HASSAN EL-BANNA ZIDAN
AND U. PETER SVENSSON, AES Member
Acoustics Group, Department of Electronics and Telecommunications, Norwegian University of Science and Technology, NO 7491, Trondheim, Norway
In a video conference setup, the microphone is often placed on a table and thus might act like a boundary, or pressure-zone, microphone. However, a table typically is small enough that the diffraction of its edges might significantly affect the frequency response, rather than give the ideal+6 dB effect. In this paper a microphone’s frequency response and directivity is studied using an edge diffraction-based calculation method. Measurements are done in an anechoic room. Comparisons between the calculated and measured frequency responses indicate that the simulation gives 1/3 octave-band levels that are typically within 1 dB of measured values. Furthermore, for a smaller table the response might be affected by several dB, but a larger table decreases these variations.
0 INTRODUCTION
The microphone is the first link of the electroacous- tic transmission chain in many communication systems such as audio/video conferencing and tele-presence sys- tems. Any loss of quality occurring at this stage, through the pick-up of too much reverberation, or extraneous noise, is very difficult to compensate for at subsequent stages. An audio/video conferencing situation is challenging because several sources will be active at more or less unknown lo- cations. In some installations fixed microphone positions might be chosen, e.g., hanging microphones from the ceil- ing. Hanging microphones might give relatively similar dis- tances to source/talker positions, with corresponding simi- lar levels, but they might also pick up problematic levels of background noise and reverberant sound.
A very common situation is that microphones are handled by the users without any sound engineer present, and then one of the few practical solutions is that microphones are placed on a table. Such a solution has some advantages as it is the idea behind boundary microphones (e.g., the Pres- sure Zone Microphone, PZM) [1]. A boundary microphone has its membrane mounted so close to a sound-reflecting plate or boundary that the microphone membrane receives direct and reflected sounds in phase at all frequencies of interest, avoiding negative interference between them. This doubles the pressure, so boosts the level by 6 dB for the di- rect sound and in addition, the directivity index is increased by +3 dB due to the shielding of the diffuse field. These speculative benefits apply if the microphone is placed on a
very large table and other significant early reflections are ignored. The effect of a finite-sized reflector on a bound- ary microphone is often described in handbooks and white papers on microphones [2,3, 4], but this effect seems not to have been studied quantitatively much. Probably, this is due to a lack of practical simulation methods. The boundary element method would be suitable for such studies but is computationally quite demanding for high-frequency stud- ies. This paper uses an edge diffraction-based method that permits low- and high-frequency studies with relatively little computational efforts. This approach has been used before for the study of the influence of loudspeaker cabi- nets. However, previous attempts have used high-frequency asymptotic methods [5], as well other edge-based methods [6], but here a formulation without asymptotic limitations is employed [7].
The effect of finite-sized reflectors is important and well- known in a number of situations: a microphone placed at a lecture podium, a near-field monitoring loudspeaker placed on top of a mixing console, the shape and size of a loud- speaker enclosure [5,8], the in-situ surface reflection factor measurement technique [9], auditorium ceiling reflectors [10], etc. Some of these cases have been analyzed to a large extent [5,8,10] but others have not. Therefore, the approach in this paper might prove useful also for other applications. Recently, the same edge diffraction-based method as in [7] has been used to study the influence of a loudspeaker’s finite baffle on its measured frequency response [11].
The paper is structured as follows. In Section 1, the pre- diction model that is based on an edge diffraction method
Microphone Diameter, D
(a)
(b)
Point reciever, elevated D/2 Point source
Fig. 1. (a) Illustration of a typical audio/video conference setup with a loudspeaker (representing a talking person) and a micro- phone (b) a simplified model
is explained. In Section 2 experiments and comparisons between the measurements and the predicted values are presented. Section 3 will show the results and conclusions are given in Section 4.
