29th  TONMEISTERTAGUNG  –  VDT  INTERNATIONAL  CONVENTION,  November  2016  Stability of the Frequency Response Estimate in Listening Rooms
A. Mäkivirta1, T. Lund1
1

Genelec Oy, Iisalmi, Finland. Email: thomas.lund@genelec.com

Abstract
In-room estimates of loudspeaker responses for professional use are typically taken either at one
microphone location, replacing the listener with a microphone, or averaging in space, at multiple locations atand relatively close to the listening location. In this work, a number of listening rooms were measured using 18
precisely defined locations. In-space averaging in combination with frequency domain averaging can increase thestability of the frequency response estimate. However, the spatial averaging points used in taking a measurement
should be chosen based on the room acoustics and on the application. Spatial averaging across a wide area may comewith the risk of compromising the result at the main listening position.

1.   Introduction

1.1.  Target curve

Professional loudspeakers intended for critical monitoring ofaudio are positioned and equalised to reduce the acousticalinfluence of the listening space [3] as room effects tend to
reduce the accuracy of monitoring even in high quality
professional listening rooms having controlled acoustic
characteristics [1].

While there is a consensus that a neutral loudspeaker has aflat anechoic frequency response, several researchers havebeen commenting on the suitability of an allpass target for
the in-room frequency response. Some researchers suggest adown sloping character across the full or at least a part of theaudio 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 of confusion’. Thisrefers a self-referenced system where existing recordings areused to evaluate the room sound [10, 13].

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]. Adjustablefilters make room equalization much easier and have been
widely available already in the vacuum tube era (see forexample [15]). More versatile parametric equalizer filters
were introduced by several inventors in the early 1970s [14,16] and finally digital signal processing has made bothmeasurements and room equalization easy and precise while
alleviating the signal quality concerns that were earlier
associated with equalization.
Because the requirement in professional monitoring is tohear the audio recording content in a neutral way, without
adding or removing anything, the setup ideally approximatesan allpass system within the audible frequency range,
jω
(1)

H (e

) =1

This implies a system with a flat frequency response andpossibly causing a delay to the audio signal. International
recommendations consequently call for the room response of
the monitoring system to be flat at the listening location andthe reverberation time in the listening space to be the samefor all frequencies. As the loudspeaker is a 3D radiator andthe listening room is a 3D medium for audio, there is also
consideration about the way the loudspeaker radiates atdifferent frequencies. Because of this, there is also arequirement for directivity characteristics in therecommendations [1].
With loudness-based production spreading globally, thespectral response of the monitoring system and its level
calibration has become a cornerstone of recommendations
for broadcast and streaming [11, 12].

The present work concentrates on enabling reliablemeasurement of the in-room frequency response at thelistening 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 variationsin 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
reduced by time domain windowing the impulse response
estimate and by applying in-frequency smoothing with asliding variable-width averaging window to the frequency
response. These techniques are usually able to sufficiently
reduce acoustic comb filtering and tend to reduce spatial
locality of a measurement, thereby rendering the measurement usable for the practical purposes of evaluating roominduced sound colorations.
Spatial averaging is used in the context of cinema dubbing
stage and cinema theatre equalization with even spatialsampling of the frequency response across the floor area
intended for listeners [2]. Increasing the number ofmicrophone positions can provide a more complete pictureof room acoustics. Such measurements estimate the power
output of the loudspeaker in the room and using that forsystem equalization particularly at low frequencies [4].

29th  TONMEISTERTAGUNG  –  VDT  INTERNATIONAL  CONVENTION,  November  2016  1.3.  Scope of the work
Instead of sampling the acoustic field in the whole space, thepresent work aims to help minimize reliably a local effect,
the room influence at one listening position. Spatialsampling of the room response in the vicinity of thislistening location is one potential method of improving thereliability of the measurement of the acoustic response
audible to the listener.
The purpose of this work is to study the sufficiency of thesingle microphone position acquisition of the acousticalresponse 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 thepotentially local acoustic effects that may occur if only one
microphone position is used.
The present study is conducted predominantly in the context
of professional reproduction spaces. Therefore we haveselected rooms with acceptably low reverberation time andlevel of the early reflections at the listening position.

room

vol.

base

RT60

TER

LER

(m3)

width

(s)

(ms)

(dB)

(m)

L

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

Table 1. Listening rooms used in the study. Reverberation time
(RT60), highest early reflection level (LER) and the associatedearly reflection delay (TER) at the listening location for left (L) andright (R) loudspeakers.

