ENGINEERING REPORTS

Requirements for Low-Frequency Sound
Reproduction, Part II:
Generation of Stimuli and Listening System Equalization*

JAN ABILDGAARD PEDERSEN, AES Member

Research & Development, Bang & Olufsen a/s, DK-7600, Struer, DenmarkAND
AKI MÄKIVIRTA, AES Member
Genelec Oy, FIN-74100 lisalmi, Finland
In part I of two papers the requirements for low-frequency sound reproduction were investigated by the variation of lower cutoff frequency and slope and by the introduction of different
levels of amplitude ripple and group delay ripple in the passband of a high-performance soundreproduction system. Listening tests were performed at three different sound pressure levels
using both loudspeakers in an anechoic chamber and headphones in an audiometric booth.
Two reproduction setups were used to confirm that equal results of the listening tests could
be obtained in the two cases when proper equalization was implemented.
It is described how DSP was used to generate stimuli and perform equalization of the two
reproduction setups. The shape and magnitude of amplitude and group delay ripple were
derived from room simulations of an IEC 268-13 sized room with varying reverberation time.
Proper equalization included the introduction of head-related transfer functions in the signal
path to the headphones. This ensured that the sound pressures at the ear drums were very
similar in two cases –– a person sitting in front of the loudspeakers in the anechoic chamber
and a person wearing headphones in the experimental booth. Level calibration was
performed on both setups using pink noise. The nonlinearities measured in the physicalloudspeakers were introduced into the signal path to the headphones using a nonlinearity
simulator program.

0 INTRODUCTION
The aim of this work was to study the psychoacoustically determined performance requirements for the designof a loudspeaker system for high-quality reproduction of
low-frequency sound in small rooms.
This is part II in a series of papers, and it describes how
digital signal processing was used for the generation of
stimuli and the equalization of the listening system. Part I
described the actual listening experiments, including
experimental strategy, procedure, and results [1].
The increasing use of digital surround sound systems,
such as 5.1 systems, increases the attention to lowfrequency reproduction. Considering 5.1 systems, especially the .1 channel and modern program material, loudspeaker manufacturers have the desire to quantify therequirements for low-frequency sound reproduction.
* Manuscript received 2001 April 27; revised 2002 March 22.
J. Audio Eng. Soc., Vol. 50, No. 7/8, 2001 July/August

In order not to limit the applicability of the conclusions
it was decided to assume that the system variables were
those available in a system employing digital signal processing (DSP) for all the filtering and control tasks.
The essential requirements for high-quality soundreproduction at low frequencies are the lower cutoff frequency and slope because these are linked to maximum
displacement of drivers, system tuning, and power
requirements. In this context it was also decided to focus
on two additional parameters––amplitude ripple andgroup delay ripple, both in the passband. Amplitude ripple
sets the requirements for how much the amplitude
response can be allowed to deviate from an ideal response.
Requirements regarding maximum group delay ripple
impose a limit on how rapidly the phase is allowed tochange. Both amplitude and delay ripple can arise due toa number of physical phenomena such as variations in theparameters of the loudspeaker drive units, resonances in
the cabinet, diffraction around the cabinet, reflections, and581

PEDERSEN AND MÄKIVIRTAENGINEERING REPORTS

modes in the listening room. The experiments weredivided into two separate groups––lower cutoff frequency
and slope in the first group and amplitude and group delay
ripples in the second group. All parameters in each groupwere required to be varied independently, that is, orthogonally.
The work reported both here and in paper I formed partof the EUREKA Project 1653 Medusa (Multichannel
Enhancement of Domestic User Stereo Applications). The
Medusa project was a 3.5-year joint research project withthe following partners: British Broadcasting Corporation,
Institute of Sound Recording at University of Surrey,
Nokia Research Centre, Genelec Oy, and Bang & Olufsen
a/s.

gram item A relative to pink noise,N 1! pink 7 n A

GA 

n0
N 1

! A 7nA

2

Ppink



(1)

PA

2

n0

Stimuli for the listening tests were produced by different filtering of seven selected program pieces. First thelower cutoff frequency and slope were changed and thenboth amplitude and group delay ripples in the passband
were added.

where pink [n] is the time signal of pink noise and A[n] thetime signal of program item A, N is the number of samples
in the program pieces, Ppink is the total power content ofpink noise, and PA is the total power content of program
item A. The total power content is given in Table 1 foreach of the seven pieces.
Power spectra of all the program items were calculatedusing the 1 min of each program item. Fig. 1 gives thepower spectra of the two training items and Fig. 2 those of
the four items that were used in the actual experiment. The
original program items were turned into Microsoft wave
files with two channels, 16 bits, and 44 100-Hz sampling
frequency. All the programs for processing had Microsoft
wave files as both input and output files.

