evaluation of a concentric rigid and open spherical microphone

evaluation of a concentric rigid and open spherical microphone
A MBISONICS S YMPOSIUM 2009
June 25-27, Graz
EVALUATION OF A CONCENTRIC RIGID AND OPEN SPHERICAL
MICROPHONE ARRAY FOR SOUND REPRODUCTION
Abhaya Parthy1 , Craig Jin2 , André van Schaik2
1
2
School of Information Technologies, The University of Sydney, Australia (aparthy@it.usyd.edu.au)
School of Electrical and Information Engineering, The University of Sydney, Australia (craig@ee.usyd.edu.au)
Abstract: We present an empirical evaluation of a third-order sound field recording and reproduction system which has
been designed to operate over a frequency range of 900 Hz to 16 kHz. The system consists of a spherical microphone
array which is a concentric rigid and open spherical microphone array (64 microphones in total) and also a spherical
loudspeaker array (24 loudspeakers) in a hemi-anechoic room. The concentric rigid and open spherical microphone array
was designed to improve the frequency range of the standard spherical microphone array. We present some measurements
comparing performance to an ideal third-order sound field recording and reproduction system.
Key words: microphone arrays, high-order ambisonics, sound field recording and reproduction
1 INTRODUCTION
reflections. The CRO-SMA, shown in Figure 1, consists
of two concentric spherical microphone arrays, one inside
the other, each having 32 microphones. The inner of the
two spherical microphone arrays is baffled by a rigid scatterer and the outer open array is designed to be acoustically
transparent. The CRO-SMA has been previously characterised for use as a beamformer and for near-field acoustic
holography, and a detailed analysis of its design and performance is presented in [8, 9, 10].
A system for recording and reproducing a real sound field
is useful in many applications including audio displays, virtual reality, audio-only gaming, cinema, and auditory research. The most widely used system for recording and reproducing a sound field is the first-order Ambisonics system
originally developed by Gerzon [4]. The first-order Ambisonics system uses a sound field microphone to record a
sound field to a first-order spherical harmonic representaWe present an empirical evaluation of the combined CROtion. This spherical harmonic representation of the sound
SMA and loudspeaker array system when it is used as a
field is then used to drive an array of loudspeakers to recreate the original sound field, correct to a first-order approximation. The first-order Ambisonics system is in wide
use and performs quite well in most applications, however,
there is a significant benefit in using higher order systems as
they have an increased spatial fidelity, especially at higher
frequencies, and a larger listening area at the centre of the
loudspeaker array [12]. Much research has been done on
higher order sound field recording and reproduction systems, including work by Poletti [11], Li et al. [6], Abhayapala and Ward [12, 1], Daniel et al. [3], and Bertet et al.
[2].
We have built a sound field recording and reproduction system capable of operating at up to third-order in the frequency range of 900 Hz to 16 kHz, up to second-order down
to 400 Hz, and at first-order down to 60 Hz. The system
uses a 24-loudspeaker spherical loudspeaker array for reproduction, and a 64-microphone concentric rigid and open
spherical microphone array (CRO-SMA) for recording. The
spherical loudspeaker array, shown in Figure 2, is situated
inside a hemi-anechoic room, which has walls and a ceiling that are anechoic down to 100 Hz, and a floor which
Figure 1: This figure shows a photo of the 64-microphone
has thick carpet and two underlays to minimise the floor
rigid and open spherical microphone array.
sound field recording and reproduction system. The performance of this system is evaluated by measuring its ability
to record and reproduce a sound field generated by a single plane wave sound source. The CRO-SMA is placed at
the centre of the spherical loudspeaker array and is used to
measure a plane-wave sound field. The centre of the loudspeaker array is termed the "sweet-spot", because it is the
position at which the recreated sound field is the most accurate. The measured plane-wave sound field is compared to
ideal first, second and third-order plane-wave sound fields.
The main contribution of this paper is that we show that a
dual, concentric SMA provides a solid basis for a practical
and broadband three-dimensional third-order sound field
recording and reproduction system, and we present empirical measurements comparing the performance of the system
to an ideal third-order sound field recording and reproduction system.
2 METHODS
The performance of the sound field recording and reproduction system we have constructed was evaluated by measuring its ability to record and reproduce a sound field generated by a single plane wave sound source. The CRO-SMA
was placed at the centre of the spherical loudspeaker array,
