currently being tested together with thefixed midrange and treble level ratio setting found in the previous stage. Also, f1 and f2 now definethe ‘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 canthen 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, f1 and f2 now define the ‘loudspeaker pass band’ (Table 7). The user can select both values. 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 improvementcompared 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.
Optimisation stage
Preset bass roll-off
Find midrange/ treble ratio
Set bass tilt and level
Reset bass roll-off
Set treble tilt
Total
Total re. direct search

Large
6
49
35
6
5
101
0.2%

Type of loudspeaker
3-way
2-way
6
6
49
35
5
6
6
4
96
21
1.1%
26%

Small 2-way
3
5
3
2
13
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 toperform the same optimisation. Further improvements in the software have improved run times by
about 30%.
3.4
3.4.1

Algorithm Features
Frequency Range of Equalisation

The default equalisation frequency range is from the loudspeaker low frequency –3 dB cut-off fLF to
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 fLF, when off-axis loudspeaker location reduces
significantly the high frequency level, when a loudspeaker is positioned behind a screen, or whenthe 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 frequencies 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 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 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 cubic feet or 150 cubic meters) as defined in ANSI/SMPTE 202M-19987. The curve is flat up to 2

Proceedings of the Institute of Acoustics

kHz and rolls off 1.5 dB per octave above 2 kHz. Tolerance lines are set to ±3 dB – see footnote
1. This is a target response commonly used in the movie industry.
5. ‘X Curve – Large Room’ will give the closest approximation to the X Curve for a large room as
defined in ANSI/SMPTE 202M-19987. The curve is flat from 63 Hz to 2 kHz and then rolls off at 3dB per octave above 2 kHz. Below 63 Hz there is also a 3 dB roll off, with 50 Hz being down by 1dB and 40 Hz by 2 dB. Tolerance lines are set to ±3 dB with additional leeway at low and highfrequencies – see footnote 1.

4

PERFORMANCE OF THE OPTIMISATION ALGORITHM

To assess the performance of the combination of optimisation algorithm and equalisation in the
loudspeakers, the analysis compares the unequalised in-situ frequency response to the response
after equalisation. The MLS measurement technique was used to measure the in-situ acousticalfrequency responses. The acquisition system parameters are shown in Table 10. The values in parentheses are the parameters used for acquiring the impulse response for models that have a bass
extension below 30 Hz.
The room response control settings were calculated for each loudspeaker response according to
the algorithm discussed in Section 3 and statistical data for each measurement before and after
equalisation was recorded. The statistical data is analysed to study how the objective quality of thesystem magnitude response has been improved by using the proposed algorithm for setting theroom response controls.
Table 10. Acoustic measurement system parameters.
Parameter
Measurement System
Microphone
Sample rate, fs
MLS sequence order
Averages
Impulse response length
Time window
FFT size
Frequency resolution

4.1

Equipment / Setting
WinMLS200039
40
Neutrik 3382
48 kHz14 (16)1
0.341 s (1.36 s)
Half-cosine
16384 (65536)
2.93 Hz (0.733 Hz)

Statistical Data Analysis

Statistical analysis was conducted to assess the ability of the equalisation algorithm to attain a target response. The target in the study was a flat frequency response, and several statistical descriptors were employed to indicate how much the equalised response deviates from the flat target. The
performance was separately studied for narrowband and wideband deviations.
The frequency bands considered in the study were the full loudspeaker passband, and its subsections called ‘LF’, ‘MF’ and ‘HF’ (see Table 11), collectively referred to as ‘subbands’. These subbands correspond roughly to the bandwidths of each driver in a three-way system.
Several statistical descriptors of sound pressure were calculated to indicate the ability of equalisation to reduce narrow band variation of sound pressure. These were the minimum, maximum, range(of magnitude dB values), median, upper and lower quartiles, 5% and 95% percentiles calculated
for the full loudspeaker passband and in each subband, as well as the root-mean-square (RMS) deviation of sound pressure from the median within each subband (value expressed in dB). In order tocalculate these, the median broadband (Table 11) magnitude response for each loudspeaker was
standardised to zero dB.
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.