1.1 Program Material
Seven items of program material were selected from awide set of materials [1]. Two items were used during thetraining of subjects, whereas four other items were used in
the actual experiment. The last item was used for calibration purposes only. The spectral distribution, especiallybelow 200 Hz, was of special interest when selecting theseven items of program material. Table 1 lists the specifications for the selected seven pieces.
Total loudness at the listening position was used to calibrate the playback level. The calculation of total loudness
required a stationary signal, which was chosen to be pinknoise, as seen in Table 1. The reproduction level of pinknoise was adjusted from loudness measurements, which
are described in Sections 3.1 and 3.3, and the levels of theother six pieces were individually adjusted relative to pinknoise, based on calculations of the total power content of
the seven pieces. Eq. (1) gives the relative gain GA of pro-

1.2 Variable Lower Cutoff Frequency and Slope
The lower cutoff frequency was varied from 20 to 50
Hz by prefiltering the program material using a digital
high-pass filter with variable cutoff frequency. The range
from 20 to 50 Hz was considered to be a typical range oflower cutoff frequencies. An intermediate value of 35 Hz
was chosen as a third cutoff frequency. Additional information about the experimental plan was presented in partI [1]. Fig. 3 illustrates the variation of the lower cutoff
frequency.
It is not only the cutoff frequency that is of importancewhen considering the lower rolloff of a loudspeaker system, but also the order, that is, slope. A closed-box system
is of second order and a vented box is of fourth order.
Considering these very commonly used systems, it waschosen to vary the order of the high-pass filter between
second, fourth, and sixth order. Fig. 3 shows this variationof the slope from second order up to sixth order.

1 GENERATION OF STIMULI

Table 1. Specifications of selected program material.*
Title

Main
ArtistRush

Eric Clapton

Fourplay

RecordCompany

Number

Track

Time

Reprise926794-2

2

Fourplay

Warner Bros.

7599-266565-2

10Ray of Light

Madonna

Maverik/Warner Bros.

9362-46847-2

5

Bladerunner

Vangelis

East West

4509-96574-2

1

The Hunter

Jennifer Warnes

BMG

261974

9

Amused to Death

Roger Waters

Columbia468761-2

3

0:00
1:00
0:25
1:25
0:40
1:40
1:00
2:00
3:40
4:40
0:05
1:05
0:00
1:00

Pink noise

Power†
(dB)
18.8
12.9
8.9
16.2
13.9
25.3
9.7

* The first two programs were used during training and the following four during the actual experiment. Pink noise was used forcalibration.
† Power averaged over the whole duration of each program item. Only relative levels were necessary for level alignment of program pieces.
582

J. Audio Eng. Soc., Vol. 50, No. 7/8, 2002 July/August

ENGINEERING REPORTS

LOW-FREQUENCY SOUND REPRODUCTION, PART II

1.3 Amplitude and Group Delay Ripple
Ripples both in amplitude response and in the groupdelay are found in practical usage of loudspeaker systems.
Ripples can arise for a number of reasons, such as tolerances of components, limited possibilities of equalization,

poor tuning of the system, diffraction of the cabinet, reflections, and modes in the listening room. When designingand installing a loudspeaker system, it would be useful tohave knowledge about how large the ripples are allowed to
be. Ripples of different magnitudes were added to the test
items before playback by introducing a digital filter com-

Fig. 1. Power spectrum (one-third) of first two music segments for training (aligned).

Fig. 2. Power spectrum (one-third) of four music segments for actual test (aligned).
J. Audio Eng. Soc., Vol. 50, No. 7/8, 2002 July/August583

PEDERSEN AND MÄKIVIRTAENGINEERING REPORTS

prising a nonflat amplitude response or a nonlinear phase
response. A nonflat amplitude response in the passband of
the loudspeaker yielded amplitude ripple and a nonlinear
phase response yielded a nonconstant group delay, that is,group delay ripple.
The shape and magnitude of both amplitude and groupdelay ripple were calculated from room simulations of an
IEC 268-13 sized room [2]. The room simulations werebased on the principle of mirror images and carried out
using a developed program [3]. The room simulator program was used to calculate the first 1000 ms of theimpulse response in a specified receiver position, given a
specified source position. Both source and receiver wereassumed to be omnidirectional. The impulse response was
sampled at a rate of 4 kHz, which was appropriate considering the bass region of a loudspeaker system.
The simulated room was a rectangular room with dimensions of 5.03 m  6.02 m  2.50 m (width  length height). The source position was chosen to be (X, Y, Z) 
(0.30 m, 0.40 m, 0.35 m), which was considered to be arealistic corner position that would excite all room modes,
which in turn would yield large ripples. The receiver position was chosen to be at a typical listening position near
the center of the room, but offset about 0.30 m to avoid
abnormal effects due to perfect symmetry, such as perfectcancellation: (X, Y, Z)  (2.20 m, 2.70 m, 1.10 m).
These parameters of the room simulation were fixed inall simulations, but the reverberation time T60 was varied
from an anechoic environment to 0.8 s in order to control
the magnitude of the ripples, that is, a hard room yielded
large ripples compared to a well damped room. The reverberation times of the simulated rooms were estimated bytime-reversed integration of the squared impulse response.
Eq. (2) was used to calculate a Schroeder integral plotrp[n], based on the impulse response h[n], which was oflength N,
N2

rp 7 n A  !h 7 i A .

