Quantification of Subwoofer Requirements,
Part I: Generation of Stimuli and Listening System Equalization
Jan Abildgaard
Pedersen(1) and Aki Mikivit-ta(1) Bang & Olufsen, Denmark(2) Genelec Oy, Finland5084 (C - 1)

(2)

Presented at
the 108th Convention
2000 February 19-22
Paris, France

AUDIO

-

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Review Board. The AES takes no responsibility for thecontents.
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Journal of the Audio Engineering Society.

AN AUDIOENGINEERING

SOCIETYPREPRINTQUANTIFICATIONPREPRINT 5084

PEDERSEN AND MAIVIRTA

Quantification
Generationof subwoofer

of stimuli

requirements,and listening

Jan Abildgaard

OF SUBWOOFER

part I:

system equalization

Pedersen

Research & Development, Bang & O lufsen, DK-7600, Struer, Denmark
Tel: +45 96 84 48 97, Fax: +45 97 84 12 50
E-mail: jgp@bang-olufsen.dk,
andAki M tikivirta
Genelec Oy, O lvitie 5, FIN-741 00 lisalmi, Finland
Tel: +358 17 813311, Fax: +358 17 812267
aki.makivirta@genelec.com,
E-mail:Abstract
Lower cut-off frequency & slope, amplitude ripple and group delay ripple
have been examined. Shape and magnitude of both amplitude and groupdelay ripple were calculated from room simulations. Listening tests are tobe performed using both loudspeakers in an anechoic chamber andheadphones, which were equalized in an attempt to obtain equal results.

0 Introduction
The aim of this work is to study the psychoacousticallydetermined performancerequirements for a subwoofer loudspeaker. The work is part of EUREKA Project
1653, which is referred to as “MEDUSA” (Multichannel Enhancement of Domestic
User Stereo Applications). The “MEDUSA” project is a 3.5 years joint research
project with the following partners: British Broadcasting Corporation, Institute ofSound Recording at University of Surrey, Nokia Research Centre, Genelec Oy and
Bang & O lufsen A/S.
This is part I in a series of papers, and this paper describes how DSP is used forgeneration of stimuli and equalization of the listening system. Part II in this series of
papers: “The influence of lower system cut-off frequency and slope, and pass-band
amplitude and group delay ripple” describes the actual listening experiments, i.e.
experimental strategy, procedure and results [l].
The increasing use of digital surround sound systems, like 5.1 systems, leads to anincreased attention of low frequency reproduction.
Considering
5.1 systems,
especially the “.l” channel and modern programme material, loudspeaker manufacturers has a desire to quantifying the requirements of subwoofers. It has been
assumed that Digital Signal Processing (DSP) is employed for all filtering and control

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tasks in the subwoofers considered.
applicability of the conclusions.

QUANTIFICATIONOF SUBWOOFERThis was decided to avoid limitations

on theEssential requirements of subwoofers are the lower cut-off frequency and slope,
because these are linked to maximum displacement, system tuning and power
requirements. In this context it is chosen to focus on two additional parameters:
amplitude ripple and group delay ripple, both in the pass band. Amplitude ripple sets
the requirement to how much the amplitude response is allowed to deviate from theideal response, which could be a flat response. Deviations could arise from variations in the parameters of the loudspeaker drive units, influence of the room etc.
Requirements regarding maximum group delay ripple imposes a limit on how rapid
the phase is allowed to change.
The experiments are divided into 2 separate groups of experiments: lower cut-off
frequency and slope in the first group and amplitude and group delay ripples in thesecond group. All the parameters in each group must be able to be varied independently, i.e. orthogonal variation of the parameters.

1 Generationof Stimuli

Stimuli for the tests are produced by different filtering of 7 selected programme
pieces. First the lower cut-off frequency and slope are changed and then both amplitude and group delay ripples in the pass band are added.
1 .I Programme material
Seven pieces of programme material is selected from a wide set of consideredmaterial. Two pieces are used during training of subjects, while 4 pieces are used in
the actual experiment. The last piece is used for calibration purposes only. The
spectral distribution, especially below 200 Hz, are of special interest when selecting
the 7 pieces of programme material. Figure 1 includes a table, which specifies theselected 7 pieces.
Total loudness at the listening position is used to calibrate the playback level of theexperiments. The calculation of total loudness requires a stationary signal, which is
chosen to be “Pink Noise”, as seen in figure 1. The reproduction level of “Pink Noise”
is adjusted from the loudness measurements, and the levels of the other 6 pieces
are individually adjusted relatively to “Pink Noise” based on calculations of the total
power contents of the 7 pieces. Equation 1 gives the relative gain of programme
piece “A” relative to “Pink Noise” and the total power content is given for each of the
7 pieces in figure 1. Since the power levels given in figure 1 are already expressed in
dB, the relative gain of any of the programme pieces can be found simply bysubtracting the power of the actual programme piece from the power of “Pink Noise”.

