Genelec response controls User Manual

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 graph ic equaliser is set to minimise the least squares deviation from linear
within the passband in a smoothed acoustical response. The resulting equalisation perfor mance 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 co louration 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 the
perceived quality of sound reproduction in a listening
environment. Electronic equalisation to improve the
subjective sound quality has been widespread for at
least 40 years (an early example is [1]). Equalisation is
prevalent in professional sound repro duction such as
recording studios, mixing rooms and sound rein­forcement. In-situ response equalisation is often im­plemented using third-octave equalisers, which are
normally set with the help of real time analysers. This
measurement and equalisation combination is cheap,
readily available and a relatively simple concept to
grasp with a little training [2-4]. Room response cor ­recting equalisers are now also increasingly b uilt 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 of
substantially 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 can
become very position sensitive [6,7]. Even with these
limitations, in-situ equalisers have the potential to sig­nificantly improve perceived sound quality. The prac­tical challenge is to find the best compromise for the
parameters in the in-situ equaliser. An acceptable
equalisation is typically a compromise to minimise the
subjective coloration in the audio due to room effects.
Despite advances in psychoacoustics, it is difficult to
quantify what the listener actually perceives the sound
quality to be [8-10], or to optimise equalisation based
on that evaluation. Because of this, in-situ equalisation
typically attempts to obtain the best fit to some objec-

GOLDBERG AND MÄKIVIRTA OPTIMISED EQUALISATION COMPARISON

AES 116TH CONVENTION, BERLIN, GERMANY, 2004 MAY 8-11 2

tively measurable target known to relate to the percep­tion of sound as being free from coloration, such as a
flat third-octave smoothed magnitude response.

The purpose of this paper is to investigate how the
standard 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 a
graphical 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 a
graphical equaliser compared to some three to five
separate settings with two to seven discrete values in
the room response equaliser. This would appear to
suggest 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 the
higher degrees of freedom alone could be taken as an
indication of how much better or worse one method is
compared to another.

This paper presents a performance comparison of a
room 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 flat
in-room magnitude response. To make possible this
comparison, an optimisation algorithm was developed
to set the gains of a 31-band graphical equaliser. This
method is described. The performance of the equalisa­tions and optimisation algorithms is investigated by
studying the statistical properties of 67 in-situ magni­tude responses before and after equalisation.

2. IN-SITU EQUALISATION

The room response controls were previously described
in [12-14]. A constant-Q type 31-band DSP graphic
equaliser [15] was constructed using bi-quadratic
transfer functions of the form,

2

2

1

1

2

2

1

10

1

)(

−−

−−

++

++

=

zaza

zbzbb

zH

(1)

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

()

20

0

0

10

2

2sin

1

G

S

A

QA

/ff

a=+=

π

(2)

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,

(

)

()

()

()

()

0

0

2

0

0

1

0

0

2

0

0

1

0

0

0

2

2sin

1

2cos2

2

2sin

1

2cos2

2

2sin

1

a

QA

/ff

a

a

/ff

a

a

Q

/ff

A

b

a

/ff

b

a

Q

/ff

A

b

S

S

S

S

S

⎟

⎟
⎠

⎞

⎜

⎜
⎝

⎛

−

=

−

=

⎟

⎟
⎠

⎞

⎜

⎜
⎝

⎛

−

=

−

=

⎟

⎟
⎠

⎞

⎜

⎜
⎝

⎛

+

=

π

π

π

π

π

(3)

where f

0

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, instead
a magnitude response tolerance is given to allow for
design differences between manufacturers. For this
study Q = 4.33,

33.4

1010

10

05.005.0

0

=

−

==

−+ nn

n

B

f

Q

(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, no
positive 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.

3. OPTIMISATION OF THE EQUALISATION

3.1. Room Response Control Optimiser

The five-stage algorithm previously described in
[12,14] to find optimal settings for room response
control exploits the heuristics of experienced system
calibration engineers, thereby achieving computa­tional efficiency by avoiding unrealistic filter setting
combinations. A fast optimisation time is also
achieved by breaking down the process into stages.