Proceedings of the Institute of Acoustics

When a response is flat in a broadband sense, the medians calculated over various (large) frequency bands are similar. In this study, differences of median sound pressure between subbands
are taken to indicate that broadband tonal balance of a response is not flat. An improvement in the
broadband tonal balance due to equalisation is then indicated by a reduction of median value differences.
Table 11. Frequency band definitions the statistical data analysis; fLF is the frequency of the lower –3 dB limit of the frequency range.
Bandwidth Name
Broadband
LF
MF
HF

4.2

Frequency Range Limit
Low
High
fLF
15 kHzfLF
400 Hz400 Hz3.5 kHz
3.5 kHz
15 kHz

Example of Statistical Data Analysis

Figure 1 shows an example where room response control settings are calculated according to the
optimisation algorithm. The equalisation target is a flat magnitude response (straight line at 0dB
level). The in-situ frequency response of the loudspeaker was recorded before equalisation, i.e.
when all the room response controls were set to their default position, which has no effect to the response. The appropriate room response control settings were calculated using the optimisation algorithm, applied to the loudspeaker and the corrected in-situ frequency response plotted. The loudspeaker’s passband (triangles) and the frequency band of equalisation (crosses) are indicated on
the graphical output. The proposed room response control settings are shown and the effect ofthese settings is visualised in the response plot. The treble tilt, midrange level and bass tilt controls
have been set. The equalisation corrects the low frequency alignment and improves the linearity
across the whole passband. The optimised result is displayed in green and dark grey boxes. The
green boxes are room response controls that should be set on the loudspeaker. The light greyboxes are room response controls that are not present on the loudspeaker. Also displayed in thisarea is the error function, which is an RMS of the optimised frequency response pass band.
Figure 2 shows a statistical analysis of the same loudspeaker presented in graphical form. The upper three plots were calculated before equalisation and the lower three plots after equalisation. The
plots display the values of percentiles in the magnitude value distribution (box plot), the histogram ofvalues and the fit of the magnitude values to normal distribution before and after equalisation.
These plots clearly show that the deviation in magnitude data has been reduced. This is illustrated
by the reduced range in the box plot and the value histogram, as well as a better fit to a normal distribution in the normal probability plot.
Two detailed case studies can be seen in38. Responses before an after equalisation are shown together with room acoustic analysis to show that the algorithm performs well, even in widely varying
conditions.

Proceedings of the Institute of Acoustics

x(f)y(f) x0(f)Figure 1. Graphical output of the optimiser software. Original response x(f), target response x0(f)and equalised response y(f), cut-off frequencies (triangles), optimisation range (crosses) and target
tolerance (dotted lines). Output section on the right displays possible settings and values to bechanged (green background) as well as the error function value and processing time.

Figure 2. Case example, statistical analysis output.
4.3

Results

63 loudspeakers were measured before and after equalisation (12 small two-way, 22 two-way, 30
three-way and three large systems). Depending on the product type, not all of the room responsecontrols are available (Tables 1–4). Table 12 shows the number times a control was used whenavailable on a loudspeaker. The midrange level control is used the most frequently and the bassroll-off the least.

Proceedings of the Institute of Acoustics

Table 12. Use of available room response controls.
Room Response Control
Midrange Level
Treble Level
Bass Tilt
Treble Tilt
Bass Level
Bass Roll-off