relativesain-of-A=

C Pink-Noise(c IA(n)?
i(1)Power spectra of all the programme pieces has been calculated using the full 1
minute of each programme piece. Figure 2 gives the power spectrum of the 2

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training pieces, i.e. the first 2 pieces in figure 1 and figure 3 gives the power
spectrum of the 4 pieces that is used in the actual experiment, i.e. the next 4 pieces
in figure 1. The original programme pieces are turned into “.WAV” files (Microsoft
Wave Files): 2 channels, 16 bits and 44100 Hz sampling frequency. All processing
on the programme pieces are performed in this format, i.e. the programme pieces
stays “.WAV” files right until conversion to analog signals.
1.2 Variable lower cut-off frequency and slope
The lower cut-off frequency is varied from 20 Hz to 50 Hz by prefiltering the
programme material using a digital high-pass filter with variable cut-off frequency.
The range from 20 Hz and 50 Hz are considered to be a typical range of lower
cut-off frequencies for a subwoofer. An intermediate value of 35 Hz is chosen as athird cuf-off frequency. Additional information about the experimental plan is found inpart II in this series of papers [I]. Figure 4 illustrates the variation of lower cut-off
frequency.
Not only the cut-off frequency is of importance when considering the lower roll off ofa subwoofer, also the order, i.e. slope, is important. A closed box system is of 2ndorder and a vented box is of 4th order. Considering these very commonly usedsystems, it is chosen to change the order of the high-pass filter between 2nd, 4th
and 6th order. Figure 4 shows this variation of the slope from 2nd order up to 6thorder.
1.3 Amplitude and group delay ripple
Ripples, both in amplitude response and in the group delay, are found in practicalusage of subwoofers. Ripples can arise for a number of reasons, e.g. tolerances ofcomponents, limited possibilities of equalization, poor tuning of the system, diffraction, reflection and room modes. Knowledge about how large ripples are allowed to
be would be useful, when designing and installing a subwoofer system. Ripples ofdifferent magnitude can be added to the programme material before playback byintroducing a digital filter comprising a non-flat amplitude response or a non-linear
phase response. Non-flat amplitude response in the pass band of the subwoofer
yields amplitude ripple and non-linear phase response yields a non-constant groupdelay, i.e. group delay ripple.
Shape and magnitude of both amplitude and group delay ripple are calculated fromroom simulations of an IEC 268-13 sized room. The room simulations are based on
the principle of mirror images and carried out using a developed program: “ConSim”.
Documentation of the development and usage of “ConSim” was published in an
earlier paper [2]. “ConSim” calculates the first 1000 msec. of the impulse response ina specified receiver position, given a specified source position. Both source andreceiver are assumed to be omni directional. The impulse response is sampled at a
rate of 4 kHz.
The simulated room is a rectangular room with dimensions 5.03m x 6.02m x 2.50m(width x length x height)=(X,Y,Z).
The source position was chosen to be(X,Y,Z)=(0.30m, 0.40m, 0.35m), which is considered to be a realistic corner position,that will excite all room modes, which in turn will yield large ripples. The receiver
position was chosen to be at a typical listening position near the centre of the room,

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but offset about 30 cm to avoid(X,Y,Z)=(2.20m, 2.70m, l.lOm).

abnormaleffectsdue

QUANTIFICATIONOF SUBWOOFER

to perfectsymmetry:

All the above parameters of the room simulation are fixed in all simulations, but thereverberation time (TG~)is varied from anechoic environment to 0.8 sec. to control themagnitude of the ripples, i.e. a hard room yields large ripples compared to a welldamped room. The reverberation time of the simulated rooms are estimated by time
reversed integration of the squared impulse response. Equation 2 can be used to
calculate a reverberation plot, rp[n] based on the impulse response h[n], which is oflength N. Further information about time reversed integration can be found in [3].