(2)

in

Further information about time-reversed integration canbe found in [4]. The reverberation time T60 was foundthrough inspection of a plot of the Schroeder integral bydetermining the time where the level was decreased 60
dB relative to the initial level. Note that the length of thesimulated impulse response was longer than the true
reverberation time in order to avoid errors in the
Schroeder integration.
Four levels of ripples were calculated by simulating
four rooms with different reverbation times T60: 0 s (anechoic), 0.2 s, 0.4 s, and 0.8 s. The reverberation time wasadjusted by changing the reflection coefficients of thewalls, floor, and ceiling. Table 2 lists the reflection coefficients for the six surfaces in each of the four rooms. The
amplitude and phase responses of each room were normalized according to the anechoic room, that is, the anechoic case yielded zero amplitude ripple and zero groupdelay ripple. The group delay was calculated from theunwrapped phase response by differentiation. Figs. 4 – 6
show all four levels of amplitude ripple and group delay
ripple. Please note that ripples were only implemented
from these target curves up to a certain upper frequency,that is, to emulate the upper frequency limit of a sub-Fig. 3. Variation of cutoff frequency and slope.
Table 2. Reflection coefficients of walls, floor, and ceiling

584

T60

Walls

Floor

Ceiling

Anechoic
0.2 s
0.4 s
0.8 s

0.000
0.650
0.805
0.895

0.000
0.440
0.540
0.600

0.000
0.290
0.360
0.400
J. Audio Eng. Soc., Vol. 50, No. 7/8, 2002 July/August

ENGINEERING REPORTS

LOW-FREQUENCY SOUND REPRODUCTION, PART II

Fig. 4. Amplitude ripple implemented up to 80 Hz in four cases. From top––anechoic, T60  0.2 s, T60  0.4 s, T60  0.8 s. For clarity, 0-dB level has been shifted to 60 dB, 20 dB, 20 dB, and 60 dB, respectively, as indicated by bold horizontal lines.

Fig. 5. Amplitude ripple implemented up to 120 Hz in four cases. From top––anechoic, T60  0.2 s, T60  0.4 s, T60  0.8 s. For clarity, 0-dB level has been shifted to 60 dB, 20 dB, 20 dB, and 60 dB, respectively, as indicated by bold horizontal lines.

Fig. 6. Group delay ripple in four cases. From top –– anechoic, T60  0.2 s, T60  0.4 s, T60  0.8 s. Both 80 and 120 Hz are marked
as upper limits for implementing the ripples. For clarity, 0-s level has been shifted to 600 s, 200 s, 200 s, and 600 s, respectively,
as indicated by bold horizontal lines.
J. Audio Eng. Soc., Vol. 50, No. 7/8, 2002 July/August585

PEDERSEN AND MÄKIVIRTAENGINEERING REPORTS

woofer. Two upper frequency limits were implemented toinvestigate the influence of the range in which ripples
were implemented: 80 Hz as indicated in Fig. 4, and 120
Hz as indicated in Fig. 5. Both 80 Hz and 120 Hz are indicated for the group delay ripple in Fig. 6. 80 Hz was considered to be a typical crossover frequency for a subwoofer and 120 Hz was the specified crossover frequency
for the low-frequency enhancement (LFE) channel of a
5.1-channel system.
In order to minimize the influence of loudness differences between the four different amplitude ripple filters, it
was decided to normalize the total power relative to theanechoic filter, that is, 0-dB filter. The power of each
amplitude ripple filter was calculated in the frequency
range from 20 to 80 Hz in Fig. 4 and from 20 to 120 Hz in
Fig. 5. Then a pure gain was applied to the individual filters in order to obtain equal total power in the specified
frequency ranges.

dB). The introduction of delay ripple also introduced
some unwanted amplitude ripple. But the opposite was not
the case, that is, the introduction of amplitude ripple did
not introduce any unwanted delay ripple. It follows fromthis that amplitude ripple and delay ripple were not completely orthogonal, and as a consequence it was decided
not to use the test results obtained from the stimuli where
any delay ripple was introduced [1].
The convolution was performed in floating-point arithmetic, and the source and destination files were 16-bit
fixed point, sampling frequency 44.1 kHz. The low-passsection was processed at a sampling frequency of 4410 Hz(decimation by 10). Distortion and noise levels were studied at each step of the process, and proper dithering wasapplied at quantizations to maintain linearity throughout
the processing chain and to minimize noise.

