Audio Engineering Society

Convention Paper
Presented at the 141st Convention
2016 September 29–October 2 Los Angeles, USA
This paper is peer-reviewed as a complete manuscript for presentation at this Convention. This paper is available in the AES
E-Library, http://www.aes.org/e-lib. All rights reserved. Reproduction of this paper, or any portion thereof, is not permitted
without direct permission from the Journal of the Audio Engineering Society.

Spatial stability of the frequency response estimate
and the benefit of spatial averaging
Aki Mäkivirta1 and Thomas Lund1
1

Genelec Oy, Iisalmi, Finland

Correspondence should be addressed to Thomas Lund (thomas.lund@genelec.com)

ABSTRACTIn-room estimates of loudspeaker responses at the listening location are typically taken either at one microphone
location, replacing the listener with a microphone, or averaging in space, at multiple microphone locations at andrelatively close to the listening location. In-frequency averaging can attenuate the locality of the frequency
response features in mid and high frequencies. In-space averaging extracts the common frequency responsefeatures visible in all the measurement positions. Spatial weighting combined with frequency domain averaging
can increase the stability of the frequency response estimate for the features relevant for the subjective
compensation of the sound color at the listening location. Spacing out the spatial average measurement points
affects the nature of the spatial average and the focus on the frequency response features common to themeasurement points. The spatial averaging points used in taking a measurement should be chosen based on theintention of the room equalization.

1 Introduction
Professional loudspeakers intended for critical monitoring of audio are positioned and equalised toreduce the acoustical influence of the listening space[3] as room effects tend to reduce the accuracy ofmonitoring even in high quality professional listening rooms having controlled acoustic characteristics[1].
H. Tremaine’s Audio Cyclopedia claims that RCA’s
John Volkman was the first to use electronic filters
for room response equalization already in the 1920s[17]. Adjustable filters make room equalizationmuch easier and have been widely available alreadyin the vacuum tube era (see for example [15]). Moreversatile parametric equalizer filters were introduced
by several inventors in the early 1970s [14],[16] andfinally digital signal processing has made both measurements and room equalization easy and precise

while alleviating the signal quality concerns thatwere earlier associated with equalization.
Because the requirement in professional monitoringis to hear the audio recording content in a neutral
way, without adding or removing anything, ideallythe listening setup approximates an allpass system inthe frequencies audible to a human,H ( e j )  1 .

(1)This implies a system with a flat frequency response
and possibly causing a delay to the audio signal.
International recommendations consequently call forthe room response of the monitoring system to beflat at the listening location and the reverberation
time in the listening space to be the same for all
frequencies. As the loudspeaker is a 3D radiator andthe listening room is a 3D medium for audio, there isalso consideration about the way the loudspeakerMäkivirta and Lund

Spatial stability of the frequency responseradiates at different frequencies. Because of this,
there is also a requirement for the directivity characteristic in recommendations [1].
With loudness-based production spreading globally,
the spectral response of the monitoring system andits level calibration has become a cornerstone ofrecommendations for broadcast and streaming[11],[12].
1.1 Target curve
While there is a consensus that a neutral loudspeakerhas a flat anechoic frequency response, several
researchers have been commenting on the suitabilityof the allpass target for the in-room frequency response. Some researchers suggest a down sloping
character across the full or at least a part of the audio
band. This seems to be largely motivated by listenerpreference [4],[5],[6],[7],[8],[9] while little attention
has been paid to solving the problem of the ‘circle ofconfusion’. This refers a self-referenced system
where existing recordings are used to evaluate theroom sound [10],[13] .
The present work concentrates on enabling reliablemeasurement of the in-room frequency response at
the listening location, but not on the preferred in-situ
response, which we regarded a separate issue.
1.2 One or more measurement locations
The sound pressure measurable in a room at a single
microphone location is relatively local, and large
variations in the pressure can be seen when the
microphone location is moved. This is particularly
evident at high frequencies where large and very
local comb filtering effects can happen because of
acoustic reflections. That effect is usually reducedby time domain windowing the impulse response
estimate and by applying in-frequency smoothingwith a sliding variable-width averaging window to
the frequency response. These techniques are usuallyable to sufficiently reduce acoustic comb filteringand tend to reduce spatial locality of a measurement,
thereby rendering the measurement usable for thepractical purposes of evaluating room-induced soundcolorations.
Spatial averaging is used in the context of cinema
dubbing stage and cinema theatre equalization witheven spatial sampling of the frequency response