rp[n] = EEn h[i12The reverberation time, TCO,can then be found by inspection of the reverberation
plot, by determining the time, where the level is decreased 60 dB relative to the initiallevel. Note that the length of the simulated impulse response should be longer than
the true reverberation time. If that is not the case, then the reverberation plot will
decrease below 60 dB simply because there are no further samples in the impulse
response.
Four levels of ripples are calculated by simulating 4 rooms with different reverberation time (TeO): anechoic, 0.2 set, 0.4 set and 0.8 sec. The reverberation time isadjusted by changing the reflection coefficients of the walls, floor and ceiling. Figure
5 includes a table of the reflection coefficient for the 6 surfaces in each of the 4rooms. Amplitude and phase response of each room are normalised according to theanechoic room, i.e. the anechoic case yields zero amplitude ripple and zero groupdelay ripple. The group delay is calculated from the unwrapped phase response bydifferentiation. Figure 6 and 7 shows all 4 levels of amplitude ripple and group delay
ripple. Please note, that ripples are only implemented from these target curves up toa certain upper frequency, i.e. to emulate the upper frequency limit of a subwoofer.
Two upper frequency limits are implemented to investigate the influence of the range
in which ripples are implemented in: 80 Hz and 120 Hz.
1.4 Implementation
Variation of the lower cut-off frequency and slope are implemented using digital highpass filters with variable cut-off frequency of 2nd, 4th and 6th order according to theexperimental plan [I].
The amplitude and delay deviating filters, or ripple filters, were designed based on
the impulse responses produced by simulated room response calculations, found insection 1.3. Only deviations in the bass range are included, so deviations in
amplitude and delay are only included up to a certain frequency, and no deviations
exist above this frequency.
The experimental design [l] has three variables for the ripples: the limiting frequency
below which the deviations exist (two values), the amount of amplitude deviation(four values), and the amount delay deviation (four values). The amounts ofdeviation were implemented
by varying the reverberation
time of the room
simulation.
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Two filter designs for each value of the reverberation time were then produced - alinear phase filter containing the the amplitude deviations but no delay deviations,and an all-pass filter containing just the delay deviations but no amplitude deviations.
The delay filter was made causal by adding a constant delay.
The experimental plan [I] uses the amplitude deviation data from one reverberation
time simulation with the delay deviation data from any of the four reverberation times.
This was implemented by convolving an amplitude filter with a delay filter, producing
one filter for each of the amplitude/delay
deviation combinations. A filter has asampling rate of 4kHz. It is 2.04s in length (8996 samples) when it contains both
amplitude and phase deviating properties.
The audio sample files (.WAV files) containing the desired deviations are produced
using a multi-rate convolution process. The audio data is crossover filtered at one ofthe desired two frequencies, the lowpass section is convolved with the deviation
filters described above, and the final signal is produced by summing the two signals
with necessary gain and delay alignment. For delay ripple filtering, the delayalignment can not be exact over the whole crossover frequency band, and this willproduce small changes in the amplitude and delay properties at the crossover point.
However, these changes are small, and do not effect the results. The convolution isdone in IEEE floating point arithmetic, and the source and destination files are 16-bit
fixed point, sampling frequency 44.1kHz. The lowpass section was processed atsampling frequency 4410Hz (decimation by 10). Distortion and noise levels werestudied at each step of the process and proper dithering was applied at quantizations
to maintain linearity througout the processing chain and to minimize noise.

