Performance Comparison of Graphic
Equalisation and Active Loudspeaker Room
Response Controls
Andrew Goldberg and Aki Mäkivirta
Genelec Oy, Olvitie 5, 74100 Iisalmi, Finland

ABSTRACT
We compare the room response controls available in active loudspeakers to a third-octave graphical equaliser. The
room response controls are set using an automated optimisation method presented in earlier AES publications. A
third-octave ISO frequency constant-Q graphic equaliser is set to minimise the least squares deviation from linear
within the passband in a smoothed acoustical response. The resulting equalisation performance of the two methods
is compared using objective metrics, to show how these standard room response equalising methods perform. For all
loudspeaker models pooled together, the room response controls improve the RMS deviation from a linear response
from 6.1 dB to 4.7 dB (improvement 22%), whereas graphic equalisation improves the RMS deviation to 1.8 dB(improvement 70%). Both equalisation techniques achieve a similar improvement in the broadband balance, which
has been shown to affect a subjective lack of colouration in sound systems. The optimisation time for a graphic
equaliser is up to 48 times longer compared to that for active loudspeaker room response controls.

1. INTRODUCTION
The purpose of room equalisation is to improve theperceived quality of sound reproduction in a listening
environment. Electronic equalisation to improve thesubjective sound quality has been widespread for atleast 40 years (an early example is [1]). Equalisation isprevalent in professional sound reproduction such asrecording studios, mixing rooms and sound reinforcement. In-situ response equalisation is often implemented using third-octave equalisers, which arenormally set with the help of real time analysers. Thismeasurement and equalisation combination is cheap,
readily available and a relatively simple concept tograsp with a little training [2-4]. Room response correcting equalisers are now also increasingly built into
active loudspeakers, but these equalisers have an entirely different approach as to how the equaliser addresses any acoustic problems of the reproduction.

Since the loudspeaker-room transfer function is ofsubstantially higher order than the equalisation filters,
the effect of either type of equalisation is to gently
shape the acoustic response [5]. The room transfer
function is position dependent, which poses major
problems for all equalisation techniques. At high frequencies the required high-resolution correction canbecome very position sensitive [6,7]. Even with theselimitations, in-situ equalisers have the potential to significantly improve perceived sound quality. The practical challenge is to find the best compromise for theparameters in the in-situ equaliser. An acceptableequalisation is typically a compromise to minimise thesubjective coloration in the audio due to room effects.
Despite advances in psychoacoustics, it is difficult toquantify what the listener actually perceives the soundquality to be [8-10], or to optimise equalisation basedon that evaluation. Because of this, in-situ equalisation
typically attempts to obtain the best fit to some objec-

GOLDBERG AND MÄKIVIRTA

OPTIMISED EQUALISATION COMPARISON

tively measurable target known to relate to the perception of sound as being free from coloration, such as aflat third-octave smoothed magnitude response.
The purpose of this paper is to investigate how thestandard room response controls available in active
loudspeakers [11] compare to the industry standard
method for sound system equalisation, i.e. a 31-band
third-octave graphic equaliser. It is obvious that agraphical equaliser has many more adjustment degrees
of freedom compared to the standard room response
equalisers employed in active loudspeakers – there are
31 gains with fixed Q’s and centre frequencies in agraphical equaliser compared to some three to five
separate settings with two to seven discrete values in
the room response equaliser. This would appear tosuggest that a graphical equaliser should achieve a superior outcome if set properly. However, the centre
frequencies, and fixed Q, of a graphical equaliser are
not designed to cope with typical room response problems and it is rather naïve to simply suggest that thehigher degrees of freedom alone could be taken as anindication of how much better or worse one method iscompared to another.
This paper presents a performance comparison of aroom response control set available in active loudspeakers and a standard 31-band graphic equaliser.
Optimisation algorithms are used to set both equalisers to achieve the best possible fit to the desired flatin-room magnitude response. To make possible thiscomparison, an optimisation algorithm was developed
to set the gains of a 31-band graphical equaliser. Thismethod is described. The performance of the equalisations and optimisation algorithms is investigated bystudying the statistical properties of 67 in-situ magnitude responses before and after equalisation.
2. IN-SITU EQUALISATIONThe room response controls were previously describedin [12-14]. A constant-Q type 31-band DSP graphic
equaliser [15] was constructed using bi-quadratictransfer functions of the form,H ( z) =b0 + b1 z −1 + b2 z −2
1 + a1 z −1 + a2 z − 2sin (2π f 0 /f S )2QA
GA = 10 20⎛
sin (2π f 0 /f S ) ⎞⎜⎜1 + A
⎟⎟
2Q
⎝
⎠
b0 =
a0
b1 =