The present work does not address the topic of how themeasurement will be used for room equalization or what thesuitable equalization target should be.

2.   Materials and methods
2.1.  Room selection criteria
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 location in Denmark or
Finland, low background noise, acceptable reverberation
time, and reasonably low level and acceptable direction ofearly reflections at the listening position.
All twelve rooms appointed for the study are reported,meaning that once a room had been selected, it was not
excluded post-measurement. They key parameters of therooms are summarized in Table 1.

2.2.  Microphone grid
Locality of the frequency response is studied by using one
main microphone position and 17 offset microphone
positions (in total 18 microphone positions) located atincreasing 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 the back, see Figure 1.
The microphone position layout was chosen to reflect the
typical professional critical listening application where theengineer is located at a defined position, typically seated at
the console or audio workstation.

Fig 1. The full measurement grid. The main listening position (red)is one point of an equilateral triangle with the loudspeakers. Offset
mic positions 0.1, 0.25 and 0.5 m plus 1.0 or 1.5 m to the back.
Details in figure 2, sharing the same colour coding.

29th  TONMEISTERTAGUNG  –  VDT  INTERNATIONAL  CONVENTION,  November  2016  The measurements are taken at a fixed microphone height
set to be the same as the listener’s ear height. The
microphone positioning accuracy is ensured by using a matwith the positions marked and a pointer on the microphone
giving a positioning accuracy better than 2 mm for thedefined measurement positions and between rooms in
relation to the stereo pair. The loudspeakers were set up in astandard stereo pair configuration relative to the main
microphone position (or ‘listening position’ or ‘C’).
The measurement setup in the room is generally arranged on
the left-right centre axis so that the room has the best
possible left-right symmetry acoustically relative to themeasurement setup and the loudspeaker locations. The
listening direction frequently corresponds with the longest
dimension of the listening room.

2.3.  Loudspeakers and microphone

The impulse responses are processed to generate threedifferent 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 the microphone responses at 0.1 m distanceoffset, (3) main response averaged with the responses at 0.25
m offset, and (4) main response averaged with the responses
at 0.5 m offset.
The 1.0 and 1.5 m mic positions offset back from the main
microphone position are used for reference to see how muchthe response will change in the front-to-back direction.
The spatial average is compared to the single microphone
position measurement statistically. The mean difference
between the main position measurement and the spatial
average, abbreviated MSAD, as well as the difference histogram, is calculated for each of the spatial average cases A-C.

The loudspeakers used were mainly a two-way design with a
5 in woofer, 2/3 in tweeter and linearized phase response(type Genelec 8330 or similar).
The measurement microphone has an electret capsule withomnidirectional characteristics and has been calibrated tohave a flat response when it is pointing upwards, resulting invery similar frequency response for all source directions on
the same horizontal plane at a given height relative to themicrophone. The effect of the height related response
variation in the microphone is small and not significant forthe 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 foreach of the microphone locations.
Both the left and right loudspeakers in the stereo pair aremeasured, generating two sets of 18 measurements for eachroom. In total, 432 measurements in 24 series are taken in
the study.
The magnitude response measurements are smoothed infrequency using the industry standard 1/3 octave smoothing
window and 1/12 octave smoothing window.

Fig 2. Definitions of the spatial average cases A to C. Main mic
position is red. Spatial averaging areas (other colours) incl. numberof measurement positions used.