Usage vs. availability
27/33
22/33
37/67
11/37
8/33
10/67

% Usage
82%
67%
55%
30%
24%
15%

Appendix D shows quartile difference and RMS deviations for each loudspeaker in the study, for thebroadband and each subband. The quartile difference or RMS deviation after equalisation is subtracted from the same before equalisation. An improvement will produce a negative value of difference. Quartile difference and RMS deviation values represent different ways to look at the deviationfrom the distribution median value. Quartile limits are more robust to outlier values while the RMS
value is affected by them.
For small two-way systems (Figures 9-1041), the main improvement is seen at low frequencies infour out of 12 cases. Only in one case is there is a significant improvement in the broadband flatness.
The broadband flatness of the two-way systems is improved in four (quartile data, Figure 11) or
41
eight (RMS data, Figure 12 ) cases out of 22. An equal number of reductions and increases of low
frequency quartile values can be seen. MF subband quartile values improve in one case and deteriorate in 5 cases while there are no changes in the HF subband. The flatness in the broadband and
LF subband as indicated by RMS deviation data has improved, indicating a reduction of outlier values. The MF and HF subbands show no changes or a slight increase of the RMS deviation.
Three-way systems show in most cases a clear reduction of both the quartile difference (Figure
414113 ) and RMS deviation (Figure 14 ) for the broadband and LF subband. There is no significant
change in the MF and HF subbands.
A similar trend is seen for the three large systems included in this study (Figures 15-1641). Mainly
the LF subband flatness is improved and this is reflected in broadband flatness improvement.
Some responses appear to worsen in terms of quartile difference and RMS deviation in the subband analysis. This was not evident in the broadband metrics, indicating that the arbitrary definitionof subband frequency division introduced some error. The cases where this happened originally suffered from severe response anomalies due to extremely bad room acoustics. The equalisation was
not designed to compensate for such problems.
Subband median level differences (Figure 3) demonstrate the broadband frequency balance.
Acoustical loading of a loudspeaker by nearby boundaries is reflected in the LF subband medianlevel before equalisation, especially for three-way models that are typically flush mounted. The median level of the LF subband is reduced by equalisation, indicating that equalisation compensates
well for this loading. Smaller difference in median values across subbands shows that equalisation
has improved broadband flatness. The largest improvement is seen in three-way loudspeakers. For
two-way systems equalisation has improved broadband flatness only marginally. The broadband
flatness improvement is mainly a result of better alignment of the LF subband with the MF and HF
subbands. The equalisation has not only reduced the variation inside individual subbands but also
improved the broadband flatness of the acoustical response. This should translate to a reduced audio colouration at the listening position.
All loudspeakers pooled together (Figure 3), equalisation reduces median value variance for the LF
subband for all loudspeaker types. Only in three-way systems an improvement is seen also in MF
and HF subband median value variances.
Figure 4 shows pooled results for all products and results for each product cathegory, excluding thethree main monitors. For all models, the broadband flatness has been improved (by 0.4 dB), andthe RMS deviation has been reduced. The largest reduction is seen in three-way systems. To someextent, the result is similar for the quartile difference but the small two-way and two-way systems do
not experience such large improvement. This indicates that the improvement is mainly a reductionof extreme magnitude values (peak height and notch depth) in the low frequency response.

Proceedings of the Institute of Acoustics

Level, dB

Level, dB

Subband Median Levels - All Models

5

5

4

4

3

3

2

2

1

1
0

0
-1

LF

-2

MF

HF

LF

Original

MF

HF

-1

MF

HF

LF

Original

MF

HF

Equalised-3

Level, dB

Level, dB

Subband Median Levels - 2-way models

Subband Median Levels - 3-way models

5

5

4

4

3

3
2

2

1

1
0

0
-2

LF

-2

Equalised-3-1

Subband Median Levels - Small models

LF

MF

HF

Original

-3

LF

MF
Equalised

HF

-1
-2

LF

MF
Original

HF

LF

MF

HF

Equalised-3

Figure 3. Mean and standard deviation of subband median levels before and after equalisation.

5

DISCUSSION

The objective of this paper is to present an automated system for choosing appropriate room response control settings once an in-situ frequency response measurement has been made and toevaluate objectively the efficacy of the proposed method of selecting the settings.
Active loudspeakers room response controls implement a discrete set of filter parameter values
rather than providing a continuous value range. The number of possible setting combinations canbe quite large and even an experienced operator can find it difficult to systematically choose the optimal settings.
The task of an automated optimiser is to find the best filter setting combination. The cost of performing a brute force search of all possible value combinations and then choosing the best is prohibitivein terms of computer processing time. We exploit heuristics of experienced calibration engineers to
reduce the number of alternatives by dividing the task into subsections that can reliably be solved
independently. A significant part of this heuristics is the order in which these choices should betaken.
A considerable improvement in the speed of optimisation was achieved relative to an exhaustive
search. The optimisation algorithm is robust to a wide variety of situations, such as variations ofroom acoustics, differently sized loudspeakers with differing anechoic responses and varying in-situ
responses42. The optimisation is sufficiently efficient making the software fast enough to be usedroutinely at in-situ loudspeaker calibrations.
A case study demonstrates the statistical changes due to the optimisation algorithm’s recommended room response control settings. The settings achieve improved equalisation in the form ofa smaller RMS deviation from the target response. The improvement is not limited by the optimisation method but by the room response controls not intended to correct for narrow-band deviations.
Examples of these are response variations resulting from acoustic issues such as cancellations associated comb filtering due to reflections. These should be solved acoustically rather than electronically.
The statistical analysis of 63 loudspeakers shows that the automated equalisation is able to systematically reduce the variability in the equalised responses and to improve the frequency response
flatness relative to the target response. It achieves this by improving both the broadband frequency
balance and by reducing narrow-band variability in the response, particularly at low frequencies.
The main improvement is the reduction of extreme (outlier) values at low frequencies.
It is interesting to note that when a control was available, the most commonly activated control was
the midrange level, followed by the treble level and bass tilt. In addition, broadband flatness wasProceedings of the Institute of Acoustics