− 2 cos(2π f 0 /f S )a0⎛sin (2π f 0 /f S ) ⎞⎜⎜1 − A
⎟⎟
2Q
⎝
⎠
b2 =
a0
a1 =

(3)

− 2 cos(2π f 0 /f S )a0⎛ sin (2π f 0 /f S ) ⎞
⎜⎜1 −
⎟⎟
2QA
⎝
⎠
a2 =
a0
where f0 is set to the centre frequency of each of the
31 filter bands according to ISO and IEC [16,17].
These standards do not explicitly define the Q, insteada magnitude response tolerance is given to allow for
design differences between manufacturers. For thisstudy Q = 4.33,

Q=

f0
10 n
= n + 0.05
= 4.33B 10− 10 n − 0.05

(4)where n is a value that gives the third-octave band
centre frequency, e.g. n = 3 for 1 kHz, and B is the
bandwidth of the third-octave resonance.
As is common practice in most commercially available hardware, the gain G is bound between 0 and –12
dB. Note that contrary to most hardware solutions, nopositive gain is allowed and there is no overall makeup gain to compensate for broadband attenuation. Engineers commonly use this technique to avoid overloading the loudspeaker.

(1)
3. OPTIMISATION OF THE EQUALISATION

where the scaling of the transfer function is given by
the coefficients,

a0 = 1 +with the centre frequency f0, sampling frequency fS,
gain of the resonance A, calculated from the dB-gain
value G, and the resonance goodness Q. The filter coefficients are then defined as,(2)

3.1. Room Response Control Optimiser
The five-stage algorithm previously described in[12,14] to find optimal settings for room responsecontrol exploits the heuristics of experienced systemcalibration engineers, thereby achieving computational efficiency by avoiding unrealistic filter setting
combinations. A fast optimisation time is alsoachieved by breaking down the process into stages.

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GOLDBERG AND MÄKIVIRTA

OPTIMISED EQUALISATION COMPARISON

3.2. Graphic Equaliser OptimiserWith Q and centre frequency f0 fixed for each thirdoctave band, the remaining variable available for adjustment is the gain G. This is bound between 0 and –12 dB. A least squares method, Matlab’s“lsqnonlin” function [18], minimises the objectivefunction,f2

min E =m∫f = f1am ( f ) x( f )x0 ( f )

2

df

(5)

where x(f) is the third-octave smoothed [19] magnitude of the loudspeaker in-situ frequency response,am(f) is the graphic equaliser magnitude response, x0(f)is the target response and frequencies f1 and f2 define
the optimisation band, i.e. –3 dB lower cut-off frequency for the loudspeaker in question and the highfrequency limit for the optimisation at 15 kHz.
The optimised filter values are rounded after optimisation 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 statisticalanalysis.
Visual inspection of the optimised responses showsthat the algorithm is robust to finding the global minimum.
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 depending on the loudspeaker model, whereas the graphicalequaliser optimisation algorithm takes 30–60 s, i.e.
10…20 times longer. The longer run time is explainedby the higher degrees of freedom in a graphical equaliser. The large optimisation time variation is due todiffering in-situ responses causing variations in the
run time because the optimisation continues until therequired 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 wascalculated. The optimal room response control settings
were calculated for each loudspeaker response. Statistical data was recorded for each magnitude response
measurement before and after equalisation to study

how the objective quality was improved. Further statistical analysis is conducted on all measurements inthree frequency bands (Table 1) “LF”, “MF” and“HF”, collectively called “subbands” and corresponding roughly to the bandwidths for each driver in athree-way system.
Table 1. Frequency band definitions the statistical data
analysis: fLF is the frequency of the lower –3 dB limitof the frequency range.
Bandwidth Name
Broadband
LF
MF
HF

Frequency Range Limit
Low
High
fLF
15 kHzfLF
400 Hz400 Hz3.5 kHz
3.5 kHz
15 kHzFor each loudspeaker, the broadband median pressure
is calculated. Pressure deviations from this median arerecorded within each subband and for the broadband.
These deviations are then used to describe the properties and extent of deviations from a flat response. Medians calculated for subbands, defined above, are recorded. The differences from the broadband median tosubband medians are calculated and then used as anindicator for broadband balance of the frequency response. Both statistical descriptors are recorded before
and after equalisation for each frequency band andeach equalisation method.
The quartile difference and RMS deviation are calculated for the four loudspeaker categories determinedby 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 effects.
4.2. Data Analysis Case Study
Figure 5 in Appendix C shows the third-octavesmoothed and unsmoothed in-situ response of a large
soffit mounted system [5]. The measurement technique 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 tothe 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