1.4 Implementation
Variation of the lower cutoff frequency and slope was
implemented using digital high-pass filters with variable
cutoff frequency of second, fourth, and sixth order according to the experimental design [1].
The amplitude and group delay ripple filters were
designed based on the impulse responses produced by thesimulated room response calculations found in Section
1.3. Only ripples in the bass range were included, meaning that ripples in amplitude and delay were only included
up to a certain frequency, and no ripples existed above thisfrequency.
The experimental design [1] had three variables for theripples: the limiting frequency below which the ripples
exist (two values), the amount of amplitude ripple (fourvalues), and the amount of delay ripple (four values).
Two filter designs for each value of the reverberation
time were then produced––a linear phase filter, whichcontained the amplitude ripples but no delay ripples, andan all-pass filter, which contained just the delay ripples
and no amplitude ripples. The delay filters were madecausal by adding a constant delay.
The experimental design [1] used the amplitude ripple
data from one reverberation time simulation, combinedwith the delay ripple data from any of the four reverberation times. This was implemented by convolving an amplitude filter with a delay filter, producing one filter for eachof the amplitude/delay deviation combinations. The filters
had a sampling rate of 4410 Hz. The filter length was 2.04
s (8996 samples) when it contained both amplitude anddelay ripple.
The audio files containing the desired deviations were
produced using a multirate convolution process. The audio
data were crossover filtered at one of the two desired frequencies, the low-pass section was convolved with the ripple filters described, and the final signal was produced bysumming the two signals with the necessary gain anddelay alignment. For delay ripple filtering, the delay alignment could not be exact over the whole crossover frequency band, and this produced changes in the amplitude
and delay properties at the crossover point (maximum 1.5

The experiments were carried out using two different
setups––loudspeakers in an anechoic chamber and headphones in quiet surroundings.

586

2 EXPERIMENTAL SETUPS

2.1 Setup in Anechoic Chamber
The processed audio samples were played back using apair of reference loudspeakers built especially for this purpose. These reference loudspeakers extended down to 20
Hz (2.5 dB) and kept the harmonic distortion below 2%(90 dB SPL at 1 m) at low frequencies, in the range from
20 to 50 Hz. Above 50 Hz, in the range from 50 to 250 Hz,
the harmonic distortion was below 0.5% (90 dB SPL at 1m). Above 50 Hz the group delay was kept below 10 ms,
in the frequency range from 50 Hz to 20 kHz. The groupdelay was kept below 20 ms in the full frequency range,from 20 Hz to 20 kHz. It was an active three-way closedbox system. Crossover frequencies were 160 Hz and 1.6
kHz (fourth order). The separate power amplifiers for thethree bands were 400 W, 160 W, and 120 W.
The setup comprised two reference loudspeakers and alistening position placed in a 3-m equilateral triangle in alarge anechoic chamber, as shown in Fig. 7. The subjects
were seated in a chair. Both loudspeakers and the chair
were placed on grids that were held in place by poles

Fig. 7. Setup in anechoic chamber, comprised of two reference
loudspeakers and a chair for listening. Both loudspeakers andchair were placed on grids held in place by poles extending to thebottom of the anechoic chamber.
J. Audio Eng. Soc., Vol. 50, No. 7/8, 2002 July/August

ENGINEERING REPORTS

extending to the bottom of the anechoic chamber. The anechoic chamber is located at the Technical University ofDenmark, Department of Acoustic Technology. The freespace in the anechoic chamber is about 1000 m3. The three
dimensions are of similar magnitude, but not equal, andthe lower limiting frequency is 43.7 Hz. A detailed
description can be found in [5].
A computer-based system for automated control of thelistening tests was utilized. The system is known as
GuineaPig [6], [7]. This software was run in a workstation(Silicon Graphics Octane) that included eight channels of
24-bit (ADAT) input and output. Graphical user interface
and feedback from the subject were handled by a laptop
PC connected to the workstation.
Control of analog level and conversion from digital toanalog were performed using a digital mixing console(YAMAHA O3D). This mixer utilized 20-bit linear 8
oversampling digital-to-analog converters. Fig. 8 shows
an overview of the entire signal path starting at the original program pieces located on the original Compact Discs(CDs). The program material from the original CDs wasprocessed prior to the listening experiments and put onto
the hard disk of the workstation. During the actual listening experiments the program material was taken from thehard disk of the workstation.
2.2 Headphone Setup
As an alternative to using an anechoic chamber, headphones were utilized in an attempt to simulate the setup in