GOLDBERG AND MÄKIVIRTA OPTIMISED EQUALISATION COMPARISON

AES 116TH CONVENTION, BERLIN, GERMANY, 2004 MAY 8-11 3

3.2. Graphic Equaliser Optimiser

With Q and centre frequency f

0

fixed for each 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 objective
function,

df

fx

fxfa

E

f

ff

m

m

2

0

2

1

)(

)()(

min

∫

=

=

(5)

where x(f) is the third-octave smoothed [19] magni­tude of the loudspeaker in-situ frequency response,

a

m

(f) is the graphic equaliser magnitude response, x0(f)

is the target response and frequencies f

1

and f2 define
the optimisation band, i.e. –3 dB lower cut-off fre­quency for the loudspeaker in qu estion and the high
frequency 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 statistical
analysis.

Visual inspection of the optimised responses shows
that 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 graphical
equaliser optimisation algorithm takes 30–60 s, i.e.
10…20 times longer. The longer run time is explained
by the higher degrees of freedom in a graphical equal­iser. The large optimisation time variation is due to
differing in-situ responses causing variations in the
run time because the optimisation continues until the
required fitting tolerance is achieved.

4. METHODS

4.1. Statistical Data Analysis

To assess the performance of the combination of
optimisation algorithm and equalisation in the
loudspeakers, the analysis compares the unequalised
in-situ magnitude response to the equalised response.

The third-octave smoothed magnitude response was
calculated. The optimal room response control settings
were calculated for each loudspeaker response. 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 in
three frequency bands (Table 1) “LF”, “MF” and
“HF”, collectively called “subbands” and correspond-
ing roughly to the bandwidths for each driver in a
three-way system.

Table 1. Frequency band definitions the statistical data
analysis: f

LF

is the frequency of the lower –3 dB limit

of the frequency range.

Frequency Range Limit
Bandwidth Name Low High
Broadband fLF 15 kHz
LF fLF 400 Hz
MF 400 Hz 3.5 kHz
HF 3.5 kHz 15 kHz

For each loudspeaker, the broadband median pressure
is calculated. Pressure deviations from this median are
recorded within each subband an d 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 broadb and median to
subband medians are calculated and then used as an
indicator for broadband balance of the frequency re­sponse. Both statistical descriptors are recorded before
and after equalisation for each frequency band and
each equalisation method.

The quartile difference and RMS deviation are calcu­lated for the four loudspeaker categories determined
by the type of built-in room response controls in the
loudspeakers. Both the quartile difference and RMS
deviation values represent two slightly different ways
to look at the deviation from the median value of the
distribution. The quartile values are more robust to
outlier values while the RMS values include these ef­fects.

4.2. Data Analysis Case Study

Figure 5 in Appendix C shows the third-octave
smoothed and unsmoothed in-situ response of a large
soffit mounted system [5]. The measurement 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 to
the optimisation algorithm [12-14]. The equalisation
target is a flat magnitude response, i.e. a straight line
at 0 dB level. The loudspeaker’s passband (triangles)
and the frequency band of equalisation (crosses) are

GOLDBERG AND MÄKIVIRTA OPTIMISED EQUALISATION COMPARISON

AES 116TH CONVENTION, BERLIN, GERMANY, 2004 MAY 8-11 4

indicated on the graphical output (Figure 2). The con­trol settings and before and after equalisation re­sponses are shown. The treble tilt, midrange level and
bass tilt controls have been set. The equalisation cor ­rects the low frequency alignment and improves the
linearity 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. These
plots 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 a
steeper curve in the normal probability plot. The fit to
a 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 Figu re 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 for
resonances 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. This
is illustrated by the reduced range in the box plot and
the 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

do not coincide with the centre frequencies of third­octave filter bands. A good example of this can be
seen at 600 Hz.