2 Experimental

Setups

The experiments are to be carried out using two different setups: loudspeakers in an
anechoic chamber and using headphones in a “Quiet room”. One aim is to investigate if headphones could substitute the usage of an expensive large anechoic
chamber when quantifying the requirements of subwoofers.
2.1 Anechoic Chamber
The processed audio samples were played back using a pair of “Reference
Loudspeakers” especially build for this purpose. These “Reference Loudspeakers”
extends down to 20 Hz (+/- 2.5 dB) and keeps the harmonic distortion below 2% (90dB SPL at 1 m) in the range from 20 Hz to 50 Hz, while harmonic distortion is below
0.5% (90 dB SPL at 1 m) in the range from 50 Hz to 250 Hz. Group delay is kept
below 10 ms from 50 Hz to 20 kHz, and below 20 ms from 20 Hz to 20 kHz. It is anactive three way closed box system. Crossover frequencies are 160 Hz and 1.6 kHz(4th order). The separate power amplifiers for the three bands are 400 W, 160 W
and 120 W.
The setup comprises two “Reference Loudspeakers” placed in a 3 m isosceles triangle in a large anechoic chamber, which can bee seen on the plan of the setup in
figure 8. The subjects are to be seated in the chair. Both loudspeakers and the chairare placed on grids that are held in place by poles extending from the bottom of theanechoic chamber. The anechoic chamber is located at the Technical University ofDenmark, Department of Acoustic Technology. The free space in the anechoic
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chamber is about 1000 m3. The three dimensions are of similar magnitude, but notequal, and the lower limiting frequency is about 50 Hz. A detailed description can befound in [4].
A computer based system for automated run and control of the listening tests are
utilized. The system is known as “GuineaPig”, and the system was presented at
AES-16 [5]. Additional
information
about “GuineaPig” can be found in [6].
“GuineaPig” was run at a Silicon Graphics workstation: Octane. This workstation
includes 8 channels of 24 bit (ADAT) input and output. Graphical presentation to thesubjects and feedback from the subject will take place using a Laptop PC connectedto the workstation.
Control of analog level and conversion from digital to analog are performed in a
Digital Mixing Console: YAMAHA 03D. This mixer comprises 20 bits linear 8 times
oversampling D/A converters. Figure 9 shows an overview of the signal path startingat the original programme pieces located on the original Compact Disks (CD).
2.2 Headphones
As an alternative to using an anechoic chamber, headphones are utilized in an
attempt to obtain equal results. A number of different headphones were tested andan electrostatic type was chosen: SENNHEISER HE 60, Electrostatic. The amplifier
for this headphone is SENNHEISER HEV 70.
Figure 10 includes measurements of the distortion of the headphone at a max. 100
dB SPL level. The headphones were placed on a Briiel & Kjaer “HATS” (Head andTorso Simulator: B&K 4128), and measurements were taken using a Briiel & Kjser
Audio Analyzer: B&K 2012. The “HATS” was mounted with “Hard Ears” as an option
from Briiel & KjBr. Measurements took place in the anechoic chamber at Bang &O lufsen. The levels of both 2nd and 3th harmonic are generally more than 75 dB(0.02%) below the fundamental, except for a number of frequencies, where the levelis 60 dB (0.1%) below the fundamental.
The levels of both 2nd and 3th harmonics
are raising to about 50 dB (0.3%) below the fundamental at 20 Hz.
During listening experiments, subjects will be seated in a “Quiet room” with theheadphones mounted. The “Quiet room” is located in the basement of the department for Research & Development at Bang & O lufsen. The background noise levelhas been found to be max. 25 dB(A) SPL (“Slow” averaging).
In an attempt to obtain equal results, it was decided to include a non-linear simulation of the “Reference Loudspeaker’,, such that distortion due to non-linearities of the“Reference
Loudspeaker,, is added to the signals before playback using theheadphones. Section 3.2 describes how the program “LoDist” is used to perform thissimulation. In order to make the sound pressure at the ear drums as similar as possible in the two cases: listening to real loudspeakers in the anechoic chamber andlistening via headphones, advanced equalization (EQ) has to be performed on thesignals before playback via headphones. Section 3.3 describes this equalization indetail. Figure 11 shows the signal path in use when headphones are used in the“Quiet room”.