LOW-FREQUENCY SOUND REPRODUCTION, PART II

the anechoic chamber. A number of different headphones
were tested and an electrostatic type was chosen(Sennheiser HE 60, electrostatic, amplifier Sennheiser
HEV 70). This choice was motivated by a wide frequency
response and low distortion.
Fig. 9 gives measurements of the distortion of the headphone at a maximum level of 100 dB SPL. The headphones were placed on a Brüel & Kjær head and torso
simulator (B&K 4128), and measurements were takenusing a Brüel & Kjær audio analyzer (B&K 2012). The
head and torso simulator was mounted with hard ears
(optional). Measurements took place in an anechoic chamber at Bang & Olufsen. The levels of both second and third
harmonics were generally more than 75 dB (0.02%) below
the fundamental, except for a number of frequencies
where the level was 60 dB (0.1%) below the fundamental.
The levels of both second and third harmonics rose toabout 50 dB (0.3%) below the fundamental at 20 Hz.
During listening experiments, subjects were seated in
quiet surroundings, an audiometric booth. The audiometric booth was located next-door to the anechoic chamber
described in Section 2.1.
In an attempt to simulate the reference loudspeakers in
the anechoic chamber, it was decided to include a nonlinear simulation of the reference loudspeakers, that is, distortion due to nonlinearities of the reference loudspeaker
was added to the signals before playback using the headphones. Section 3.2 describes how a nonlinear simulator
program was used to perform this simulation. The soundFig. 8. Signal path from original CD to playback in anechoic chamber using reference loudspeakers. Program material from CD wasprocessed prior to listening experiments and put onto hard disk of workstation.

Fig. 9. Fundamental, second, and third harmonics measured with head and torso simulator and headphones used in the experiment.
Maximum SPL at 9 kHz was 100 dB.
J. Audio Eng. Soc., Vol. 50, No. 7/8, 2002 July/August

587

PEDERSEN AND MÄKIVIRTA

pressures at the ear drums in the two setups were madesimilar by applying advanced equalization to the signals
before playback via the headphones. Section 3.3 describes
this equalization in detail. Fig. 10 shows the signal pathwhen headphones were used. The graphic user interface
and feedback from the subject were handled directly by
the workstation.
3 LISTENING SYSTEM EQUALIZATION AND
CALIBRATIONThe setup in the anechoic chamber was measured using
pink noise, and calibration was performed. Both the nonlinearities of the loudspeaker and the difference in linear
transfer functions of the headphones compared to listening in the anechoic chamber were taken into account in theequalization process.
3.1 Anechoic Chamber
The middle curve in Fig. 11 shows a measurement of
the left reference loudspeaker placed in the anechoic
chamber according to Fig. 7. The measurement was takenusing a free-field microphone (B&K 4133), measurement
amplifier (B&K 2690: NEXUS), and an audio analyzer

ENGINEERING REPORTS(B&K 2012). The free-field microphone was placed at thelistening position pointing directly toward the left reference loudspeaker. The first mode of the anechoic chamberis clearly seen in Fig. 11 at approximately 35 Hz, which
was a frequency so low that the damping in the room wasinsufficient to be anechoic. This mode was unavoidable,
so it was decided to leave the system like it was and takethe response in Fig. 11 as part of the circumstances for theexperiment.
During the listening experiment three different playback levels, spaced 10 dB between each level, were used.
The highest level was found by applying full-scale pinknoise, and adjusting the level to 2 dB below the level
where clipping is indicated on the rear of the loudspeaker.
Adjusted to this level, a sound pressure level of 69 dB (lin,slow) was measured using the free-field microphone at thelistening position, when pink noise was applied to the left
reference loudspeaker. In an IEC 268-13 standard listening room [2], this adjustment corresponded to approximately 80 dB (lin) sound pressure level.
Still using the free-field microphone and playing thepink noise, the loudness level was measured to 22 sones
via a loudness meter (B&K 2144). This loudness meter
was based on ISO 532B “Zwicker” loudness [8]. When aFig. 10. Signal path from CD to playback in audiometric booth using headphones. Program material from CD was processed prior tolistening experiments and put onto hard disk of workstation.

Fig. 11. Transfer functions. From top –– left loudspeaker to left ear, left loudspeaker to right ear, left loudspeaker to free-field microphone, left headphone and right headphone both mounted on head and torso simulator. Curves were shifted apart to increase clarity.
Free-field microphone measurement was lowered 30 dB relative to HRTFs, e.g., left loudspeaker to left ear.
588