In the room response control equalisation , bass boost
caused by soffit mounting the loudspeaker is corrected
using 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 is
clear 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 contro l equali­sation’s magnitude response (Figure 3) differs from
the graphic equalisation’s magnitude response (Figure

8). 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 and
the 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 and
after 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 the
broadband 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 of
the 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 equalisation
compensates well for the loudspeaker loading, how­ever cancellations cannot be equalised. Improvements
in the flatness across subbands of the average su bband
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 result
of better alignment of the LF subband with the MF
and HF subbands, and a reduction of variation in the

GOLDBERG AND MÄKIVIRTA OPTIMISED EQUALISATION COMPARISON

AES 116TH CONVENTION, BERLIN, GERMANY, 2004 MAY 8-11 5

LF subband as indicated by the smaller errors bars.
For all loudspeakers pooled together (Figure 1), the
equalisation 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 product
type. The change in quartile difference and RMS de­viation for the broadband and the subbands is illus-

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.

Median Levels in Subbands - Small Two-way Systems

-6

-4

-2

0

2

4

6

8

LF MF HF LF MF HF LF MF HF

Original Room Reponse Controls Graphic Equaliser

Median Levels in Subbands - Three-way Systems

-6

-4

-2

0

2

4

6

8

LF MF HF LF MF HF LF MF HF

Original Room Reponse Controls Graphic Equaliser

Median Levels in Subbands - Two-way Systems

-6

-4

-2

0

2

4

6

8

LF MF HF LF MF HF LF MF HF

Original Room Reponse Controls Graphic Equaliser

Median Levels in Subbands - All Systems

-6

-4

-2

0

2

4

6

8

LF MF HF LF MF HF LF MF HF

Original Room Reponse Controls Graphic Equaliser

Median Levels in Subbands - Large Systems

-6

-4

-2

0

2

4

6

8

LF MF HF LF MF HF LF MF HF

Original Room Reponse Controls Graphic Equaliser

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 the
equaliser controls for each loudspeaker group. The
upper graph (a) shows how the graphic equaliser is
used 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 the
optimisation frequency range in all cases.

The small two-way models (Figure 9) show a general
trend of bass reduction, –3 to –5 dB, but with some
additional large midrange adjustments and small high

frequency balancing. The standard deviations are
large, indicating that there is little consistency in the
required equalisation across loudspeakers.

The two-way models (Figure 10) show a general trend
of 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, less
equalisation is required than for the small two-way
systems.

GOLDBERG AND MÄKIVIRTA OPTIMISED EQUALISATION COMPARISON

AES 116TH CONVENTION, BERLIN, GERMANY, 2004 MAY 8-11 6

Similar trends are seen for the three-way systems
(Figure 11) except that the bass reduction av erages –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 general
trend is a need for approximately 3 dB to 4 dB of bass
attenuation, 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) demonstrate
that a high median level in the LF subband is reduced
by the equalisation. This indicates that equalisation
compensates 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 the
broadband 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 for
all products and for each product type. The change in
quartile 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 the
mean reduction in the LF subband RMS deviation im­provement is 5.9 dB. The graphic equaliser is able to
compensate, 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 the
room 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 equalisation
achieves a response closer to the target. For all loud­speaker models pooled together, the room response
controls improved the RMS deviation from 6.1 dB to

4.7 dB (improvement 22%), whereas graphic equalisa-

tion improved the RMS deviation to 1.8 dB (im­provement 70%). The main improvement is seen at
low frequencies. The better performance by the
graphic 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 graph ic
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 case
is 47.97 times longer.

6. DISCUSSION

The room response controls in active loudspeakers
implement discrete filter parameter values rather than
a continuous parameter value range. A 31-band
graphic equaliser typically allows for control of the
gain in each of the third-octave centred bands over a
range of ±12 dB and an overall make-up gain over the
same range. In this study the gains were constrained to
a 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 achieve
a 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 a
third-octave graphic equaliser or the room response
control 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 detail
is not corrected. Correcting fine detail may not be
very 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 of
this can be seen in averaged median values of the
large 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