across the floor area intended for listeners [2].
Increasing the number of microphone positions canprovide a more complete picture of room acoustics.
Such measurements estimate the power output of theloudspeaker in the room and using that for system
equalization particularly at low frequencies [4].
1.3 Aims of the work
Instead of sampling the acoustic field in the whole
space, the present work aims to help minimize reliably a local effect, the room influence at one listening position. Spatial sampling of the room responsein the vicinity of this listening location is one
potential method of improving the reliability of themeasurement of the acoustic response audible to thelistener.
The purpose of this work is to study the sufficiencyof the single microphone position acquisition of theacoustical response at the listening position.
The working hypotheses are that (1) spatial averaging is able to extract the common acoustic features
and therefore enables focusing of the system
equalization to these essential features, and (2) spatial average will be able to prevent the potentiallylocal acoustic effects that may occur if only one
microphone position is used.
The present study is conducted predominantly in thecontext of professional reproduction spaces. Therefore we have selected rooms with acceptably low
reverberation time and level of the early reflections
at the listening position.
The present work does not address the topic of how
the measurement will be used for room equalizationor what the suitable equalization target should be.

2 Material and methods
2.1 Criteria for selecting rooms
A variety of listening rooms were included in the
study. The rooms are or have been in use for stereo
mixing or editing.
Most rooms lack refined acoustic design or extensive acoustic treatment. Room selection criteria also
included repeated availability, geographical locationin Denmark or Finland, low background noise,
acceptable reverberation time, and reasonably low

AES 141st Convention, Los Angeles, USA, 2016 September 29–October 2
Page 2 of 10

Mäkivirta and Lund

Spatial stability of the frequency response

level and acceptable direction of early reflections at
the listening position.
All twelve rooms appointed for the study arereported, meaning that once a room had been
selected, it was not excluded post-measurement.
They key parameters of the rooms are summarizedin Table 1.
room

vol.
(m3)

base
width
(m)

RT60
(s)

TER
(ms)
L

The microphone positioning accuracy is ensured byusing a mat with the positions marked and a pointeron the microphone giving a positioning accuracy
better than 2 mm for the defined measurement positions and between rooms in relation to the stereo
pair. The loudspeakers were set up in a standard
stereo pair configuration relative to the main
microphone position (later ‘listening position’).

LER
(dB)
R

L

R

A

29.6

1.30

0.49

8.9

2.7

-11.9

-11.8

B

115.1

1.30

0.66

1.5

1.7

-10.5

-10.3

C

39.5

1.17

0.43

8.6

8.7

-10.8

-14.0

D

39.5

1.32

0.46

2.4

2.5

-13.5

-13.2

E

39.5

1.20

0.44

3.3

3.3

-15.9

-16.7

F

16.6

1.15

0.31

0.85

0.85

-10.5

-11.8

G

97.6

2.27

0.19

5.6

5.7

-10.8

-11.7

H

22.6

0.86

0.50

4.0

3.7

-16.7

-17.7

I

18.2

1.01

0.56

5.9

7.5

-17.2

-12.2

J

69.4

1.30

0.55

4.6

11.0

-14.8

-20.9

K

80

1.31

0.48

4.1

4.2

-17.2

-16.7

L

90.5

1.31

0.48

4.6

6.2

-20.9

-20.0

Figure 1. The definitions of the spatial averaging
measurement positions; ’main position’ is thenominal listener/microphone position.