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GOLDBERG AND MÄKIVIRTA

indicated on the graphical output (Figure 2). The control settings and before and after equalisation responses are shown. The treble tilt, midrange level andbass tilt controls have been set. The equalisation corrects the low frequency alignment and improves thelinearity across the whole passband.
Figure 3 in Appendix A 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
three types of plot display outliers and percentiles in
the magnitude value distribution (box plot), the histogram of values, with a 1 dB resolution, and the fit of
the magnitude values to a normal distribution. Theseplots show that the distribution in the magnitude data
has been reduced. This is illustrated by the reduced
range in the box plot and the value histogram and asteeper curve in the normal probability plot. The fit toa normal distribution is shown but not discussed further. The time taken for the optimisation was 2.43 s.
4.2.2. Graphic Equalisation
Appendix C shows the same case example as above,
but using a graphic equaliser with settings calculated
according the algorithm detailed in Section 3.2. The
settings are shown in Table 2 and plotted in Figure 6.
The effect on the in-situ response can be seen in
Figure 7. Most of the equalisation takes place below
100Hz but some minor adjustment in the in-situ response is also made in the midrange to compensate forresonances due to room modes or constructive interference due to reflections. An improved linearity
across the whole passband is seen and, in particular,
the low frequency alignment has become better. The
statistical analysis shown in Figure 8 demonstrates
that the magnitude distribution has been reduced. Thisis illustrated by the reduced range in the box plot andthe value histogram, and the steeper curve in the normal probability plot. The time taken for the optimisation was 29.66 s.
4.2.3. Equalisation Comparison
Comparing the two equalisation techniques, the box
plot, histogram and steeper line in the normal probability plot all indicate that the distribution of the data
is smaller when graphic equalisation is used. The
room response controls do achieve a good broadband
balance (Figure 2) but the finer detail is not corrected.
In addition to an improved broadband balance,graphic equalisation is able to correct for local features in the response (Figure 7) but only with limited
success. Resonances due to room modes or constructive interference due to reflections in the response
cannot be corrected accurately when the frequencies

OPTIMISED EQUALISATION COMPARISON

do not coincide with the centre frequencies of thirdoctave filter bands. A good example of this can beseen at 600 Hz.
In the room response control equalisation, bass boost
caused by soffit mounting the loudspeaker is correctedusing a single bass tilt filter control set to –8 dB.
Graphic equalisation requires seven filters for this although better low frequency linearity is seen. It isclear that accurately setting a combination of seven
filters is not a trivial task, especially if time is at a premium.
The distribution of the room response control equalisation’s magnitude response (Figure 3) differs fromthe graphic equalisation’s magnitude response (Figure8). In the latter, there is a skew towards negative values as only negative gain can be applied to the response. In other words, the upward deviations (resonances or constructive interference) are equalised andthe downward deviations (antiresonances or destructive interference) are not.
The graphic equaliser optimisation took 12.2 times
longer than that for the room response equalisation
optimisation.
5. RESULTS
A total of 67 loudspeakers were measured before andafter equalisation. Of these, 12 were small two-way
systems, 22 were two-way systems, 30 were threeway systems and three were large systems.
5.1. Room Response Control Equalisation
The detailed results of a statistical analysis for the individual loudspeakers were discussed in detail in [13].
The subband median levels (Figure 1) illustrate thebroadband frequency balance between the subbands.
Loudspeaker loading from nearby boundaries is reflected in the LF subband median level before equalisation, especially in the often flush-mounted threeway and large models. Cancellations from nearby
boundaries are reflected in the low median value ofthe LF subband of the small two-way and two-way
systems.
High median levels in the LF subband are reduced after equalisation, which indicates that equalisationcompensates well for the loudspeaker loading, however cancellations cannot be equalised. Improvementsin the flatness across subbands of the average subband
median level demonstrates that equalisation can improve the broadband flatness. The largest improvement is seen in the three-way and large systems. The
broadband flatness improvement is mainly the resultof better alignment of the LF subband with the MF
and HF subbands, and a reduction of variation in the

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GOLDBERG AND MÄKIVIRTA

OPTIMISED EQUALISATION COMPARISON

trated. Across all models, the broadband flatness is
improved by 1.4 dB and the mean reduction in the LF
subband RMS deviation is 2.0 dB.
The average time taken for room response control
optimisation is 1.83 s ± 0.68 s. The best case is 1.12 s
and the worst case is 2.97 s.