Before averaging, differences in the measurement point
distances are removed by level normalization. Monitor
loudspeakers are essentially point source radiators, with thecharacteristic inverse square law reduction of the sound levelwith increasing distance to the monitor. The various
measurement positions in the study cause differences in the
distance which translate to level differences.

Each spatial average response is calculated using the 1/3
octave and 1/12 octave smoothed data. All measurements
receive the same weight. The weight received by anindividual measurement depends on the number of measurements included in the spatial average.

The level normalization removes the effect of geometricdistance variation. Without level normalization, individual
measurements being averaged receive a weight related theirdistance. This is not desirable as we want each measurement
to have equal weight. Measurements are therefore normalized in level using the mean response level across the 500
Hz to 5 kHz.

Cumulative histograms of the differences between the main
position measurement and the spatial averages are calculated
for all rooms and measurements. The cumulative histogramis calculated using a 0.1 dB bin size.

29th  TONMEISTERTAGUNG  –  VDT  INTERNATIONAL  CONVENTION,  November  2016  3.   Results
3.1.  Effect of measurement point distance
The spatial averaging is an additional averaging process on
top of the normally applied smoothing in frequency.
Both frequency smoothing and spatial averaging have theeffect of reducing the extreme differences in measurements,
particularly narrow band differences. The room acoustic
influences to the loudspeaker frequency response are thestrongest at low frequencies. This is where the largest
differences are seen between a single position measurementsmoothed in frequency and a spatial average calculated using
several such smoothed measurements taken at and near thelistening position. The largest differences are seen at the
rapid turns in the frequency response, typically close tonotches that remain 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 of
the microphone. The other spatial averaging cases (0.25 and
0.5 m offsets) have microphone positions on the line at thesingle microphone position or towards the back of the room.
The spatial average with 0.1 m displacement exhibits thesmallest difference to the single point measurement, anddifferences increase with the increasing spatial average
displacement.

3.2.  Case example: MSAD
Each microphone position represents a full acoustic
measurement. To keep the paper length manageable, typicalsingle room data is provided only, see Figure 4. The full data
set for all the rooms is summarized later.
The single position measurement and the 0.1 m off-position
spatial average show the best agreement (area A). When thespatial average distance increases to 0.25 and to 0.5 meters(areas B and C) more differences are seen towards low
frequency.

roughly model locations of the left and right ears for the casewhere the main microphone position C is located at thegeometrical centre of where the listener’s head would be.
The level difference graphs L-C and R-C in the caseexample (Figure 3) display the typical level differences weobserved, showing symmetrical but opposite L/R
excursions around the 0 dB level below 500 Hz.

3.3.  Case example: cumulative histograms
A cumulative histogram is calculated for three frequency
bands (30-100 Hz, 100-1000 Hz and 1-10 kHz) as this better
illustrates how differences between the single position
measurement and the spatial average are rather frequency
dependent, see Figure 5. Above 1 kHz agreement between
the single point measurement and the spatial average is
generally good for all the off-position displacements tested.
The spatial average systematically deviates from the single
position measurement for all cases of the spatial average.
The spatial average shows a slightly smaller SPL than the
single position measurement. This seems to be related to thefact that spatial average attenuates the visibility of local
acoustic effects (gain maxima and minima) more than asingle point measurement after smoothing in frequency.
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 thesmoothing in frequency alone. In principle, a similar effectcould be achieved by using a slightly wider smoothing-infrequency range. For the example Room A, this effect of"additional smoothing" is not large, about 0.5 dB in the SPL
estimation. The other room measurements do notsignificantly deviate from this behaviour when the room
reverberation is modest.
Data is also divided into IEC octave bands (IEC61260:2014)
and the mean difference statistic is calculated for eachoctave band for the left and right monitors separately (roomA results, see Figure 6), for all monitors in the study.
The differences in the higher frequency octave bands up
from 1 kHz are negligible except in the highest octave where
the aiming of the monitor in combination with its increasing
directivity will affect the results. Larger differences are seen
for frequencies where the room exerts large acoustic
influences, typically below 1 kHz.