Table 1. Listening rooms used in the study.
Reverberation time (RT60), highest early reflectionlevel (LER) and the associated early reflection delay(TER) at the listening location for left (L) and right(R) loudspeakers.
2.2 Microphone grid
Locality of the frequency response is studied byusing one main microphone position and 17 offset
microphone positions (in total 18 microphone positions) located at increasing offsets from the main
listener/microphone location. The offset distances
are 0.1 meters to the front, 0.1, 0.25, and 0.5 meters
to the side and back, as well as 1.5 meters to theback, see Figure 1.
The microphone position layout was chosen toreflect the typical professional critical listening
application where the engineer is located at adefined position, typically seated at the console oraudio workstation.
The measurements are taken at fixed microphoneheight set to be the same as the listener’s ear height.

Figure 2. The principle of the loudspeaker layout
follows the standard stereo pair placement. The main
microphone position is marked.
The angle to the loudspeakers is 30 degrees relative
to the front-to-back direction in the room and the
distance between the loudspeakers is the same as the
distance from the loudspeaker fronts to the listening
position.

AES 141st Convention, Los Angeles, USA, 2016 September 29–October 2
Page 3 of 10

Mäkivirta and Lund

Spatial stability of the frequency response

The measurement setup in the room is generally
arranged on the left-right centre axis so that theroom has the best possible left-right symmetry
acoustically relative to the measurement setup andthe loudspeaker locations. The listening direction
frequently corresponds with the longest dimensionof the listening room.
2.3 Loudspeakers and microphone
The loudspeakers used were mainly a two-way
design with a 5 in woofer and 2/3 in tweeter (typeGenelec 8320 or similar).
The measurement microphone has an electret
capsule with omnidirectional characteristics and has
been calibrated to have a flat response when it ispointing upwards, resulting in very similarfrequency response for all source directions on thesame horizontal plane at a given height relative tothe microphone. The effect of the height related
response variation in the microphone is small andnot significant for the purposes of this study.
2.4 Processing of measurements
The impulse response data acquisition is done using
a log sine sweep with length 256 kilo-samples,
resulting in an impulse response with length 2.97 s
sampled at 44.1 kHz for each of the microphone
locations.
Both the left and right loudspeakers in the stereo pairare measured, generating two sets of 18 measurements for each room. In total, 432 measurements in
24 series are taken in the study.
The magnitude response measurements aresmoothed in frequency using the industry standard
1/3 octave smoothing window.
Before averaging, differences in the measurement
point distances are removed by level normalization.
Monitor loudspeakers are essentially point source
radiators, with the characteristic inverse square law
reduction of the sound level with increasing distanceto the monitor. The various measurement positionsin the study cause differences in the distance whichtranslate to level differences.

Case A

Case B

Case C
Figure 3. Definitions of the spatial average cases A
to C showing the spatial averaging areas (shaded)
and the numbers of measurement positions used(dark colour).

AES 141st Convention, Los Angeles, USA, 2016 September 29–October 2
Page 4 of 10

Mäkivirta and Lund

Spatial stability of the frequency response

The level normalization removes the effect ofgeometric distance variation. Without levelnormalization, individual measurements being averaged receive a weight related their distance. This is
not desirable as we want each measurement to haveequal weight. Measurements are therefore normalized in level using the mean response level acrossthe 500 Hz to 5 kHz.
The impulse responses are processed to generate
three different spatial averages in a manner that
could be expected for practical applications.
The cases include (1) the main microphone position
alone, (2) main position response averaged with themicrophone responses at 0.1 m distance offset, (3)main response averaged with the responses at 0.25 m
offset, and (4) main microphone response averaged
with the responses at 0.5 m offset.
The 1.5 m microphone position offset back from themain microphone position is used as the reference to
see how much the response will change in the frontto-back direction.
The spatial average is compared to the single microphone position measurement statistically. The meandifference between the main position measurement
and the spatial average, as well as the difference
histogram, is calculated for each of the spatial
average cases A-C.
Each spatial average response is calculated using the
1/3 octave smoothed data. All measurements receive
the same weight. The weight received by anindividual measurement depends on the number ofmeasurements included in the spatial average.
Cumulative histograms of the differences between
the main position measurement and the spatial
averages are calculated for all rooms and measurements. The cumulative histogram is calculated using
a 0.1 dB bin size.