LF subband as indicated by the smaller errors bars.
For all loudspeakers pooled together (Figure 1), theequalisation reduces the variance in the median level
for the LF subband. In Figure 4, Appendix B, the results are pooled for all products and for each producttype. The change in quartile difference and RMS deviation for the broadband and the subbands is illus-

Median Levels in Subbands - All Systems
8
6
4
2
0
-2

LF

-4

MF

HF

LF

Original

MF

HF

LF

Room Reponse Controls

MF

HF

Graphic Equaliser-6Median Levels in Subbands - Small Two-way Systems

Median Levels in Subbands - Two-way Systems

8

8

6

6

4

4

2

2

0
-2

0
LF

MF

HF

Original

-4

LF

MF

HF

LF

Room Reponse Controls

MF

HF

Graphic Equaliser

-6

-2

LF

MF

-4

MF

HF

LF

MF

HF

Graphic Equaliser

Median Levels in Subbands - Large Systems

8

8

6

6

4

4

2

2

0

-4

LF

Room Reponse Controls-6Median Levels in Subbands - Three-way Systems-2

HF

Original

0
LF

MF

HF

Original

LF

MF

HF

Room Reponse Controls

LF

MF

HF

Graphic Equaliser

-6

-2
-4

LF

MF

HF

Original

LF

MF

HF

Room Reponse Controls

LF

MF

HF

Graphic Equaliser-6

Figure 1. Mean and standard deviation of subband median levels before and after room response control and graphic
equalisation.
5.2. Graphic Equalisation
Appendix D (Figures 9-13) depicts the use of theequaliser controls for each loudspeaker group. The
upper graph (a) shows how the graphic equaliser isused including the use of 0 dB settings. The lower
graph (b) shows how it is used excluding the use of 0
dB settings and therefore demonstrates how much EQ
is required when it is used. Values for the 16 kHz and
20 kHz bands can be ignored as they are outside theoptimisation frequency range in all cases.
The small two-way models (Figure 9) show a generaltrend of bass reduction, –3 to –5 dB, but with some
additional large midrange adjustments and small highfrequency balancing. The standard deviations arelarge, indicating that there is little consistency in therequired equalisation across loudspeakers.
The two-way models (Figure 10) show a general trendof bass reduction, –2 to –4 dB, slightly less midrange
reduction, –1 to –2 dB, adjustment and small high frequency shelving too. Equalisation is required in lower
frequency bands as these systems have a deeper bass
extension. The standard deviations are small indicating that there is more consistency in the required
equalisation across loudspeakers. In general, lessequalisation is required than for the small two-way
systems.

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GOLDBERG AND MÄKIVIRTA

Similar trends are seen for the three-way systems(Figure 11) except that the bass reduction averages –3
to –5 dB and some additional roll-off shape is seen at
the very lowest frequencies of the loudspeakers.
As there were only three large system responses(Figure 12), all taken from same room, the standard
deviations indicate the equalisation consistency.
Across all of the loudspeakers (Figure 13), the generaltrend is a need for approximately 3 dB to 4 dB of bassattenuation, 2 dB from 200 Hz to 500 Hz and only 1
dB above 500 Hz. A 0 to –12 dB gain range is sufficient. Across the whole study, only one of the thirdoctave bands inside the optimisation frequency range
was set to the maximum attenuation, –12 dB.
The subband median levels (Figure 1) demonstratethat a high median level in the LF subband is reducedby the equalisation. This indicates that equalisationcompensates for acoustical loading of the loudspeaker.
The better match across subbands of the average subband median level demonstrates that equalisation has
improved the broadband flatness, and the largest improvement is seen in the three-way and large systems.
The broadband flatness improvement is mainly the
result of better alignment of the LF subband with the
MF and HF subbands. The equalisation has reduced
the variation between subbands and also improved thebroadband flatness of the acoustical response. For all
loudspeakers pooled together, the equalisation reduces
the variance in the median level for the LF subband.
In Figure 14, Appendix E, the results are pooled forall products and for each product type. The change inquartile difference and RMS deviation for the broadband and the subbands is illustrated. For all models,
the broadband flatness is improved by 4.3 dB and themean reduction in the LF subband RMS deviation improvement is 5.9 dB. The graphic equaliser is able tocompensate, to some extent, the severe anomalies attributable to extremely bad room acoustic conditions
seen within some of the pre-equalisation responses.
The average time taken for graphic equalisation
optimisation is 31.40 s ± 16.64 s. The best case is
14.61 s and the worst case is 116.29 s.
5.3. Equalisation Comparison
Appendix F, Figure 15, represents the difference between the change in sound level deviation due to theroom response controls and the graphic equalisation
techniques. For each subband, quartile difference and
RMS deviation from the median are plotted. A value
below 0 dB indicates that graphic equalisationachieves a response closer to the target. For all loudspeaker models pooled together, the room responsecontrols improved the RMS deviation from 6.1 dB to
4.7 dB (improvement 22%), whereas graphic equalisa-