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3 Listening

QUANTIFICATIONOF SUBWOOFER

System Equalization

The setup in the anechoic chamber is measured and calibration is performed using“Pink Noise” and a Loudness meter. In order to compare the two setups, both the
non-linearities of the loudspeaker and the difference in linear transfer function of theheadphones compared to listening in the anechoic chamber are taken into account.
3.1 Anechoic Chamber
The middle curve in figure 12 shows a measurementof the left “Reference
Loudspeaker,’ placed in the anechoic chamber according to figure 8. The measurement was taken using a free field microphone (B&K 4133), measurement amplifier(B&K 2690: NEXUS) and an Audio Analyzer (B&K 2012). The free field microphone
was placed at the listening position pointing directly towards the left reference
loudspeaker. The first mode of the anechoic chamber clearly shows in figure 12 at
approximately 35 Hz, which is a frequency so low that the damping is insufficient tobe anechoic. This mode in not desirable, but it was decided to leave the system likethis and take the response in figure 12 as part of the circumstances for theexperiment.
During the listening experiment 3 different playback levels, which are spaced by 10
dB between each level, are to be use. The highest level is found by applying fullscale “Pink Noise”, and adjusting the level to 2 dB below “clipping” indication on therear of the loudspeaker. Adjusted to this level, a sound pressure level of 68.8 dB(LIN) was measured using the free field microphone at the listening position, when
“Pink Noise” was applied to the left LLReference Loudspeaker,‘. In an IEC 268-13
standard listening room this adjustment corresponds to approximately 80 dB (LIN)
sound pressure level.
Still using the free field microphone, the loudness level was measured to 22.15
Sones via a loudness meter: B&K 2144. This loudness meter is based on IS0 532B:
Zwicker Loudness. When a 1 kHz, full scale on a CD, was applied using this adjustment, 78.4 dB (LIN) was measured via the free field microphone. The two lower
playback levels are simply 10 dB and 20 dB below this adjusted level.
3.2 Nonlinear simulationof subwoofer
A non-linear simulation of the “Reference Loudspeaker,, are utilized when playback is
to be performed
using headphones.
This ensures that distortiondue tonon-linearities of the “Reference Loudspeaker,’ is added to the signals before
playback using the headphones. This operation is performed using the non-linear
loudspeaker driver simulator program “LoDist”.
“LoDist” operates on the basis of position, i.e. displacement, dependant parameters:
Bl(x), Cms(x) etc. All relevant parameters are determined as a function of absolute
displacement from the neutral position. Measurements were taken on a woofer driversimilar to the ones used in the “Reference Loudspeakers”. Based on these parameters, “LoDist” solves numerically the differential equations that describes theloudspeaker driver and it environment, e.g. cabinet. More information about measuring position dependant parameters, operation and principle of “LoDist” can be foundin [7].

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PEDERSEN AND MAIVIRTAQUANTIFICATIONOF SUBWOOFERWhen running the simulation, care was taken to ensure, that the electrical voltage
applied to the simulated driver, was similar to the voltage applied to the physicaldriver in the “Reference Loudspeaker,‘. This was achieved by applying appropriatescaling, when relating the digital signal fed to “LoDist” and the corresponding analog
voltage.
3.3 Headphones
Listening tests are to be performed using both loudspeakers
in an anechoic
chamber, and headphones. In order to make the sound pressure at the ear drums as
similar as possible in the two cases, advanced equalization (EQ) was performed on
the signals before playback via headphones. Head Related Transfer Functions(HRTF) were measured in the anechoic chamber using the setup, which was
described in section 2.1. Head Related Transfer Functions are described in [8].
The “HRTF’s” were measured using the left “Reference Loudspeaker,’ and a “HATS”(Head and Torso Simulator: B&K 4128) placed in the listening position in theanechoic chamber facing a point just half way between the speakers. Figure 12
includes two HRTF measurements at the top of the figure: Left Speaker to Left Ear(the upper most curve) and Left Speaker to Right Ear. The shadow effect of the head
is obvious above 400 Hz, where Left Speaker to Left Ear is much higher than Left
Speaker to Right Ear. Below 150 Hz both HRTF’s coincides with the middle curve,
i.e. the free field microphone measurement. Perfect symmetry of the acoustic setup
is assumed when forming Right Speaker to Right Ear and Right Speaker to Left Ear,but differences in sensitivities of the two ears of the “HATS” are incorporated.
The selected headphones were placed on the “HATS”, and the transfer functions toeach ear were measured. These amplitude responses are shown at the bottom of
figure 12. As described in section 3.2, “LoDist” simulates the non-linear behavior of aloudspeaker driver, but to do so accurately it has to have the right linear response as
well, i.e. the linear response of the “Reference Loudspeaker,, is also part of the“LoDist” simulations. But the linear response of the “Reference Loudspeakers” is also
included in the measured “HRTF”: transfer function from input to the speakers to
output of the “HATS”. For this reason, an inverse filter of the linear transfer functionof “LoDist” should be included in the equalization (EQ), in order to cancel one of thetwo linear transfer functions of the “Reference Loudspeakers” found in the signal
chain.
A “.WAV” file containing a digital Dirac Impulse was created and fed through “LoDist”
at a level, that didn’t give raise to displacements of an order, where non-linearities
comes into play, e.g. a small fraction of 1 mm. Figure 13 shows the determined
amplitude response along with a bold curve, which has limited attenuation towards
lower frequencies. This limitation below 15 Hz is used to avoid dynamic/numericalproblems when inverting the transfer function.
A digital filter (EQ), to be inserted in the signal chain before the headphones, see
figure 11, was designed from the measured “HRTF’s”, transfer function ofheadphones on “HATS” and the linear transfer function of “LoDist”. When considering the selected programme pieces, the equalizer (EQ) should take the signals which
are meant to go to the “Reference Loudspeakers”, and prepare them to be fed to theheadphones in such a way that the sound pressure at the ear drums of the “HATS”

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are equal to the situation where the “HATS” is placed in the anechoic
front of the “Reference Loudspeakers”.