3 Results
3.1 Effect of measurement point distance
The spatial averaging is an additional averaging
process on top of the normally applied smoothing infrequency.
Both frequency smoothing and spatial averaging
have the effect of reducing the extreme differencesin measurements, particularly narrow band differences. The room acoustic influences to the loudspeaker frequency response are the strongest at low
frequencies. This is where the largest differences areseen between a single position measurementsmoothed in frequency and a spatial average calculated using several such smoothed measurements
taken at and near the listening position. The largest
differences are seen at the rapid turns in thefrequency response, typically close to notches thatremain after the in-frequency smoothing.
The microphone positions at 0.1 m from the main
microphone position are a special case in the present
study because this set has microphone positions also
forward from the microphone. The other spatial
averaging cases (0.25 and 0.5 meter offsets) havemicrophone positions on the line at the single microphone position or towards the back of the room.
The spatial average with 0.1 m displacement exhibits the smallest difference to the single point
measurement and differences increase with theincreasing spatial average displacement.
3.2 Case example: differences
Each microphone position is a full acoustic measurement. To keep the paper length manageable full casedata is given only for the Room A. This example isshown in Figures 4-6. The full data set for all rooms
is summarized later.
The single position measurement and the 0.1 m offposition spatial average show the best agreement.
When the spatial average distance increases to 0.25
and to 0.5 meters more differences are seen towards
low frequencies.
3.3 Case example: cumulative histograms
A cumulative histogram is calculated for threefrequency bands (30-100 Hz, 100-1000 Hz and 1-10
kHz) as this better illustrates how differences
between the single position measurement and thespatial average are rather frequency dependent.
Above 1 kHz the agreement between the single point
measurement and the spatial average is generally
good for all the off-position displacements tested.

AES 141st Convention, Los Angeles, USA, 2016 September 29–October 2
Page 5 of 10

Mäkivirta and Lund

Spatial stability of the frequency response

Figure 4. Example of a results is Room A, left and right monitors, spatial means at 0.1, 0.25, and 0.5 m distancesfrom the nominal listening position, compared to the single response at the nominal listening position; difference
between the spatial mean and the single mic position is shown with zero shifted to the level 70 dB.

The spatial average systematically deviates from thesingle position measurement for all cases of thespatial average. The spatial average shows a slightly
smaller SPL than the single position measurement.
This seems to be related to the fact that spatial
average attenuates the visibility of local acoustic
effects (gain maxima and minima) more than asingle point measurement after smoothing infrequency. Smoothing in frequency is an averaging
operation that happens in the frequency domain.

Spatial averaging multiple such measurements effectively cascades two averaging operations, so we can
expect that the spatial average has a stronger
smoothing tendency than the smoothing infrequency alone. In principle, a similar effect could
be achieved by using a slightly wider smoothing-infrequency range.
For the example Room A, this effect of "additionalsmoothing" is not large, about 0.5 dB in the SPL
estimation. The other room measurements do not

AES 141st Convention, Los Angeles, USA, 2016 September 29–October 2
Page 6 of 10

Mäkivirta and Lund

Spatial stability of the frequency response

significantly deviate from this behaviour when theroom reverberation is modest.
Data is also divided into IEC octave bands(IEC61260:2014) and the mean difference statistic is

calculated for each octave band for the left and rightmonitors separately (for case room A results, see
Figure 6) for all monitors in the study.

Figure 5. Example of results is Room A, cumulative distribution of the difference of the spatial average SPL
from the single position SPL, left monitor (top) and right monitor (bottom); the cumulative distributions arepresented in three different frequency bands (30-100 Hz, 100-1000 Hz and 1-10 kHz).