OPTIMISED EQUALISATION COMPARISON

tion improved the RMS deviation to 1.8 dB (improvement 70%). The main improvement is seen at
low frequencies. The better performance by thegraphic equaliser is achieved by using between five(large loudspeakers) and ten times (small two-ways)
more equalisation stages and far longer optimisation
times.
The additional time it takes to perform the graphic
equalisation optimisation compared to room response
equalisation optimisation is 18.54 ± 8.49 times longer.
The best case is 8.35 times longer and the worst caseis 47.97 times longer.
6. DISCUSSION
The room response controls in active loudspeakers
implement discrete filter parameter values rather thana continuous parameter value range. A 31-bandgraphic equaliser typically allows for control of thegain in each of the third-octave centred bands over arange of ±12 dB and an overall make-up gain over thesame range. In this study the gains were constrained toa range of 0 to –12 dB and a least squares optimisation algorithm designed for selecting the optimal settings.
The statistical analysis of 67 in-situ loudspeaker responses shows that both equalisation methods achievea smaller RMS deviation from the target response.
The improvement is limited by the equalisers’ inability to correct for narrow-band deviations in a magnitude response. There is little improvement in the quartile differences and RMS deviations in the MF and HF
subbands. This is because room related response
variations are too narrow band to be corrected by athird-octave graphic equaliser or the room responsecontrol equaliser. The largest improvement is seen in
the three-way and large systems. This suggests that
better room acoustics, leading to a reduced loudspeaker-room interaction, allows the equalisation
methods to operate more effectively.
The room response controls in the active loudspeakers
achieve a good broadband balance but the fine detailis not corrected. Correcting fine detail may not bevery significant because human hearing is more sensitive at detecting wideband imbalances than narrow
band deviations in the magnitude response [21, 22].
In an acoustically good room, the room response controls built into an active loudspeaker allow for good
control of the broadband balance. A good example ofthis can be seen in averaged median values of thelarge systems (Figure 1) where the three responses
show good balancing and relatively little variance.
Even the three-way systems show a balancing within a
1.5dB window with relatively low variance. This is

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GOLDBERG AND MÄKIVIRTA

also the probable cause for improving performance
towards larger systems (Figures 4 and 14) shown by asimilar trend across both equalisation methods. This
underlines the importance of primarily solving acoustical problems by treating the room before trying touse equalisers.
Graphic equalisation can yield a somewhat flatter response, but multiple filter bands may be required tocorrect for large features in the response. Some upward deviations in the response, due to resonances orconstructive interference, cannot be corrected accurately when they do not coincide with the graphicalequaliser’s centre frequencies. This complexity ofgraphical equalisers makes manual gain setting complex and therefore more prone to operator error. Whenusing computerised optimisation, the time to calculate
a graphical equaliser’s settings was 8-48 times longer
than the time to select the best room response control
settings.
Graphic equalisation achieves LF subband results
closer to the target. Both equalisation techniquesachieved a similar improvement in the broadband balance, which has previously been shown to determine a
subjective lack of colouration in sound systems.
7. CONCLUSIONSThe objective of this paper is to compare the performance of the industry standard 31-band graphic equaliser to the room response controls built into active
loudspeakers. Both equalisation techniques achieved asimilar improvement in the broadband balance, whichhas previously been shown to determine a subjective
lack of colouration in sound systems. For all loudspeaker models pooled together, the room responsecontrols improved the RMS deviation from 6.1 dB to
4.7 dB (improvement 22%), whereas graphic equalisation improved the RMS deviation to 1.8 dB (improvement 70%). The graphical equaliser achieves
this improvement by using between eight (large loudspeakers) and ten times (small two-ways) more equalisation stages, 8-48 times the optimisation time andconsiderable increases in the financial cost.
8. ACKNOWLEDGEMENTS
The authors would like to thank Louis Fielder for thequestion in a recent AES Conference in Denmark
sparking this paper’s content, Mr. Steve Fisher (SCV
London) for the original inspirational idea for the
optimiser and some of the measurements used in thestatistical analysis, Mr. Olli Salmensaari (Finnish
Broadcasting Corporation) for additional measurements, Mr. Lars Morset (Morset Sound Development)
and Genelec Oy.