J. Audio Eng. Soc., Vol. 50, No. 7/8, 2002 July/August

ENGINEERING REPORTS

1-kHz sine wave, full scale on a CD, was applied using
this adjustment, 78.4 dB (lin) was measured via the freefield microphone. The two lower playback levels were
simply 10 and 20 dB below this adjusted level.
3.2 Nonlinear Simulation
A nonlinear simulation of the reference loudspeaker
was utilized when playback was performed using headphones. This ensured that distortion due to nonlinearitiesof the reference loudspeaker was added to the signals
before playback using the headphones. This operation was
performed using a nonlinear loudspeaker driver simulator
program (LoDist) [9].
The central parameter in this nonlinear simulator program was the diaphragm position, that is, the traditional
loudspeaker driver parameters were dependent on thediaphragm position. All relevant parameters were determined as a function of absolute displacement from theneutral position. Measurements were performed on awoofer driver identical to the ones used in the reference
loudspeakers. Based on these parameters, the nonlinear
simulator program solved numerically the differential
equations that described the loudspeaker driver and its
environment, such as its cabinet. More information aboutmeasuring position-dependent parameters, and the operation and principle of the nonlinear simulator program canbe found in [9].
Care was taken to ensure that the electrical voltage
applied to the simulated driver was identical to the voltage
applied to the physical driver in the reference loudspeaker.
This was achieved by applying appropriate scaling whenrelating the digital signal feed to the nonlinear simulator
program and the corresponding analog voltage.
3.3 Headphones
The sound pressures at the ear drums in the two setups
were made similar by applying advanced equalization to
the signals before playback via the headphones. Headrelated transfer functions (HRTFs) were measured in theanechoic chamber using the setup described in Section
2.1. HRTFs are described in [10].
The HRTFs were measured using the left reference
loudspeaker and a head and torso simulator (B&K 4128)
placed in the listening position in the anechoic chamber,facing a point just halfway between the loudspeakers. The
head and torso simulator was used because it was assumed
that individual HRTFs for each subject in the listening test
were not necessary. This assumption was made because
timbre was judged to be the important parameter, whereas
exact location was judged to be a secondary issue.
Especially at low frequencies, which was the important
frequency range in this context, the individual HRTFs arevery similar, which lead to the choice of using a standard
head and torso simulator. Fig. 11 includes two HRTF
measurements at the top of the figure––left loudspeaker toleft ear (the uppermost curve) and left loudspeaker to rightear. The shadow effect of the head is obvious above 400
Hz, where left loudspeaker to left ear is much higher thanleft loudspeaker to right ear. Below 150 Hz both HRTFs
coincide with the middle curve, the free-field microphone
J. Audio Eng. Soc., Vol. 50, No. 7/8, 2002 July/August

LOW-FREQUENCY SOUND REPRODUCTION, PART II

measurement, but the curves are shifted 30 dB apart forclarity. Perfect symmetry of the acoustic setup was
assumed when right loudspeaker to right ear and rightloudspeaker to left ear were obtained, but differences inthe sensitivities of the two ears of the head and torso simulator were taken into account.
The selected headphones were placed on the head andtorso simulator, and the transfer functions to each ear were
measured. These amplitude responses are shown at thebottom of Fig. 11. As described in Section 3.2, a nonlinear
simulator program was used to simulate the nonlinear
behavior of a loudspeaker driver, but to do so accurately,
it had to have the correct linear response as well, that is,
the linear response of the reference loudspeaker. But thelinear response of the reference loudspeaker was also
included in the measured HRTFs––transfer functions
from the input of the loudspeakers to the output of thehead and torso simulator. For this reason an inverse filterof the linear transfer function of the nonlinear simulator
program was included in the equalization in order to cancel one of the two linear transfer functions of the reference
loudspeakers found in the signal chain.
The linear transfer function of the nonlinear simulator
program was found by feeding an audio file, containing a
digital Dirac impulse, through the nonlinear simulator
program. This was done at a signal level that did not giverise to displacements of an order where nonlinearities
come into play, such as a small fraction of 1 mm. Fig. 12shows the determined amplitude response along with abold curve, which has limited attenuation toward lower
frequencies. This limitation below 15 Hz was used to
avoid dynamic/numerical problems when the transfer
function was inverted.
The placement of the digital filter can be seen in Fig.
10, where the filter is marked with EQ. The filter was
designed from the measured HRTFs, the transfer functionof headphones on the head and torso simulator, and thelinear transfer function of the nonlinear simulator program. The digital filter was used to process the signals,
which were meant for playback via the reference loudspeakers, in such a way that the output signals from thedigital filter were ready for playback via headphones. Thiswas performed so that the sound pressures at the ear
drums of the head and torso simulator were identical in thetwo setups––headphones mounted on the head and torso
simulator and the head and torso simulator placed in theanechoic chamber in front of the reference loudspeakers.
During calibration with pink noise, the function of thedigital filter EQ was somewhat different. Section 3.1
described how the pink noise signal was played back via
the reference loudspeakers and how the sound pressure
was measured by a free-field microphone. In this situation
the digital filter was used to process the pink noise signal
so that the electrical output of the head and torso simulator wearing the headphones was identical to the electrical
output of the free-field microphone in the anechoic chamber, when the loudspeakers were playing the unprocessedpink noise. This was necessary because the loudness meterused required an input signal from a free-field microphone
in order to calculate the correct loudness level.
589

PEDERSEN AND MÄKIVIRTA

Fig. 13 summarizes all the considerations regarding the
calculation of the digital equalizer filter EQ in the twocases––playback of program pieces, namely, using themeasured HRTFs, and calibration with pink noise,
namely, using the free-field microphone measurement.
When a human is listening to two loudspeakers, each of
the two ears receives sound coming from both loudspeakers––crosstalk from both loudspeakers to both ears. Fig.
14 shows a schematic of how this was achieved using fourindividual filters for each equalizer EQ when the program
pieces were processed, that is, the equalizer for the program pieces consisted of the four filters, HRR, HRL, HLR,
and HLL.
HRR was calculated from the ratio of the HRTF from theright loudspeaker to the right ear divided by the product of
the transfer function of the right headphone and the linear
transfer function of the nonlinear simulator program . HRL
was calculated using the HRTF from the right loudspeakerto the left ear, the left headphone, and the linear transfer
function of the nonlinear simulator program. HLR and HLL
were calculated accordingly. The equalizer for the pink