1 PREDICTION MODEL
The transfer function from a loudspeaker to a microphone on a table can be studied using the simplified model in Fig. 1. The simple representation of the microphone with a point receiver will not capture the directivity of the micro- phone at higher frequencies but will be adequate for a study of the influence of the table at low and middle frequencies. Furthermore the simple model of the loudspeaker will ob- viously not capture the directivity of the loudspeaker, but in this study only the direct sound of the loudspeaker will be observed. Certainly more elaborate models of the loud- speaker and the microphone could be expected to increase the accuracy, and a straightforward extension would be to represent the microphone with a number of discrete point receivers, and the loudspeaker might be modeled with a number of discrete point sources, possibly even placed at a box to represent the effect of diffraction of the loudspeaker box edges.
The situation in Fig. 1(b) can be accurately and effec- tively studied numerically with the edge diffraction method [7,11]. All the edges of the table are subdivided into edge elements and the edge diffraction method calculates first, second, and possibly higher order contributions as shown in Fig. 2.
Generally, the lower frequencies will require higher or- der diffraction but here second order diffraction has been satisfactory for the studied frequency range.
By this method it is possible to compute the impulse response and find the transfer function using the fast Fourier transform (FFT). In that way, the real response for the direct sound, rather than the ideal +6 dB response, can be found.
A second important quantity is the diffuse-field response. This can be dealt with by repeating the transfer function computation for all possible incidence angles (from a fur-
(a)
(b)
Fig. 2. Illustration of edge diffraction paths of (a), first order and (b), second order
Table 1. List of the tables used
Table Size L[m]× W[m] Used for
T1 1.2× 1.2 Anechoic room meas. & sim.
T2 3.2× 1.4 Simulations
ther distance) and compute the average squared response. Once the direct sound response and the diffuse field re- sponse are known, the directivity index can be computed.
The details of the edge diffraction calculation method can be found in [7]. Here, it suffices to say that the imple- mentation in the Edge diffraction toolbox for Matlab [12] was used, with a sampling frequency of 96 kHz. The tool- box uses an accurate numerical integration technique for the first-order diffraction components. For the second-order diffraction components, all edges were subdivided into 18 mm long elements and the simple midpoint numerical in- tegration scheme was used with a subsequent splitting of each element’s contribution into the two neighboring time samples [7].
2 EXPERIMENTS
In order to compare simulations with measurements, a rather small table (T1 in Table 1) was chosen where diffrac- tion effects are expected to be stronger than for a large table. Impulse responses were measured in an anechoic chamber using the WinMLS measurement software [13]. A small two-way loudspeaker (Genelec 1029A) was used and an omnidirectional free-field equalized half-inch microphone (Norsonic 1220) was positioned in sequence steps of half a meter placed on the table.
The influence of the frequency response of the loud- speaker and microphone was suppressed by first measuring with the microphone placed on the table and then repeat- ing the measurement without the table but with the mi- crophone positioned as similarly as possible relative to the loudspeaker. By dividing those two frequency responses by each other, the effect of the uneven response of the loud- speaker was largely removed.
1.2 m
Loudspeaker
1.2 m
Pos. 1: 0.04m from front edge Pos. 2: 0.54m from front edge Pos. 3: 1.04m from front edge
Fig. 3. Top view of table T1, with the loudspeaker and micro- phone positions used for simulations and for measurements in the anechoic chamber. 1. 6 Loudspeaker, Lsp 1 1.4 m 3. 2 m
Pos. 1: 0.5 m from front edge Pos. 2: 1.5 m from front edge Pos. 3: 2.5 m from front edge Lsp 2
Lsp 3
Fig. 4. Top view of table T2 with the loudspeaker and microphone positions used in the simulation study.
A separate, larger table (T2 in Table 1) was studied in simulations. A table size was chosen that might be used in small/medium video conference setups.
Fig. 3 shows the configurations of the loudspeaker and microphone for table T1 at the measurements in the ane- choic room. The loudspeaker was placed at a horizontal distance of 1.38 m from the table and a height of 0.78 m above the table (to the center of the woofer). The mi- crophone was placed in three positions as shown and the microphone was laid down on the table, so the microphone membrane was perpendicular to the table with its center at a height of 7 mm. Both the loudspeaker and the microphone were shifted 0.125 m away from the center axis.