and impulse response measurements were measured from
each loudspeaker on the spherical loudspeaker array to each
microphone on the CRO-SMA. An additional loudspeaker
was then used to simulate a plane wave sound source and
impulse response measurements were measured from it to
the CRO-SMA. The recorded impulse response measurements from the loudspeaker simulating a plane-wave source
were then used to calculate the speaker signals for the loudspeaker array to recreate the recorded plane-wave sound
field. Using these calculated signals for the speakers in
the loudspeaker array and the original impulse responses
measured from each loudspeaker in the loudspeaker array
to each microphone in the CRO-SMA, we simulated the
recording and reproduction of the plane-wave sound field.
Snapshots of images of the recorded sound field are presented in our results and compared to ideal sound fields. In
this paper we use the CRO-SMA naively in that we only
use the microphone signals recorded from the outer open
array for frequencies below 2840 Hz and we only use the
microphone signals recorded from the inner rigid array for
frequencies above 2840 Hz. We have previously shown in
[10] how the microphone signals recorded from both arrays can be combined to improve the overall performance of
the CRO-SMA across all frequencies for near-field acoustic
holography and we are now in the process of implementing
the same algorithms for sound field recording and reproduction.
2.1. System and Equipment Setup
type 4060-BM omni-directional microphones mounted in
an approximately equally spaced arrangement as given by
[5]. When the CRO-SMA is used to beamform at thirdorder it has a signal-to-noise ratio (SNR) that is greater
than 30.0 dB for a frequency range of 900 Hz to 16 kHz,
and this SNR can be maintained by reducing the beamforming order to second-order below 900 Hz and to firstorder below 400 Hz down to 60 Hz. The signals from the
64 microphones in the CRO-SMA are amplified by eight
8-channel Digidesign PRE preamplifiers, which have digitally controlled gains so that all channels are uniformly amplified. The output from the preamplifiers are fed to four
16-channel Apogee AD-16X analogue-to-digital convertors
which were sampling the signals at 48 kHz with a 24-bit resolution. The output from the analogue-to-digital convertors
is in ADAT format and is sent to a RME ADI-648 MADI-toADAT converter, which converts the eight 8-channel ADAT
signals to one MADI format signal that transports all the
64-channels of audio. The 64 microphone signals, in MADI
format, are recorded on a standard personal computer (PC)
using a RME Hammerfall DSP MADI PCI sound card. The
64 microphone signals can then be processed on a PC to
create 24 loudspeaker signals to recreate the recorded sound
field. The 24 loudspeaker signals are output from the PC’s
RME Hammerfall DSP MADI PCI sound card in MADI
format, and are converted into ADAT format using a RME
ADI-648 MADI-to-ADAT converter. The ADAT format
loudspeaker signals have a sample rate of 48 kHz with a 24bit resolution, and are fed to two 16-channel Apogee DA16X digital-to-analogue convertor. The 24 analogue signals from the digital-to-analogue converters are fed to six
4-channel Lab Gruppen C series power amplifiers which
power 24 uncalibrated Tannoy V6 loudspeakers. The 24
loudspeakers are mounted approximately equally spaced
around a sphere with a radius of 2.8 m, however, due to
height restrictions in the hemi-anechoic room, the top and
bottom loudspeakers are closer to the centre of the loudspeaker array and their signals are appropriately time delayed. There are also 4 Whise Master Entertainer 319A
sub-woofers that sit on the floor around the spherical loudspeaker array which are used to reproduce the low frequencies. These sub-woofers were not ready at the time the measurements were being made and are not included in the results presented in this paper, however, they are being used
now and anecdotal evidence suggests that they significantly
improve the sense of presence and the spatial image.
2.2. Sound Field Signal Processing
We assume that the CRO-SMA records a sound field in
which all the sound sources are in the far-field, and we assume that the loudspeakers are ideal plane wave sources.
To recreate the sound field recorded by the CRO-SMA, the
loudspeakers are fed signals which are obtained by processing the signals recorded by the microphones on the CROSMA. This can be written as a matrix equation and is given
by [12, 7]
The CRO-SMA, shown in Figure 1, consists of a rigid inner
spherical microphone array of radius 1.63 cm and an outer
open spherical microphone array of radius 6.0 cm. The rigid
and open spherical microphone arrays each have 32 DPA
Page 2of 5
Pa = cb,
(1)
Figure 2: This figure shows a photo of the spherical loudspeaker array inside the hemi-anechoic room.
where c is a constant, a is a vector of unknown weights der N is given by
to be assigned to each loudspeaker, P is the loudspeaker
 PM