AES 141st Convention, Los Angeles, USA, 2016 September 29–October 2
Page 7 of 10

Mäkivirta and Lund

Spatial stability of the frequency response

Figure 6. An example of results is Room A. The mean difference in IEC octave bands between the spatial
average SPL from the single position SPL, both after 1/3 octave smoothing in frequency, left monitor (left) andright monitor (right).

mean
std
min
max

spatial average offset
0.1 m
0.25 m
0.5 m
0,074
0,190
0,327
0,67
0,89
1,02
-3,50
-2,65
-3,00
4,30
3,30
4,80

Table 2. Pooled octave band statistics across all
rooms for the full audio bandwidth.

mean
std
min
max

spatial average offset
0.1 m
0.25 m
0.5 m
0,0
0,016
0,011
0,16
0,27
0,24
-0,45
-0,80
-0,35
0,40
0,60
0,70

Table 3. Pooled octave band statistics across all
rooms for the octave bands 500 Hz and higher.
The differences in the higher frequency octave bands
up from 1 kHz are negligible except in the highestoctave where the aiming of the monitor in combination with its increasing directivity will affect theresults.
Larger differences are seen for frequencies where
the room exerts large acoustic influences, typicallybelow 1 kHz.
3.4 Results of pooled data
The data of all the twelve rooms is pooled in theoctave bands.

Comparing to the single point measurement, theoctave band mean difference increases with increasing displacement distance of the additional microphone positions used for the spatial averaging.
The largest differences between the single point
octave mean levels and the spatial average octave
mean levels occur at low frequencies, in octave
bands with frequency lower than 500 Hz. The differences are small at 500 Hz and higher frequency
octave bands (tables 2 and 3).
Large differences (minima and maxima) are typically at very low frequencies. This can also be seenin the cumulative histograms of the difference data
(Figure 5).
The cumulative histograms are asymmetric. This isrelated to the inherently different influence of acoustic summation and cancellation in room acoustics.
This happens particularly when the modal resonances in the room are strong, resulting in larger
differences between the single point measurement
and a spatial average.
There is a slight trend where increasing displacement as well as increasing maximum room reverberation measured inside the octave bands 0.4-4 kHz
implies larger differences between the single point
measurement and the spatial average (Figure 7).
This is related to the nature of the spatial average tosuppress extremes in the frequency response morethan applying just the in-frequency smoothing alone.
This effect can also be seen in the Case A room sample response plots (Figure 4). In our material thereverberation time appears to have a stronger effecton this than the spatial average displacement

AES 141st Convention, Los Angeles, USA, 2016 September 29–October 2
Page 8 of 10

Mäkivirta and Lund

Spatial stability of the frequency response

distance. This trend is mainly created by low
frequency room effects. If only octave bands at andabove 500 Hz are considered the trend disappears(Figure 8).

Figure 7. Mean level difference in octave bands,
averaged across the audio band for the spatial offset
cases 0.1, 0.25 and 0.5 m. The reverberation time
RT60 is the maximum within the frequencies 0.4-4
kHz.

Figure 8. Mean level difference in octave bands 500
Hz and above, averaged across the audio band forthe spatial offset cases 0.1, 0.25 and 0.5 m. The
reverberation time RT60 is the maximum within thefrequencies 0.4-4 kHz.

4 Discussion
In-frequency averaging can effectively attenuate
local features at mid and high frequency. In-space
averaging can effectively extract the common frequency response features visible in all the measurement points. Spatial weighting of the average combined with frequency domain averaging of theresulting estimate can increase the stability of thefrequency response estimate for the features that are
relevant to subjective compensation of the soundcolour at the listening location.

Spatial averaging is assumed to produce a better
representation of room acoustics than single point
measurements, and thereby be more useful as areliable starting point for system equalization.
However, no significant difference was foundbetween the single point measurement and thespatial average for small spatial average displacement measurements taken in professional listening
rooms. The spatially averaged responses do notdeviate significantly from the single point measurement at the listening position for small spatial
averaging displacements (± 0.1 m).
The spatial averages show less difference relative tothe listening position compared to the individual offposition measurements. Partially, this may be related
to the fact that in this work the measurement
positions are symmetrically located relative to thesingle listening position used as the reference.
The spatial averaging was done using in-frequency
smoothed measurements. Not smoothing before thespatial averaging will not change the outcome of thecalculation as both are linear operations and spatial
averaging can be done prior to applying smoothingin frequency.
Large differences between the single point measurement and the spatial average are connected to strong
modal resonances in the room. As pronounced
modal resonances are related to small acoustic
attenuation in the room, it is likely that highreverberation time can predict larger difference
between the one point measurement and a spatial
average.
Loudness-based production in broadcast relies on
accurate monitoring for judging balance, formats,speech intelligibility, and audio quality. A controlled
in-room spectral response is the foundation of any
meaningful level calibration. The ATSC recommended practice A/85 consequently devotes anentire chapter to calibrated monitoring and to
dismantling the ‘circle of confusion’ described in
section 1.1. The use of single point equalization is asafe choice for measurement of studio monitoring
rooms having relatively low reverberation times andwell controlled room modes [3]. The use of spatial
average is not likely to significantly change or
improve the outcome of equalization in that case.
However, in rooms with pronounced modal
resonance a spatial average already with a displace-