OF SUBWOOFER

chamberin

In the situation of calibration using “Pink Noise”, the aim of the equalizer (EQ) is
somewhat different. In this situation, the equalizer (EQ) should take the “Pink Noise”,
which is meant for playback via loudspeakers, and measurement via a free fieldmicrophone and prepare it for playback via headphones mounted on the “HATS”, insuch a way that the output of the “HATS” is similar to the output of an free fieldmicrophone sitting in the anechoic chamber in front of the loudspeakers. The reason
for this desire is that the loudness meter operates on input from a free field microphone when calculating the loudness level. Figure 14 summarizes all these considerations regarding calculation of the EQ filter in the two cases: programme pieces(using “HRTF” measurements) and “Pink Noise” for calibration (using the free fieldmicrophone measurement).
When listening to two speakers in the anechoic chamber, each of the two ears canhear sound coming from both speakers, i.e. cross talk from both speakers to bothears. Figure 15 shows a schematic of how this is achieved using 4 individual filters
for each equalizer (EQ) in the situation: programme pieces, i.e. the equalizer (EQ) forthe programme pieces consists of the four filters: HRR, HRL, HLR and HLL. HR~ is calculated from the ratio of the “HRTF” from Right Speaker to Right Ear and the product of
the transfer function of the Right Headphone and the linear transfer function of“LoDist”. HRL is calculated using the HRTF from Right Speaker to Left Ear, Left
Headphone and the inverse transfer function of “LoDist”. HLR and HLL are calculated
accordingly. The equalizer (EQ) for the “Pink Noise” doesn’t have cross talk because
the free field microphone is used. Due to the assumption of perfect acoustic symmetry, the numerator in figure 14 is exactly the same considering both right and left
speaker. The only difference is between the two headphones, i.e. in the denominatorin figure 14. This leaves only two filters for this equalizer (EQ).
Figure 16 shows all 4 filters, that forms the equalizer (EQ) for the programme pieces,
HRR and HLL are the two upper curves between 400 Hz and 8000 Hz. Figure 17
shows the two filters forming the equalizer (EQ) for the “Pink Noise”, which is used
for calibration. All measurements are taken using l/24 octave logarithmic frequency
resolution, and the filter design uses a FFT size of 65536. This calls for interpolation,
which is performed in the complex plane after removing the pure time delays of all
the relevant transfer functions. After interpolation, all pure time delays are reintroduced to ensure the correct time response. The final impulse response of the equalizing filters are truncated after 10000 samples. Filtering is then performed directly on
the “.WAV” files using a convolution program developed for this purpose, based on
floating point arithmetic.
The fixed point nature of “.WAV” files, i.e. 16 bits, is taken into account by down
scaling the equalizing filters appropriately and reintroducing the removed gains whenconverting to analog signals. The level calibration using “Pink Noise” and the appropriate equalizing filters lead to an adjustment of the gain in the Digital Mixing
Console, so that the resulting Loudness level was 21.8 Sones and the soundpressure level was 69.0 dB (LIN) for one channel playing.

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4 Conclusion
Seven programme pieces have been selected for use as stimuli in listening experiments: 2 for training sessions, 4 for the actual listening experiment and 1 for level
calibration of the setups. “Pink Noise” was used to calibrate the loudness level of thetwo setups: “Reference Loudspeakers” in anechoic chamber and headphones in a
“Quiet room”. Three different reproduction levels were used, each 10 dB apart. The
loudest level was calibrated to 22 Sones (69 dB SPL) for one channel playing in theanechoic chamber.
Three different lover cut-off frequency was implemented: 20 Hz, 35 Hz and 50 Hz,
combined with 3 different orders/slopes: 2nd, 4th and 6th order. Based on room
simulations 4 different levels of amplitude ripples and group delay ripples in the passband were implemented. Amplitude ripples vary between 0 dB and +/- 20 dB, andgroup delay vary between 0 ms and +/- 200 ms. These variations are found byvarying the reverberation time, T 60, from anechoic to 0.8 sec. in room simulations ofan IEC 268-l 3 sized room.
The setup in the anechoic chamber cornprizes 2 “Reference Loudspeakers” and alistening position arranged in a 3 m isosceles triangle. The anechoic chamber has
1000 m3 of free space. Listening tests are to carried out using an automated system:“GuineaPig” installed on a Silicon Graphics Octane Workstation, which cornprizes 8channels of 24 bit input and output. The second setup is placed in a “quiet room” andcornprizes a pair of electrostatic headphones.
In an attempt to obtain equal results in the 2 setups, advanced equalization of thesignals and simulation of the non-linear behavior of the woofer drivers were
performed before feeding the signals to the headphones. The equalization was
based on measurementsof Head Related Transfer Functions in the anechoic
chamber, transfer function of the “Reference Loudspeakers” using a free field microphone, transfer function of headphones mounted on a Head and Torso Simulator
and the linear transfer function of “LoDist”, which is the simulation program for the
non-linear simulation of loudspeaker drivers. All signal processing was performed
directly on Microsoft Wave files (.WAV).