decoding matrix, and for a second-order system is given by
1
0
j=1 αj p(k, Ωj ) b0 Y0
P
 M α p(k, Ω ) 1 Y −1 
 j=1 j

j b1 1
 PM
1
0 


α
p(k,
Ω
)
Y
j
j
b1 1 
 Pj=1

 0
M
1
1 

0
0
α
p(k,
Ω
)
Y
Y0 (Ω2 ) · · · Y0 (ΩL )
Y0 (Ω1 )
j b1 1 

j=1 j
,
b=
(4)
..
 Y1−1 (Ω1 ) Y1−1 (Ω2 ) · · · Y1−1 (ΩL ) 



 0
.


0
0

 Y1 (Ω1 )
Y1 (Ω2 ) · · · Y1 (ΩL ) 
PM

 1
 j=1 αj p(k, Ωj ) b1N YN−N 
1
1

 Y1 (Ω1 )
(Ω
)
·
·
·
Y
(Ω
)
Y


L
2
1
1


..


 , (2)
..
..
..
.
P=


.
.


.
.
.
PM

 −N.
1
N
−N
−N

Y
j=1 αj p(k, Ωj ) bN YN
 N (Ω1 ) YN (Ω2 ) · · · YN (ΩL )


.
.
.
.
..
..
..
..