3.4.  Results of pooled dataFig 3. Example of results. Room A, left. Difference of the soundpressure at position L to the Main position (dashed black) andposition R to the Main position (solid red), 100 Hz to 10 kHz. 1/3
octave smoothing has been applied.

In addition to the MSAD, responses at single microphone
positions L and R (see Figure 2) were compared to the main
microphone position C. Microphone locations L and R

The data of all the twelve rooms, considering left and rightspeakers, is pooled in the octave bands, see one example in
Figure 6.
Comparing to the single point measurement, the octave bandmean difference increases with increasing displacement
distance of the additional microphone positions used for the
spatial averaging.

29th  TONMEISTERTAGUNG  –  VDT  INTERNATIONAL  CONVENTION,  November  2016  Fig 4. Example of results. Room A, left. Spatial means area A, B, C vs the response at the main position, "pos(7)". MSAD is shown with 0
dB on the blue line. 1/3 octave smoothing (upper), 1/12 octave smoothing (lower).

Fig 5. Example of results. Room A left. Cumulative distribution of the difference of the A, B, C average and the single position SPL. The
cumulative distributions are presented in three different frequency bands (30-100 Hz, 100-1000 Hz and 1-10 kHz). 1/3 octave smoothing(upper), 1/12 octave smoothing (lower).

Fig 6. Example of results. Room A left. The mean difference in IEC octave bands between the spatial average SPL and the single position
SPL. 1/3 octave smoothing (left), 1/12 octave smoothing (right).

29th  TONMEISTERTAGUNG  –  VDT  INTERNATIONAL  CONVENTION,  November  2016  The largest differences between the single point octave meanlevels 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 seen in the cumulative
histograms of the difference data (Figure 4). The cumulative
histograms are asymmetrical. This is related to the inherently
different influence of acoustic summation and cancellationin 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.
spatial average offset

This effect can also be seen in the Case A room sample
response plots (Figure 3). In our material the reverberation
time appears to have a stronger effect on this than the spatial
average displacement distance. This trend is mainly createdby low frequency room effects. If only octave bands at andabove 500 Hz are considered the trend disappears (Figure 8).

Fig 8. Mean level difference in octave bands 500 Hz and above,
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 thefrequencies 0.4-4 kHz.

0.1 m

0.25 m

0.5 m

mean

0,074

0,190

0,327

std

0,67

0,89

1,02

min

-3,50

-2,65

-3,00

4.   Discussion

max

4,30

3,30

4,80

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

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

spatial average offset
0.1 m

0.25 m

0.5 m

mean

0,0

0,016

0,011

std

0,16

0,27

0,24

min

-0,45

-0,80

-0,35

max

0,40

0,60

0,70

Table 3. Pooled octave band statistics across all rooms for theoctave bands 500 Hz and higher.

There is a slight trend where increasing displacement as wellas 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 to suppress extremes in the frequency response morethan applying just the in-frequency smoothing alone.

Fig 7. Mean level difference in octave bands, averaged across theaudio 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.

Spatial averaging is sometimes assumed to produce a better
representation of room acoustics than single point
measurements, and thereby be more useful as a reliable
starting point for system equalization. However, nosignificant difference was found between the single point
measurement and the spatial average for small spatial
average displacement measurements taken in professional
listening rooms.
The spatially averaged responses do not deviate significantly
from the single point measurement at the listening position,
for small spatial averaging displacements (± 0.1 m),
including the specific L and R locations at "ear distance"
relative to the main position. The symmetrical L/R
differences observed below 500 Hz point to the main
position as the generally benign common denominator forthe purposes of frequency response calibration in thelistening room.
The spatial averages show less difference relative to thelistening position compared to the individual off-position
measurements. Partially, this may be related to the fact thatin this work the measurement positions are symmetricallylocated relative to the single listening position used as thereference.
The spatial averaging was done using in-frequency
smoothed measurements. Not smoothing before the spatial
averaging does not change the outcome of the calculation as29th  TONMEISTERTAGUNG  –  VDT  INTERNATIONAL  CONVENTION,  November  2016  both are linear operations, and spatial averaging can be done
prior to applying smoothing in frequency.
Large differences between the single point measurement andthe spatial average are connected to strong modal resonancesin the room. As pronounced modal resonances are related tosmall acoustic attenuation in the room, it is likely that highreverberation time can predict larger difference between the
one point measurement and a spatial average.