Fig. 4 shows the table used in simulations, table T2, with a length of 3.2 m and a width of 1.4 m. The loudspeaker was placed in three different locations, representing possible talker’s locations. First location is at a horizontal distance of 0.5 m from the table front edge, a height of 0.4 m above the table, and sideways it was centered to the center axis of the table. The second and third locations are along the long sides of the table at a horizontal distance of 0.5 m from the side edge of the table and at the same height as Pos. 1: 0.4 m. The microphone was centered to the center axis of the table and placed in three positions. A boundary microphone was simulated with the membrane at 1 mm height above the table.
3 RESULTS
3.1 Verification of Simulation Method with Small Table T1
Fig. 5 shows the measured frequency responses in the anechoic room and the simulations done using the edge
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Meas., pos. 3 (+10 dB) Meas., pos. 2 (+5 dB) Meas., pos. 1 Sim., pos. 3 (+10 dB) Sim., pos. 2 (+5 dB) Sim., pos. 1Fig. 5. Measured and simulated frequency responses of a mi- crophone on table T1 in an anechoic room. The responses are 1/3 octave band smoothed and the thin solid lines represent the ideal +6 dB. Note that two of the curves have been shifted, and grid lines have been removed, for clarity.
diffraction prediction model. As described in Section 3, the free-field response of the loudspeaker was measured separately and used to suppress the effect of the loudspeaker and microphone response.
It can be noticed that the simulations are very close to the measurements. Between 200 Hz and 10 kHz the differ- ence is on average 0.94 dB. Apparently the simple point source modeling worked well. Furthermore, the +6 dB can- not be practically achieved across all the frequencies for a relatively small sized table.
This comparison confirms that the edge diffraction method can predict quite accurately the effect of a table on the microphone’s frequency response.
3.2 Diffuse Field Response for the Microphone on the Small Table T1
In a reflective room, the ideal +6 dB for the direct sound is complemented by an ideal +3 dB for a dif- fuse incidence sound field. In order to simulate the dif- fuse field response in an anechoic room, a set of 1000 sources regularly distributed over a sphere (of radius 1000 m) around each one of the three microphone positions is constructed.
The simulated response, for all incidence angels, was squared and averaged for each microphone position and the results are shown in Fig. 6. Also for the diffuse field response, the table causes quite a deviation from the ideal +3 dB. At high frequencies, the microphone height of 7 mm causes a strong roll off around 10 kHz.
3.3 Simulations for Typical Table Size, T2, Distributed Talkers and a True Boundary Microphone
Simulations were done to investigate the effect of a slightly larger and more realistically sized table, table T2, on the direct sound for different positions of talkers around the table.
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Sim. pos 1 + 10 dB Sim. pos 2 + 5 dB Sim. pos 3Fig. 6. Simulations of the effect of placing a microphone on table T1 on the average/diffuse field frequency response. The responses are 1/3 octave bands smoothed and the thin solid lines repre- sent the ideal +3 dB. Note that two of the curves are shifted for clarity.
Figs. 7 (a)–(c) show the simulation results for the three loudspeaker/talker positions around the table as illustrated in Fig. 4.
Comparisons can be made between the results for the slightly larger table in Figs. 4 and 7 and the smaller table in Figs. 3 and 5.
First, it is clear that placing a microphone at 1 mm height rather than 7 mm height reduces the high-frequency dip as can be seen in Figs. 7(a)–(c). Furthermore, the low- frequency roll-off, which was prominent in Fig. 5, is quite substantial also for the lager table T2 in Fig. 7.
For the studied case, it seems that this roll-off starts from a peak around 2 kHz except for positions 1 and 2 in Fig. 7(a), where the roll-off starts at a lower frequency. Apparently, where this “cut-off frequency” ends up will depend on the arrival times of the two distinct diffraction contributions, from the two edges that are perpendicular to the line from loudspeaker to microphone. The longer the distance to these two edges, the further down in frequency this roll-off can be pushed.