AES 141st Convention, Los Angeles, USA, 2016 September 29–October 2
Page 9 of 10

Mäkivirta and Lund

Spatial stability of the frequency response

ment as small as 0.1 m can be useful in avoiding
very local phenomena and may lead to more reliablereproduction system equalization.
Spatial averaging across a wide area may come withthe risk of compromising the result at the main
listening position. The spatial averaging positions
should therefore be chosen based on the intention of
the room equalization.

32nd International AES Conference: DSP For
Loudspeakers (September 2007).
[8]

Toole Floyd, Loudspeaker Measurements andTheir Relationship to Listener Preferences:
Part 1, J. Audio Eng. Soc., vol. 34, 4 pp. 227235, (1986).

[9]

Toole Floyd, Loudspeaker Measurements andTheir Relationship to Listener Preferences:
Part 2, J. Audio Eng. Soc., vol. 34, 5 pp. 323348, (1988).

References[1]

International Telecommunication Union,
Recommendation ITU-R BS.1116-3, (2015).

[10]

[2]

Giulio Cengarle, Toni Mateos, Effect ofMicrophone Number and Positioning on the
Average of Frequency Responses in Cinema
Calibration, J. Audio Eng. Soc., vol. 63, no.
10 (2015).

Toole F.E. Sound Reproduction, Focal Press(2008).

[11]

Aki Mäkivirta and Christophe Anet, The
Quality of Professional Surround Audio
Reproduction: A Survey Study, 9th Int. AES
Conference: Surround Sound - Techniques,Technology, and Perception (2001).

Advanced Television System Committee(ATSC), ATSC Recommended Practice:Techniques for Establishing and Maintaining
Audio Loudness for Digital Television(A/85:2013), ATSC A/85

[12]European Broadcasting Union (EBU), R128
Loudness Normalisation And Permitted
Maximum Level Of Audio Signals, (2014) .

[3]

[4]

Jan Abildgaard Pedersen, Loudspeaker-RoomAdaptation for a specific Listening Position
using Information about the Complete Sound
Field, AES 121st Convention (2006).

[13]

Toole F.E. The Measurement and Calibrationof Sound Reproduction Systems, J. Audio
Eng. Soc., Vol. 63, No. 7/8, pp. 512-541(2015).

[5]

Sean E. Olive, John Jackson, Allan
Devantier, David Hunt and Sean M. Hess,The Subjective and Objective Evaluation of
Room Correction Products, AES 127th
Convention (2009).

[14]

Flickinger D. Amplifier system utilizing
regerative and degenerative feedback toshape the frequency response, US Patent
3752928 (1973).

[15]

[6]

Pedersen Jan A., Morten, Henrik A., Natural
Timbre in Room Correction Systems, 122nd
AES Convention, (2007).

Villard J.R. Adjustable frequency selective
apparatus, US Patent 2672529 (1954).

[16]

Massenburg G. Parametric Equalization,
AES 42th Convention (1972).

Pedersen Jan A., Fares El-Azm, Natural
Timbre in Room Correction Systems (Part II),

[17]

Tremaine H., Audio Cyclopedia, 2nd. ed.,
H.W. Sams, Indianapolis, (1973).

[7]

AES 141st Convention, Los Angeles, USA, 2016 September 29–October 2
Page 10 of 10