improved by equalisation, mainly because extreme magnitude values at low frequencies were reduced (LF subband).
The lack of improvement in midrange and high frequencies (MF and HF subbands) is because theroom related response variation in these frequencies is narrow-band. Somewhat better equalisation
could be obtained by using controls offering response tilting or shaping within these frequencies.
The largest variation in the improvement at low frequencies can be explained by listening rooms
acoustics43. At low frequencies, radiation from a loudspeaker is typically omnidirectional and thesound field is usually not diffuse. This results in strong room effects and hence large variations in
the magnitude response at these frequencies.

Level, dB

25% to 75% Percentile Difference
Change due to Equalisation - All models

Level, dB
1

1

0

0
Broadband

LF

MF

HF

LF

MF

HF

-4

-3

-5

Level, dB

25% to 75% Percentile Difference
Change due to Equalisation - Small models

Level, dB

RMS Deviation
Change due to Equalisation - Small models

1

1

0

0
Broadband

LF

MF

HF

-1

-1

Broadband

LF

MF

HF

-2
-3

-2

-4

-3

-5

Level, dB

25% to 75% Percentile Difference
Change due to Equalisation - 2-way models

Level, dB

RMS Deviation
Change due to Equalisation - 2-way models

1

1

0

0
Broadband

LF

MF

HF

-1

Broadband

LF

MF

HF

-2

-1

-3

-2

-4

-3

-5

Level, dB

25% to 75% Percentile Difference
Change due to Equalisation - 3-way models

Level, dB

RMS Deviation
Change due to Equalisation - 3-way models

1

1

0

0
Broadband-3

Broadband

-3

-2

-2

-1
-2

-1

-1

RMS Deviation
Change due to Equalisation - All models

LF

MF

HF

-1

Broadband

LF

MF

HF

-2
-3
-4
-5

Figure 4. Change in sound level deviation due to equalisation. For each subband, quartile difference
and RMS deviation from the median. The error bar indicates the standard deviation.
The largest improvement seen for three-way systems can be explained by two main factors. Firstly,
rooms in which these loudspeakers are installed typically have a high quality acoustical design,
producing a well-controlled sound field. Smaller loudspeakers are often installed in rooms with little
or no acoustical control, making response correction by equalisation a very challenging task. Sec-

Proceedings of the Institute of Acoustics

ondly, three-way systems have more room response controls than two-way systems, with a higher
capability to compensate for room problems. The type of equalisation the room response controls
are designed for is a gentle shaping of the response. High order narrow band corrections are notpossible, and therefore room characteristics and the quality of its acoustical design will always playa major role.

6

CONCLUSIONSThe low-order room response adjustment filters in active loudspeakers can significantly improve theperceived quality of audio reproduction. The automated optimisation algorithm presented in this paper is used to select an optimal combination of filter settings in loudspeakers where a room response equaliser is implemented as a filter having discrete-valued settings. The algorithm proves tobe useful because it performs systematically with varying types of loudspeakers, with differing filter
sets in multiple types of acoustical installations. The efficiency and reliability of the algorithm has
been achieved by exploiting heuristics of experienced sound system calibration engineers. The
automated methodology obtains systematically and consistently the best combination of available
filter settings, performing quickly irrespective of the operator. The algorithm has been implemented
in a loudspeaker calibration tool used by specialists who set up and tune studios and listening
rooms.

7

ACKNOWLEDGEMENTS

The authors would like to thank Mr. Steve Fisher (SCV London) for the original inspirational idea
and some of the measurements used in the statistical analysis, Mr. Olli Salmensaari (Finnish
Broadcasting Corporation) for additional measurements, Mr. Lars Morset (Morset Sound Development) and Genelec Oy. Parts of this work are presented in more detail as an MSc Thesis at theHelsinki University of Technology42.