ENGINEERING REPORTS

noise did not have crosstalk, that is, only two equalizer filters, because the HRTFs were replaced by the free-fieldmicrophone measurements. Due to the assumption of perfect acoustic symmetry, the numerator in Fig. 13 wasexactly the same for both right and left loudspeakers. The
only difference was between the two headphones, that is,in the denominator in Fig. 13.
Fig. 15 shows all four filters that formed the equalizer
for the program pieces, HRR and HLL being the two upper
curves in the frequency range from 400 to 8000 Hz. Fig.
16 shows the two filters that formed the equalizer for thepink noise. All measurements were taken using 1/24
octave logarithmic frequency resolution, and the filters
were designed using an FFT size of 65 536. This called forinterpolation, which was performed in the complex plane
after removal of the pure time delays of all the relevanttransfer functions. After interpolation, all pure time delays
were reintroduced to ensure the correct time responses.
The final impulse responses of the equalizer filters weretruncated after 10 000 samples. Filtering was then performed using a convolution program developed for thisFig. 12. Measured linear transfer function of nonlinear simulator program. Transfer function was limited below 15 Hz to avoid highgains when implementing inverse filter.

Fig. 13. Calculation of equalization filters EQ for either program
material using HRTF measurements or pink noise using freefield microphone measurements.
590

Fig. 14. Four different filters used to generate signals for headphone playback based on two signals for loudspeaker playback.
J. Audio Eng. Soc., Vol. 50, No. 7/8, 2002 July/August

ENGINEERING REPORTS

purpose, based on floating-point arithmetic.
The fixed-point nature of the audio files, that is, 16 bits,
was taken into account by down-scaling the equalizer filters appropriately and reintroducing the removed gains in
the conversion process to analog signals. The level calibration was performed by adjusting the gain of the digitalmixing console, so that the resulting loudness level was 22
sones. This corresponded to a sound pressure level of 69
dB (lin) for one channel playing the processed pink noise.
This calibration and the equalization ensured that thetransfer function for the headphone setup was adjusted
such that for the reproduction of the same signal, thesound pressure level at the ear drum in each ear of adummy head was identical to that measured if the dummy
head was placed at the listening position in the anechoic
chamber.
4 CONCLUSION
Seven program pieces were processed using DSP inorder to prepare the program pieces of the listening exper-

LOW-FREQUENCY SOUND REPRODUCTION, PART II

iments, described in part I [1]. Pink noise was used to calibrate the loudness level of the two setups––reference
loudspeakers in an anechoic chamber and headphones in
an audiometric booth. Three different reproduction levels
were used, all 10 dB apart. The loudest level was calibrated to 22 sones, which corresponded to 69 dB SPL for
one channel playing in the anechoic chamber.
Three different lower cutoff frequencies were implemented–– 20 Hz, 35 Hz, and 50 Hz––combined withthree different orders/slopes––second, fourth, and sixthorder. Based on room simulations, four different levels of
amplitude ripples and group delay ripples in the passband
were implemented. Amplitude ripples varied between 0and 20 dB, and group delay varied between 0 and 200
ms. These variations were found by varying the reverberation time T60 from anechoic to 0.8 s in room simulationsof an IEC 268-13 sized room. When delay ripple wasintroduced, some unwanted amplitude ripple was also
introduced (maximum 1, 5 dB). No unwanted delay ripple
was introduced when amplitude ripple was introduced.
In an attempt to have similar conditions in the two

Fig. 15. Amplitude response of four filters used to generate signals for headphone playback based on signals for loudspeaker playback.

Fig. 16. Amplitude response of two filters used to process pink noise before calibration of headphone setup.
J. Audio Eng. Soc., Vol. 50, No. 7/8, 2002 July/August591

PEDERSEN AND MÄKIVIRTAENGINEERING REPORTS

setups, advanced equalization of the signals and simulation of the nonlinear behavior of the woofer drivers were
performed before the signals were fed to the headphones.
The equalization was based on measurements of HRTFs in
the anechoic chamber, the transfer function of the reference loudspeakers using a free-field microphone, thetransfer function of headphones mounted on a head andtorso simulator, and the linear transfer function of the simulator program for the nonlinear simulation of loudspeaker drivers. All signal processing was performed
directly on audio files.
5 ACKNOWLEDGMENT
The authors would like to thank their colleagues in
EUREKA Project 1653, Medusa, for countless fruitful
discussions and valuable ideas. Great effort was shown,and large tasks were carried out by our colleagues, whom
the authors would like to thank: Gert Munch, Peter
Chapman, and David Ward at Bang & Olufsen and Ari
Varla at Genelec. The authors would especially like tothank Søren Bech from Bang & Olufsen for outstanding
enthusiasm and general view of the whole process. In
addition the authors would like to thank the Department of
Acoustic Technology at the Technical University ofDenmark for the use of their large anechoic chamber andfor practical support with the measurement setup.
6 REFERENCES[1] S. Bech, “Requirements for Low-Frequency Sound
Reproduction, Part I: The Audibility of Changes in
Passband Amplitude Ripple and Lower System Cutoff
Frequency and Slope,” J. Audio Eng. Soc. vol. 50, pp.
564 – 580 (this issue).
[2] IEC 268-13, “Sound System Equipment,” Part 13:“Listening Tests on Loudspeakers,” International Electro-