OPTIMISED EQUALISATION COMPARISON

9. REFERENCES[1] Boner C. P. and Boner C. R., “Minimising
Feedback in Sound Systems and Room Ring Modeswith Passive Networks,” J. Acoust. Soc. America, vol.
37, pp. 131-135 (1965 Jan).
[2] Greiner R. A. and Schoessow M., “Design Aspects of Graphic Equalisers,” J. Audio Eng. Soc., vol.
31, pp. 394-407 (1983 Jun).
[3] Bohn D. A., “Constant-Q Graphic Equalisers,”
J. Audio Eng. Soc., vol. 34, pp. 611-626 (1986 Sep).
[4] Bohn D. A., “Operator Adjustable Equalisers:
An Overview,” Proc. 6th Int. Conf., paper 6-025 (1988
Apr).
[5] Martikainen I., Varla A. and Partanen T., “Design of a High Power Active Control Room Monitor”,
86th Conv. Audio Eng. Soc., preprint 2755, (1989Mar).
[6] 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).
[7] Genereux R., “Signal Processing Considerations for Acoustic Environment Correction,” Proc. UK
Conf. 1992, paper DSP-14 (1992 Sep).
[8] Holman T., “New Factors in Sound for Cinema
and Television,” J. Audio Eng. Soc., vol. 39, pp. 529539 (1991 Jul/Aug).
[9] Schulein R. B., “In-Situ Measurement andEqualisation of Sound Reproduction Systems,” J. Audio Eng. Soc., vol. 23, pp. 178-186 (1975 Apr).
[10] Staffeldt H. and Rasmussen E., “The Subjectively Perceived Frequency Response in a Small andMedium Sized Rooms,” SMPTE J., vol. 91, pp. 638643 (1982 Jul).
[11] Genelec Oy, http://www.genelec.com (2004
Feb).
[12] Goldberg A. P., Mäkivirta A., “Automated InSitu Frequency Response Optimisation of Active
Loudspeakers,” presented in 114th Conv. Audio Eng.
Soc., preprint 5730 (2003 March).
[13] 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., (2003May).
[14] 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, (2004 Jan).
[15] Bristow-Johnson, R., “Cookbook formulae foraudio
EQ
biquadfiltercoefficients”,
www.harmonycentral.com / Computer / Programming/

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OPTIMISED EQUALISATION COMPARISON

Audio-EQ-Cookbook.txt, "Peaking EQ (parametric
EQ block)” (2004 Feb).
[16] ISO 266:1997 “Acoustics – Preferred Frequencies, 2nd Ed”, International Standards Organisation,
Geneva (1997).
[17] IEC 1260: 1995-07: “Electroacoustics - Octave-band and fractional-octave-band filters, 1st Ed”,
International Electrotechnical Commission, Geneva(1995).
[18] The MathWorks, “MATLAB Optimisation
Toolbox (v.2.3)”, The MathWorks Inc., Natick,(2003).
[19] Moore B. C. J., Glasberg B. R., Plack C. J. andBiswas A. K., “The shape of the Ear’s Temporal Window,” J. Acoustical Soc. America, vol. 83, pp. 11021116 (1988 Mar).
[20] Klark Technik, http://www.klarkteknik.com,(2004 Feb).
[21] Toole F. E., Olive S. E., “The Modification of
Timbre by Resonances: Perception and Measurement”, J. Audio Eng. Soc., vol. 36, pp. 122-141 (1988Mar.).
[22] Olive S. E., Schuck P. L., Ryan J. G, Sally S.
L., Bonneville M. E., “The Detection Thresholds ofResonances at Low Frequencies”, J. Audio Eng. Soc.,
vol. 45, pp. 116-127 (1997 Mar.).

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OPTIMISED EQUALISATION COMPARISONAPPENDIX A – ROOM RESPONSE CONTROL CASE STUDY, STATISTICAL GRAPHS

Figure 2. Case study optimisation results using room response control equalisation.

Figure 3. Case study statistical output – box plot, histogram and normal probability plot before (upper) and after(lower) optimised room response control equalisation.

AES 116TH CONVENTION, BERLIN, GERMANY, 2004 MAY 8-11

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GOLDBERG AND MÄKIVIRTA

OPTIMISED EQUALISATION COMPARISONAPPENDIX B – MODEL GROUPED ROOM RESPONSE CONTROL EQUALISATION SUMMARY

25% to 75% Percentile Difference Change
due to Room Response Control Equalisation
5

Broad
LF
MF
HF

0

-5

-10

ALL

Small

Two-way

Three-way

Large

-15

RMS Deviation Change
due to Room Response Control Equalisation
5

Broad
LF
MF
HF

0

-5

-10

ALL

Small

Two-way

Three-way

Large

-15

Figure 4. Change in sound level deviation due to Room Response Control equalisation for each subband and thebroadband, quartile difference and RMS of deviation from the broadband median. The error bar indicates the standard deviation.