5 Acknowledgments
The authors would like to thank their colleagues in MEDUSA (EUREKA Project1653) for countless fruitful discussions and valuable ideas. Great effort were shown,and large tasks were carried out by our colleagues, whom the authors would like tothank: Get-t Munch, Peter Chapman and David Ward at Bang & O lufsen and Ari
Varla at Genelec. In addition the authors would like to thank the Department of
Acoustic Technology at The Technical University of Denmark for using their large
anechoic chamber and for practical support with the measurement setup.

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6 References[ll Soren Beth:“Quantification of subwoofer requirements, part II: The influenceof lower system cut-off frequency and slope, and pass-band amplitude andgroup delay ripple”, presented at the 108th AES Convention, Paris 2000
February 19-22.

PI

Jan Abildgaard Pedersen, Kjeld Hermansen and Per Rubak: “The Distributionof the Low Frequency Sound Field and its Relation to Room Equalization”,
presented at the 96th AES Convention, Amsterdam 1994 February 26 - March
1, preprint #3852.

[31

F. Jacobsen & J.H. Rindel: “Time Reversed Decay Measurements”,
Sound and Vibration, Vol. 117, 1987, page 187-190 (L).

PI

F. Ingerslev, O .J. Pedersen, P.K. Moller & J. Kristensen: “New Rooms for
Acoustic Measurements at the Danish Technical University”, ACUSTICA, Vol.
19, 1967/68, page 185-I 99.

[51

Nick Zacharov, Jyri Huopaniemi and Matti Hamalainen: “Round Robin Subjective Evaluation of Virtual Home Theater Sound Systems at the AES 16th International Conference”, presented at the AES 16th International Conference:“Spatial Sound Reproduction”, Rovaniemi 1999 April 10-12, page 544-556 in“The Proceedings of the AES 16th International Conference”

PI

Jussi Hynninen and Nick Zacharov: “GuineaPig - A Generic Subjective Test
System for Multichannel Audio”, presented at the 106th AES Convention,
Munich 1999 May 8-l 1, preprint #4871.

[71

Sandermann
E.
O lsen:“Nonlinear
Modeling
Loudspeakers-A
Practical Implementation”,
presented
Convention, Munich 1997 March 22-25, preprint #4469.

PI

Kiyofumi Inanaga, Yuji Yamada and Hiroshi Koizumi: “Headphone System with
Out-of-Head Localization Applying Dynamic HRTF (Head-Related Transfer
Function)“, presented at the 98th AES Convention, Paris 1995 February 25-28,
preprint #4011.

AES 108th CONVENTION,PARIS, 2000 FEBRUARY

19-22

Journal ofof
Low-Frequency
at the 102th AES

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PEDERSEN AND MAIVIRTA

OF SUBWOOFER

Figure 7: Specification of the 7 selected pieces of programme material. The
first 2 are used during training and following 4 are used during the actual
experiment. The last piece is 1 min. of ‘Pink Noise”.

Music Segments For Training (Aligned)0-10~--.--.1
I

t

I1

k

c

-70
t

20

50
32

125
80

315
200

2000

600
500

1250

5000
3150

12500
6000

20000

Frequency (Hz)-Rush - - Fourplay

Figure 2: Power spectrum of the 2 first programme pieces (for training).

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OF SUBWOOFERMusic Segments For Test (Aligned)-80

IIIIIIIII

-90

II

20

50

Cm

32

125

I

If11I1IlI

200

I
ml

315

I1Ij’l

I

12500

em0

3150

1250

500

I/
5000

2000

20000

Frequency (Hz)-Ray Of Light . - Bladerunner -The Hunter - - Amused To Death

Figure 3: Power spectrum of the 4 programme pieces, that are used during
the actual experiment.