N
N
N
where, k = 2π
YN (Ω1 )
YN (Ω2 ) · · · YN (ΩL )
λ is the wave number, λ is the wavelength,
αj is a discrete integration weighting, Ωj , is the angular position of microphone j on the spherical microphone array,
M is the number of microphones in the spherical microwhere, Ωl = (θl , φl ) is the spherical angular position of phone array, p(k, Ωj ) is the pressure recorded by the miloudspeaker l in the spherical loudspeaker array, L is the crophone at position Ωj on the spherical microphone array,
number of loudspeakers in the spherical loudspeaker array, and bn (k, r, a), is defined as
Ynm (·) are the spherical harmonic functions defined as
µ
¶
jn0 (ka)
bn (k, r, a) = 4πi jn (kr) − 0
hn (kr) ,
hn (ka)
n
(5)
s
where r is the radius of the spherical microphone array, a is
2n + 1 (n − m)! m
P (cos θ)eimφ ,
the radius of the rigid spherical baffler, jn (·), jn0 (·), hn (·),
4π (n + m)! n
0
(3) and hn (·) are the spherical Bessel function, the spherical
and b is the spherical harmonic decomposition of the sound Hankel function of the second-kind, and their derivatives,
field recorded by the CRO-SMA, and for a system with or- respectively.
Page 3of 5
Ynm (Ω)
=
Ynm (θ, φ)
=
−6
−6
−4
−4
−2
−2
0
0
2
2
4
4
6
6
−5
0
5
−5
0
Metres
−1
−0.5
−0.5
0
0
0.5
0.5
1
1
5
−1
−0.5
Metres
(a) Meas., 100 Hz, 1st ord.
−0.6
−0.4
−0.4
−0.2
−0.2
0
0
0.2
0.2
0.4
0.4
0.6
0.6
0
0.5
−0.5
0
Metres
0.5
1
−1
−0.2
−0.2
−0.1
−0.1
0
0
0.1
0.1
0.2
0.2
0.5
−0.2
−0.1
0
0.1
0.2
−0.2
(g) Meas., 2.8 kHz, 3rd ord.
−0.1
−0.1
−0.1
−0.05
−0.05
0
0
0
0
0.1
0.1
0.05
0.05
0.2
0
0.1
0.2
0.1
−0.2
−0.1
Metres
0
0.1
0.2
−0.06
−0.06
−0.04
−0.04
−0.02
−0.02
0
0
0.02
0.02
0.04
0.04
0.06
0.05
Metres
(m) Meas., 10.0 kHz, 3rd ord.
−0.05
0
0.05
0.1
0.05
−0.1
−0.04
−0.02
−0.02
0
0
0.02
0.02
Metres
−0.02
0
0.02
0.04
Metres
(n) Theo., 10.0 kHz, 3rd ord.
0.2
−0.05
0
0.05
0.1
(l) Theo., 6.0 kHz, 3rd ord.
−0.04
0.04
−0.04
0.1
Metres
(k) Meas., 6.0 kHz, 3rd ord.
0.06
0
0
Metres
(j) Theo., 2.9 kHz, 3rd ord.
0
0.1
−0.05
Metres
(i) Meas., 2.9 kHz, 3rd ord.
−0.05
−0.1
1
(h) Theo., 2.8 kHz, 3rd ord.
−0.1
−0.1
0.5
Metres
−0.2
−0.2
−0.1
Metres
(f) Theo., 1.0 kHz, 3rd ord.
0
(d) Theo., 500 Hz, 2nd ord.
−0.2
0.2
−0.5
Metres
(c) Meas., 500 Hz, 2nd ord.
Metres
(e) Meas., 1.0 kHz, 3rd ord.
0
Metres
(b) Theo., 100 Hz, 1st ord.
−0.6
−0.5
−1
(o) Meas., 16.0 kHz, 3rd ord.
0.04
−0.04
−0.02
0
0.02
0.04
Metres
(p) Theo., 16.0 kHz, 3rd ord.
Figure 3: This figure shows, for the indicated frequencies and orders, a comparison of the measured sound field and
the ideal (theoretical) sound field. The plots show the relative linear sound field pressure level across two-dimensional
space. The lighter shades denote high pressure with white being the maximum pressure represented in each plot, and the
darker shades denote a lower pressure with black being the minimum pressure represented in each plot. Note that the size
of the area plotted is inversely proportional to the frequency, and thus becomes smaller with increasing frequency. The
horizontal and vertical scales are identical and both in metres.
Page 4of 5
3
RESULTS
The sound field recording and reproduction system has [7]
been tested at a number of frequencies of interest, and the
recorded sound field is compared to an ideal sound field
recording and reproduction system which has no error. The
incoming wave direction for the tests is at an azimuth and [8]
elevation of 0◦ which is on the horizontal plane directly in
front. Figure 3 shows the ideal and recorded sound fields
for the sound field recording and reproduction system at the [9]
frequencies and orders indicated. The plots show horizontal cross sections of the sound field at an elevation of 0◦ .
It should be noted that the term ideal is used to refer to an
ideal or theoretical decoding of a plane-wave sound field at
the indicated order and not an ideal plane-wave sound field. [10]
The open spherical microphone array is used for recording
and reproducing frequencies in the range 60 Hz to 2840 Hz
and the rigid spherical microphone array is used for recording and reproducing frequencies in the range 2840 Hz to [11]
16.0 kHz.
4
CONCLUSION
[12]
We have presented an initial evaluation of a third-order
sound field recording and reproduction system, with a frequency range of 60 Hz to 16 kHz, which uses as 64microphone CRO-SMA for recording and 24-loudspeaker
spherical loudspeaker array for reproduction. The initial results look promising and we are in the process of performing further perceptual and analytical tests on the system to
more fully characterise its performance.
REFERENCES
[1] T.D. Abhayapala and D.B. Ward. Theory and design
of high order sound field microphones using spherical
microphone array. In Proc. IEEE Int. Conf. on Acoustics, Speech, and Signal Proc., volume 2, pages 1949–
1952, 2002.
[2] S. Bertet, J. Daniel, E. Parizet, L. Gros, and O. Warusfel. Investigation of the perceived spatial resolution
of higher order ambisonic sound fields: A subjective evaluation involving virtual and real 3d microphones. In Proc. 30th AES Int. Conf., Saariselka, Finland, 2007.
[3] J. Daniel, J. Rault, and J. Polack. Ambisonics encoding of other audio formats for multiple listening conditions. In 105th AES Convention, San Francisco, CA,
USA, 1998.
[4] M.A. Gerzon. Periphony: With-height sound reproduction. J. Audio Eng. Soc., 21(1):2–10, 1973.
[5] R.H. Hardin and N.J.A. Sloane. Mclaren’s improved
snub cube and other new spherical designs in three
dimensions. Discrete and Computational Geometry,
15(4):429–441, 1996.
[6] Z. Li, R. Duraiswami, and L.S. Davis. Recording and
reproducing high order surround auditory scenes for
mixed and augmented reality. In Proc. Third IEEE
Page 5of 5
and ACM Int. Symposium on Mixed and Augmented
Reality, pages 240–249, 2004.
Z. Li, R. Duraiswami, and N.A. Gumerov. Capture
and recreation of higher order 3d sound fields via reciprocity. In 10th Meeting of the International Conference on Auditory Display, Sydney, Australia, 2004.
A. Parthy, C. Jin, and A. van Schaik. Optimisation
of co-centred rigid and open spherical microphone arrays. In 120th AES Conv., Paris, France, 2006.
A. Parthy, C. Jin, and A. van Schaik. Measured and
theoretical performance comparison of a co-centred
rigid and open spherical microphone array. In Int.
Conf. Audio, Language and Image Proc., pages 1289–
1294, July 2008.
A. Parthy, C. Jin, and A. van Schaik. Acoustic holography with a concentric rigid and open spherical microphone array. In Proc. IEEE Int. Conf. on Acoustics,
Speech, and Signal Proc., pages 2173–2176, 2009.
M.A. Poletti.
A unified theory of horizontal
holographic sound systems. J. Audio Eng. Soc.,
48(12):1155–1182, Dec. 2000.
D.B. Ward and T.D. Abhayapala. Reproduction of
a plane-wave sound field using an array of loudspeakers. IEEE Trans. on Speech and Audio Proc.,
9(6):697–707, 2001.
Was this manual useful for you? yes no
Thank you for your participation!

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Download PDF

advertising