8

REFERENCES

1
2

Genelec Oy, http://www.genelec.com (2003 Feb.).
Walker R., “Equalisation of Room Acoustics and Adaptive Systems in the Equalisation of
Small Rooms Acoustics,” Proc. 15th Int. Conf., paper 15-005 (1998 Oct.).
Cox T. J. and D’Antonio P., “Determining Optimum Room Dimensions for Critical Listening
Environments: A New Methodology,” presented at 110th Conv. Audio Eng. Soc., preprint
5353 (2001 May).
Boner C. P. and Boner C. R., “Minimising Feedback in Sound Systems and Room Ring
Modes with Passive Networks,” J. Acoust. Soc. America, vol. 37, pp. 131-135 (1965 Jan).
Holman T., “New Factors in Sound for Cinema and Television,” J. Audio Eng. Soc., vol. 39,
pp. 529-539 (1991 Jul/Aug.).
Schulein R. B., “In-Situ Measurement and Equalisation of Sound Reproduction Systems,” J.
Audio Eng. Soc., vol. 23, pp. 178-186 (1975 Apr.).
Staffeldt H. and Rasmussen E., “The Subjectively Perceived Frequency Response in a
Small and Medium Sized Rooms,” SMPTE J., vol. 91, pp. 638-643 (1982 Jul.).
JBL, http://www.jblpro.com (2003 Feb.).
Geddes E. R., “Small Room Acoustics in the Statistical Region,” Proc. 15th Int. Conf., pp.
51-59 (1998 Sep.).
Greiner R. A. and Schoessow M., “Design Aspects of Graphic Equalisers,” J. Audio Eng.
Soc., vol. 31, pp. 394-407 (1983 Jun.).

3

4
5
6
7
8
9
10

Proceedings of the Institute of Acoustics

11
12
13
14
15
16

17
18
19

20

21

22
23

24
25
26
27
28
29

30

31
32

Bohn D.A., “Constant-Q Graphic Equalisers,” J. Audio Eng. Soc., vol. 34, pp. 611-626 (1986Sep.).
Bohn D.A., “Operator Adjustable Equalisers: An Overview,” Proc. 6th Int. Conf., paper 6025 (1988 Apr.).
“Motion Pictures– Dubbing Theatres, Review Rooms and Indoor Theatres– B-Chain Electroacoustic Response,” ANSI/SMPTE standard no 202M-1998 (1998).
Genereux R., “Signal Processing Considerations for Acoustic Environment Correction,”
Proc. UK Conf. 1992, paper DSP-14 (1992 Sep.).
Elliott S. J. and Nelson P. A., “Multiple Point Equalisation in a Room Using Adaptive Digital
Filters,” J. Acoustical Eng. Soc., vol. 37 (1989 Nov.).
Karjalainen M., Piirilä E, Järvinen A. and Huopaniemi J., “Comparison of Loudspeaker
Equalisation Methods Based on DSP Techniques,” J. Audio Eng. Soc., vol. 47, pp. 14-31(1999 Jan/Feb.).
Neely S. T. and Allen J. B., “Invertability of a Room Impulse Response,” J. Acoustical Soc.
America, vol. 66, pp. 165-169 (1979 Jul.).
Kirkeby O. and Nelson P.A., “Digital Filter Design for Inversion Problems in Sound Reproduction,” J. Audio Eng. Soc., vol. 47, pp. 583-595 (1999 Jul/Aug.).
Radlovic B. D. and Kennedy R. A., “Non-minimum Phase Equalisation and its Subjective
Importance in Room Acoustics,” IEEE Trans. Speech Audio Proc., vol. 8, pp. 728-737 (2000
Nov.).
Nelson P. A., Orduna-Bustamante F. and Hamada H., “Inverse Filter Design and Equalisation Zones in Multichannel Sound Reproduction,” IEEE Trans. Speech Audio Proc., vol. 3,
pp. 185-192 (1995 May).
Kirkeby O., Nelson P.A., Hamada H., Orduna-Bustamante F., “Fast Deconvolution of Multichannel Systems Using Regularisation,” IEEE Trans. Speech Audio Proc., vol. 6, pp. 189194 (1998 Mar).
Johansen L. G. and Rubak P., “Listening Test Results from a new Loudspeaker/Room Correction System,” presented at 110th Conv. Audio Eng. Soc., preprint 5323 (2001 May).
Johansen L. G. and Rubak P., “Design and Evaluation of Digital Filters Applied to Loudspeaker/Room Equalisation,” presented at 108th Conv. Audio Eng. Soc., preprint 5172
(2000 Feb.).
Fielder L. D., “Analysis of Traditional and Reverberation-Reducing Methods of Room
Equalisation,” J. Audio Eng. Soc., vol. 51, pp. 3-26 (2003 Jan/Feb.).
Nelson P. A. and Elliott S. J., Active Control of Sound (Academic Press, London, 1993).
Darlington P. and Avis M. R., “Time Frequency Response of a Room with Active Acoustic
Absorption,” presented at 100th Conv. Audio Eng. Soc., preprint 4192 (1996 May).
Avis M. R., The Active Control of Low Frequency Room Modes (Ph.D. Thesis, University ofSalford, Dep. Applied Acoustics, 2001).
Avis M. R., “IIR Bi-Quad Controllers for Low Frequency Acoustic Resonance,” presented at
111th Conv. Audio Eng. Soc., preprint 5474 (2001 Sep.).
Mäkivirta A., Antsalo P. Karjalainen M. and Välimäki V., “Low Frequency Modal Equalisation of Loudspeaker Room-Responses,” presented at 111th Conv. Audio Eng. Soc., preprint
5480 (2001 Sept.).
Karjalainen M., Esquef P. A. A., Antsalo P., Mäkivirta A. and Välimäki V. “FrequencyZooming ARMA Modelling of Resonant and Reverberant Systems,” J. Audio Eng. Soc., vol.
50, pp. 1012-1029 (2002 Dec.).
Moore B. C .J., Glasberg B. R., Plack C. J. and Biswas A. K., “The shape of the Ear’s Temporal Window,” J. Acoustical Soc. America, vol. 83, pp. 1102-1116 (1988 Mar).
Martikainen I., Varla A. and Partanen T., “Design of a High Power Active Control Room
Monitor,” presented at 86th Audio Engineering Society Convention, preprint 2755 (1989Mar.).