AES 116TH CONVENTION, BERLIN, GERMANY, 2004 MAY 8-11

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GOLDBERG AND MÄKIVIRTA

OPTIMISED EQUALISATION COMPARISONAPPENDIX C – GRAPHIC EQUALISER CASE STUDY, STATISTICAL GRAPHS
Magnitude Frequency Response - Finland, Gen Auditorium, 1036A, Left
25

Pres. [Pa] / [volts], dB

20
15
10
5
0
-5
-10

10

100

1,000

10,000Frequency [Hz]Figure 5. Unequalised in-situ acoustic measurement with smoothed and unsmoothed data.
Table 2. Graphic equaliser settings.
CentreFrequency,
Hz
20
25
32
40
50
63
80
100
125
160

CentreFrequency,
Hz
200
250
315
400
500
630
800
1,000
1,250
1,600

Gain, dB
-1.6
-6.6
-7.7
-1.4
-2.1
-8.2
-3.3
0.0
0.0
-0.9

CentreFrequency,
Hz
2,000
2,500
3,150
4,000
5,000
6,300
8,000
10,00012,50016,000Gain, dB
-0.7
0.0
0.0
0.0
-0.2
-1.3
0.0
0.0
0.0
0.0

CentreFrequency,
Hz
20,000Gain, dB
0.0
-0.1
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0

Gain, dB
0.0

Use of Graphic Equaliser - 1036AL

20k

16k

12.5k

10k

8k

6.3k

5k

4k

3.2k

2.5k

2k

1.6k

1.25k

1k

800

630

500

400

315

250

200

160

125

100

80

63

50

40

32

1/3 Octave Frequency Band, Hz
25

20

Level, dB

3
2
1
0
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
-11
-12

Figure 6. Graphic equaliser settings.

AES 116TH CONVENTION, BERLIN, GERMANY, 2004 MAY 8-11

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GOLDBERG AND MÄKIVIRTA

OPTIMISED EQUALISATION COMPARISON

Figure 7. Case study optimisation results using graphical equalisation.

Figure 8. Case study statistical output – box plot, histogram and normal probability plot before (upper) and after(lower) optimised graphical equalisation.

AES 116TH CONVENTION, BERLIN, GERMANY, 2004 MAY 8-11

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GOLDBERG AND MÄKIVIRTA

OPTIMISED EQUALISATION COMPARISONAPPENDIX D – GRAPHIC EQUALISER STATISTICAL GRAPHS

Use of Graphic Equaliser - Small models(incl. 0dB settings)

20k

16k

12.5k

10k

8k

6.3k

4k

3.2k

2.5k

2k

1.6k

1.25k

1k

800

630

500

400

315

250

200

160

125

100

80

63

50

40

32

25

20

5k

1/3 Octave Frequency Band, Hz

Level, dB

3
2
1
0
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
-11
-12

Figure 9a. Use of the graphic equaliser for small 2-way systems – including 0dB settings.

Use of Graphic Equaliser - Small models(excl. 0dB settings)

20k

16k

12.5k

10k

8k

6.3k

4k

3.2k

2.5k

2k

1.6k

1.25k

1k

800

630

500

400

315

250

200

160

125

100

80

63

50

40

32

25

20

5k

1/3 Octave Frequency Band, Hz

Level, dB

3
2
1
0
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
-11
-12
-13
-14
-15

Figure 9b. Use of the graphic equaliser for small 2-way systems – excluding 0dB settings.

AES 116TH CONVENTION, BERLIN, GERMANY, 2004 MAY 8-11

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OPTIMISED EQUALISATION COMPARISON

20k

16k

12.5k

10k

8k

6.3k

4k

3.2k

2.5k

1/3 Octave Frequency Band, Hz
2k

1.6k

1.25k

1k

800

630

500

400

315

250

160

125

100

80

63

50

40

32

25

20

200

Use of Graphic Equaliser - 2-way models(incl. 0dB settings)

Level, dB

5k

GOLDBERG AND MÄKIVIRTA

3
2
1
0
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
-11
-12

Figure 10a. Use of the graphic equaliser for 2-way systems – including 0dB settings.

20k

16k

12.5k

10k

8k

6.3k

5k

4k

3.2k

2.5k

1/3 Octave Frequency Band, Hz

2k

1.6k

1.25k

1k

800

630

500

400

315

250

160

125

100

80

63

50

40

32

25

20

200

Use of Graphic Equaliser - 2-way models(excl. 0dB settings)

Level, dB

3
2
1
0
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
-11
-12
-13
-14
-15

Figure 10b. Use of the graphic equaliser for 2-way systems – excluding 0dB settings.

AES 116TH CONVENTION, BERLIN, GERMANY, 2004 MAY 8-11

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OPTIMISED EQUALISATION COMPARISON

20k

16k

12.5k

10k

8k

6.3k

4k

3.2k

2.5k

1/3 Octave Frequency Band, Hz
2k

1.6k

1.25k

1k

800

630

500

400

315

250

160

125

100

80

63

50

40

32

25

20

200

Use of Graphic Equaliser - 3-way models(incl. 0dB settings)

Level, dB

5k

GOLDBERG AND MÄKIVIRTA

3
2
1
0
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
-11
-12

Figure 11a. Use of the graphic equaliser for 3-way systems – including 0dB settings.