technical Commission, Geneva, Switzerland (1985).
[3] J. A. Pedersen, K. Hermansen, and P. Rubak, “TheDistribution of the Low Frequency Sound Field and Its
Relation to Room Equalization,” presented at the 96th Convention of the Audio Engineering Society, J. Audio Eng.
Soc. (Abstracts), vol. 42, p. 408 (1994 May), preprint 3852.
[4] F. Jacobsen and J. H. Rindel, “Time Reversed Decay
Measurements,” J. Sound Vibration, vol. 117, pp. 187 –
190 (1987).
[5] F. Ingerslev, O. J. Pedersen, P. K. Møller, and J.
Kristensen, “New Rooms for Acoustic Measurements at
the Danish Technical University,” Acustica, vol. 19, pp.
185 – 199 (1967/1968).
[6] N. Zacharov, J. Huopaniemi, and M. Hämäläinen,“Round Robin Subjective Evaluation of Virtual Home
Theater Sound Systems at the AES 16th International
Conference,” in Spatial Sound Reproduction, Proc. AES
16th Int. Conf. (1999), pp. 544 – 556.
[7] J. Hynninen and N. Zacharov, “GuineaPig––AGeneric Subjective Test System for Multichannel Audio,”presented at the 106th Convention of the AudioEngineering Society, J. Audio Eng. Soc. (Abstracts), vol.
47, p. 513 (1999 June), preprint 4871.
[8] ISO 532, “Method for Calculating Loudness Level,”International Electrotechnical Commission, Geneva,
Switzerland (1975).
[9] E. Sandermann Olsen, “Nonlinear Modeling of
Low-Frequency Loudspeakers––A Practical Implementation,” presented at the 102nd Convention of the AudioEngineering Society, J. Audio Eng. Soc. (Abstracts), vol.
45, p. 414 (1997 May), preprint 4469.
[10] K. Inanaga, Y. Yamada, and H. Koizumi, “Headphone System with Out-of-Head Localization Applying
Dynamic HRTF (Head-Related Transfer Function),” presented at the 98th Convention of the Audio Engineering
Society, J. Audio Eng. Soc. (Abstracts), vol. 43, pp. 401,402 (1995 May), preprint 4011.

THE AUTHORS

592

J. A. Pedersen

A. Mäkivirta

Jan Abildgaard Pedersen received a master's degree inelectrical engineering from the University of Aalborg inDenmark in 1993, where he specialized in acoustics.
After graduating, Mr. Pedersen began working at
Bang & Olufsen as a DSP research engineer in theElectroacoustics Research & Development department,

and since 1998 he has been a technology specialist for
acoustics and DSP. In this capacity, he is not only
responsible for Bang & Olufsen following this technology area, but also contributes to the development of it.
He works in many other research areas including lowfrequency sound field, room equalization, near-field
J. Audio Eng. Soc., Vol. 50, No. 7/8, 2002 July/August

ENGINEERING REPORTS

LOW-FREQUENCY SOUND REPRODUCTION, PART II

acoustic measurements, subwoofer requirements, andespecially what DSP has to offer in acoustic applications. He is a member of the AES.
●

Aki Mäkivirta was born 1960 in Jyväskylä, Finland. He
received Diploma Engineer, Licentiate in Technology, andDoctor of Science in Technology degrees in electricalengineering from Tampere University of Technology,
Tampere, Finland, in 1985, 1989 and 1992, respectively.
His doctor’s thesis described applications of nonlinear
signal processing methods for haemodynamic monitoringin medical intensive care.
In 1983, Dr. Mäkivirta joined the Medical Engineering

J. Audio Eng. Soc., Vol. 50, No. 7/8, 2002 July/AugustLaboratory of the Research Center of Finland at
Tampere, where he worked in various research positionsin the field of biomedical signal analysis. In 1990 hejoined Nokia Corporation Research Center in Tampere,
Finland, where he served as a project manager, and after
1992 was the research manager responsible for building a
research group for DSP applications in television audio
and high-quality loudspeaker reproduction. In 1995 hejoined Genelec Oy, Iisalmi, Finland, where he is a R&D
manager responsible for digital system and signal processing applications.
Dr. Mäkivirta is a member of the AES and IEEE. He
holds 13 patents, and he is the author of more than 40
journal and conference papers.

593