Proceedings of the Institute of Acoustics

33
34
35
36
37
38
39
40
41

42

43

Allison R. F., “The Influence of Room Boundaries on Loudspeaker Power Output,” J. Audio
Eng. Soc., vol. 22, pp. 314-320 (1974 June).
Beranek L. L., Acoustics (Acoustical Society of America, 1993).
Kinsler L. E., Frey A. R., Coppins A. B. and Sanders J. V., Fundamentals of Acoustics (3.
ed., John Wiley and Sons, 1982).
Borwick J., Loudspeaker and Headphone Handbook (2. ed., Focal Press, 1994).
The MathWorks, “MATLAB Optimisation Toolbox User’s Guide (v. 6.1)” (The MathWorks
Inc., Natick, 2001).
Goldberg A. P., Mäkivirta A., “Automated In-Situ Frequency Response Optimisation of Active Loudspeakers” presented at 114th Conv. Audio Eng. Soc., preprint 5730 (2003 Mar).
Morset Sound Development, WinMLS2000, http://www.winmls.com (2003 Feb.).
NTI AG., Neutrik Test Instruments, 3382 Microphone, http://www.nt-instruments.com (2003
Feb.).
Goldberg A. P., Mäkivirta A., “Statistical Analysis of an Automated In-Situ Frequency Response Optimisation Algorithm for Active Loudspeakers” proceedings of the 23rd Conf. Audio Eng. Soc. (2003 May).
Goldberg A. P., “In-Situ Frequency Response Optimisation of Active Loudspeakers” (M.Sc.
Thesis, Helsinki University of Technology, Department of Acoustics and Audio Signal Processing, 2003).
Mäkivirta A., Anet C., “A Survey Study of In-Situ Stereo and Multi-Channel Monitoring Conditions” presented at 111th Conv. Audio Eng. Soc. (2001 Dec.).

APPENDIX A – SOFTWARE GRAPHICAL USER INTERFACE

Figure 5. Software graphical user interface at start up.

Proceedings of the Institute of Acoustics

APPENDIX A – SOFTWARE FLOW CHART

START
START
DIPtimiser
Display GUI
Reset GUI
Variables andGraph
Add Supported
ModelsAwait User
Inputs

CLOSE
CLOSE
DIPtimiser

Reset Graphand Outputs
Get Model
NumberStoredMeasurement

Load Impulse
Response

Model
Database

CTRL+M
Measurement
Dump

Remove DC,
Window, FFTand Smooth
Apply Mic
Compensation
Display
Original Freq
Response

StoredMeasurement

Calculate
Target Resp

Display Target
Response

Set
Frequency
Set
DIPtimisation
Range
Range
2

Figure 6. Software flow chart, part 1.

1

Microphone
Compensation

Proceedings of the Institute of Acoustics

2

1

Load Filters

Model Filters

Preset BRO

Is Large
System?

Find ML-TL
Ratio

Y

Is Small
System?

N
Set BL & BT
(wrt ML&TL)

Set BT

Reset BRO

Y

Is 3-way
System?

N
Set TT

Display Final
Tone Control
Settings
Display Final
Frequency
Response

Figure 6 continued. Software flow chart, part 2.