20k

16k

12.5k

10k

8k

6.3k

5k

4k

3.2k

2.5k

1/3 Octave Frequency Band, Hz

2k

1.6k

1.25k

1k

800

630

500

400

315

250

160

125

100

80

63

50

40

32

25

20

200

Use of Graphic Equaliser - 3-way models(excl. 0dB settings)

Level, dB

3
2
1
0
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
-11
-12
-13
-14
-15

Figure 11b. Use of the graphic equaliser for 3-way systems – excluding 0dB settings.

AES 116TH CONVENTION, BERLIN, GERMANY, 2004 MAY 8-11

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GOLDBERG AND MÄKIVIRTA

OPTIMISED EQUALISATION COMPARISON

Use of Graphic Equaliser - Large models(incl. 0dB settings)

20k

16k

12.5k

10k

8k

6.3k

4k

3.2k

2.5k

2k

1.6k

1.25k

1k

800

630

500

400

315

250

200

160

125

100

80

63

50

40

32

25

20

5k

1/3 Octave Frequency Band, Hz

Level, dB

3
2
1
0
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
-11
-12

Figure 12a. Use of the graphic equaliser for large systems – including 0dB settings.

Use of Graphic Equaliser - Large Models(excl. 0dB settings)

20k

16k

12.5k

10k

8k

6.3k

4k

3.2k

2.5k

2k

1.6k

1.25k

1k

800

630

500

400

315

250

200

160

125

100

80

63

50

40

32

25

20

5k

1/3 Octave Frequency Band, Hz

Level, dB

3
2
1
0
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
-11
-12
-13
-14
-15

Figure 12b. Use of the graphic equaliser for large systems – excluding 0dB settings.

AES 116TH CONVENTION, BERLIN, GERMANY, 2004 MAY 8-11

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GOLDBERG AND MÄKIVIRTA

OPTIMISED EQUALISATION COMPARISON

Use of Graphic Equaliser - All Models(incl. 0dB settings)

20k

16k

12.5k

10k

8k

6.3k

4k

3.2k

2.5k

2k

1.6k

1.25k

1k

800

630

500

400

315

250

200

160

125

100

80

63

50

40

32

25

20

5k

1/3 Octave Frequency Band, Hz

Level, dB

3
2
1
0
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
-11
-12

Figure 13a. Use of the graphic equaliser for all systems – including 0dB settings.

Use of Graphic Equaliser - All Models(excl. 0dB settings)

20k

16k

12.5k

10k

8k

6.3k

4k

3.2k

2.5k

2k

1.6k

1.25k

1k

800

630

500

400

315

250

200

160

125

100

80

63

50

40

32

25

20

5k

1/3 Octave Frequency Band, Hz

Level, dB

3
2
1
0
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
-11
-12
-13
-14
-15

Figure 13b. Use of the graphic equaliser for all systems – excluding 0dB settings.

AES 116TH CONVENTION, BERLIN, GERMANY, 2004 MAY 8-11

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GOLDBERG AND MÄKIVIRTA

OPTIMISED EQUALISATION COMPARISONAPPENDIX E – MODEL GROUPED GRAPHIC EQUALISATION SUMMARY

25% to 75% Percentile Difference Change
due to Graphic Equalisation
5

Broad
LF
MF
HF

0

-5

-10

ALL

Small

Two-way

Three-way

Large

-15

RMS Deviation Change
due to Graphic Equalisation
5

Broad
LF
MF
HF

0

-5

-10

ALL

Small

Two-way

Three-way

Large

-15

Figure 14. Change in sound level deviation due to graphic equalisation for each subband and the broadband, quartile
difference and RMS of deviation from the broadband median. The error bar indicates the standard deviation.

AES 116TH CONVENTION, BERLIN, GERMANY, 2004 MAY 8-11

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GOLDBERG AND MÄKIVIRTA

OPTIMISED EQUALISATION COMPARISONAPPENDIX F – COMPARISON OF EQUALISATION TECHNIQUES SUMMARY GRAPHS

25% to 75% Percentile Difference Change
between Equalisations
5

Broad
LF
MF
HF

0

-5

-10

ALL

Small

Two-way

Three-way

Large

-15

Broad

RMS Deviation Change
between Equalisations

LF

5

MF
HF

0

-5

-10

ALL

Small

Two-way

Three-way

Large

-15

Figure 15. The difference between the change in sound level deviation for the room response control and thegraphic equalisation techniques for each subband and the broadband, quartile difference and RMS of deviation fromthe broadband median are plotted. A value below 0dB indicates that graphic equalisation achieves a response closer
to the target.

AES 116TH CONVENTION, BERLIN, GERMANY, 2004 MAY 8-11

19