5

0

I

I

\,a...:-+III

II II Ill
III

A..

I

a

I

I

I

I

I

I

d
I

I ,

t
-15

10

Frequency[Hz]Figure 4: Variation of cut-off frequency and slope.

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QUANTIFICATION

T 60

Walls

Floor

Ceiling

Anechoic

0.000

0.000

0.000

0.2 sec.

0.650

0.440

0.290

0.4 sec.

0.805

0.540

0.360

0.8 sec.

0.895

0.600

0.400

OF SUBWOOFER

Figure 5: Reflection coefficient of walls, floor and ceiling in the 4 cases ofreverberation time, TeO.

80
60
40
g
; 20
-E
.n
ii 0
3
g-20
<-4o
-60
-80
IO’
Frequency [Hz]Figure 6: Amplitude ripple in 4 cases. From the top: Anechoic, T60=0.2 set,
T60=0.4 sec., T60=0.8 sec. Both 80 Hz and 120 Hz are marked as upper
limits for implementing the ripples. The 0 dB level has been shifted, for abetter view, to -60 dB, -20 dB, 20 dB and 60 dB respectively as indicated bybold horizontal lines.

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QUANTIFICATIONOF SUBWOOFER

800
600

-600
-8OO',IO’

Frequency [Hz]I IVI A I
IO'

Figure 7: Delay ripple in 4 cases. From above: Anechoic, T60=0.2 set,
T60=0.4 sec., T60=0.8 sec. Both 80 Hz and 120 Hz are marked as upper
limits for implementing the ripples. The 0 msec. level has been shifted, for abetter view, to -600 msec., -200 msec., 200 msec. and 600 msec. respectively as indicated by bold horizontal lines.

3m

Figure 8: Setup in the anechoic chamber,Loudspeakers” and a chair for listening.

AES 108th CONVENTION,PARIS, 2000 FEBRUARY

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cornprizing

2 “Reference

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OF SUBWOOFER

Anechoic Chamber

Figure 9: Signal path from original CD to playback in the anechoic chamberusing the “Reference Loudspeakers”.

80
g 60
2
cn 40
20
0
-201

' ' ' ' 1"
lo*

IO3

lo4

Frequency [Hz]2. And 3. Harmonic measured using HATS andSENNHEISER HE 60. Maximum SPL at 9 kHz was 100 dl3.

Figure10: Fundamental,

AES 108th CONVENTION,PARIS, 2000 FEBRUARY

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PEDERSEN AND MAIVIRTA

Org. CD-b

Lower cut-off
orAmp./delay +ripple

LoDist-

OF SUBWOOFER

EQ

Quiet room

Figure 11: Signal path from original CD to playback in the quiet room using
headphones.

20
IO2

lo3
Frequency [Hz]lo4

Figure 72: Transfer functions (from the top): left loudspeaker to left ear, left
loudspeaker to right ear, left loudspeaker to free field microphone, left
headphone and right headphone mounted on HATS. The curves have beenshifted apart to increase the global view.

AES 108th CONVENTION,PARIS, 2000 FEBRUARY

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10Frequency [Hz]lo3

OF SUBWOOFER

lo4

Figure 13: Determined transfer function of LoDist, which is limited below 75
Hz to avoid high gains when implementing the inverse filter.

I

I

HRTF

Free fieldmicrophone= EQ

Figure 14: Calculation of the Equalization filter for either the programmematerial using the Head Related Transfer Functions (HRTF) measurementsor the “Pink Noise” using the free field microphone measurements.

AES 108th CONVENTION,PARIS, 2000 FEBRUARY

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PEDERSEN AND MAIVIRTA

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R

QuAtdTiFicATi0~b

OF SUBVVOOFER

R

Figure 15: Four different fitters, that takes the two signals intended for the
loudspeakers into the two signals going to the headphones.

IC
C
g-IC
tz
g
g-2(3
-30
-40
IO3
Frequency [Hz]Figure 16: Amplitude response of the 4 filters, which takes the signal
through the two loudspeakers to both ears of the HATS and equalized forboth the headphones mounted on the HATS and the linear transfer functionof “LoDisK

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QUANTIFICATIONOF SUBWOOFER

-30
-40
IO2

IO3
Frequency [Hz]Figure 17: Amplitude response of the 2 filters, which takes the signal
through the two loudspeakers to the free field microphone and equalized forboth the headphones mounted on the HATS and the linear transfer functionof “LoDist”.

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