5.   Conclusion
Loudness-based production in broadcast and post relies on
accurate monitoring for judging balance, spectrum, speech
intelligibility, and audio quality.
Loudness is a perceptual property of an audio signal when it
is reproduced acoustically and listened to. It is a complex,
nonlinear function of amplitude, frequency, and time.
Because of this complex nonlinear nature of perception, acontrolled in-room spectral response is therefore thefoundation of any meaningful level calibration, which is therequirement in all global and regional loudness standards.
ATSC A/85 devotes a comprehensive chapter to calibrated
monitoring, and to dismantling the ‘circle of confusion’described in section 1.1.
The use of single point equalization is confirmed [3] as asafe choice for measurement of studio monitoring rooms
having relatively low reverberation times and well controlled
room modes. The use of spatial average is not likely tosignificantly change or improve the outcome of equalizationin that case.
However, in rooms with pronounced modal resonance a
spatial average already with a displacement as small as 0.1
m can be useful in avoiding very local phenomena and maylead to more reliable reproduction system equalization.
Spatial averaging across a wide area may come with the riskof compromising the result at the main listening position.
The spatial averaging positions should therefore be chosen
based on the intention of the room equalization and theacoustic quality of the room.

6.   References[1]  International Telecommunication Union
Recommendation ITU-R BS.1116-3, (2015).

(ITU):[2]  Cengarle G. & Mateos, T: Effect of Microphone
Number and Positioning on the Average ofFrequency Responses in Cinema Calibration, J.
Audio Eng. Soc., vol. 63, no. 10 (2015).

[3]  Mäkivirta, A. & Anet C.: The Quality of Professional
Surround Audio Reproduction: A Survey Study, 9thInt. AES Conference: Surround Sound - Techniques,Technology, and Perception (2001).

[4]  Pedersen, J.A.: Loudspeaker-Room Adaptation for a
specific Listening Position using Information about
the Complete Sound Field, AES 121st Convention(2006).

[5]  Olive, S.E. et al.: The Subjective and Objective
Evaluation of Room Correction Products, AES 127th
Convention (2009).

[6]  Pedersen, J.A. et al.: Natural Timbre in RoomCorrection Systems, 122nd AES Convention,(2007).Pedersen, J.A. & El-Azm, F.: Natural Timbre
in Room Correction Systems (Part II), 32nd
International
AES
Conference:
DSP
For
Loudspeakers (September 2007).

[7]  Pedersen, J.A. & El-Azm, F.: Natural Timbre in
Room Correction Systems (Part II), 32nd
International
AES
Conference:
DSP
For
Loudspeakers (September 2007).

[8]  Toole, F.E.: Loudspeaker Measurements and Their
Relationship to Listener Preferences: Part 1, J. Audio
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[9]  Toole, F.E.: Loudspeaker Measurements and Their
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[10]   Toole, F.E.: Sound Reproduction, Focal Press (2008).
[11]   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) .
[13]   Toole, F.E.: The Measurement and Calibration ofSound Reproduction Systems, J. Audio Eng. Soc.,
Vol. 63, No. 7/8, pp. 512-541 (2015).
[14]   Flickinger, D.: Amplifier system utilizing regerativeand degenerative feedback to shape the frequency
response, US Patent 3752928 (1973).
[15]   Villard, J.R.: Adjustable frequency
apparatus, US Patent 2672529 (1954).

selective[16]   Massenburg, G.: Parametric Equalization, AES 42th
Convention (1972).
[17]   Tremaine, H.: Audio Cyclopedia, 2nd. ed., H.W.
Sams, Indianapolis, (1973).