Finally, the general unevenness of the response is around –3 dB to +2 dB relative to the ideal +6 dB response, in the frequency range from 200 Hz to 10 kHz.
4 CONCLUSIONS
From the measurements done in the anechoic room, the simulation method used was confirmed to be accurate, with average deviations for 1/3-octave band smoothed response being around 0.9 dB from 200 Hz to 10 kHz. Conference ta- bles might, due to the finite size, lead to frequency response variations for the direct sound of+/− 2–3 dB within the frequency range 200 Hz to 10 kHz. For smaller tables, or reflectors, variations could be even larger.
As expected, the boundary microphones need to be very close to the table surface (few mm) in order to avoid clear high-frequency roll-off effects.
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Sim. pos. 3 (+10 dB) Sim. pos. 2 (+5 dB) Sim. pos. 1Fig. 7. Simulated frequency responses of a microphone placed on table T2. The responses are 1/3 octave band smoothed and the thin solid lines represent the ideal +6 dB for (a) Loudspeaker 1, (b) Loudspeaker 2, (c) Loudspeaker 3. Note that two of the curves in each diagram have been shifted for clarity.
5 REFERENCES
[1] J. Eargle, The Microphone Book, second edition (Fo- cal Press, Burlington, MA, USA , 2004).
[2] Boundary Microphone Application Guide: Boundary
Microphone Theory and Applications for Crown Bound- ary Microphones: MB, PCC and PZM Series (Crown Inc.,
Elkhart, IN, USA , 2000).
[3] Boundary Layer Solutions for Installed Sound (AKG Inc., Northridge, CA, USA ).
[4] The Directional Boundary Microphone (Bartlett Mi- crophones Inc., Elkhart, IN, USA, 2009).
[5] J. Vanderkooy, “A Simple Theory of Cabinet Edge Diffracton,” J. Audio Eng. Soc., vol. 39, pp. 923–933 (1991 Dec.).
[6] M. Urban, C. Heil, C. Pignon, C. Combet, and P. Bauman, “The Distributed Edge Dipole (DED) Model for Cabinet Diffraction Effects,” J. Audio Eng. Soc. vol. 52, pp. 1043–1059 (2004 Oct.).
[7] U. P. Svensson, R. I. Fred, and J. Vanderkooy, “An Analytic Secondary Source Model of Edge Diffraction Im- pulse Responses,” J. Acoust. Soc. Am., vol. 106, no. 5, pp. 2331–2344 (1999).
[8] H. F. Olson, “Direct Radiator Loudspeaker Enclo- sures,” J. Audio Eng. Soc., vol. 17, pp. 22–29 (1969 Jan.).
[9] E. Mommertz, “Angle-Dependent In-Situ Measure- ments of Reflection Coefficients Using a Subtraction Technique,” Appl. Acoust., vol. 46, no. 3, pp. 251–263 (1995).
[10] M. Long., Auditorium Acoustics (Academic Press, Boston, MA, USA , 2005).
[11] Y. Le, Y. Shen, and L. Xia, “A Diffractive Study on the Relation between Finite Baffle and Loudspeaker Measurement,” J. Audio Eng. Soc, vol. 59, pp. 944–952 (2011 Dec.).
[12] http://www.iet.ntnu.no/∼svensson/software/ [13] www.winlms.com
THE AUTHORS
Hassan Zidan Peter Svensson
Hassan EL-Banna Zidan was born in Cairo, Egypt, in 1975. He received a B.Sc. and a M.Sc. in electronics and telecom- munications engineering in 1998 and 2007 both from the Arab Academy for Science, Technology, and Maritime Transport (Alexandria/Cairo). Since 2008 he has been a Ph.D. candidate in the Acoustics group at the Norwegian University of Science and Technology (NTNU), Trond- heim, Norway. His research interests include audio signal processing, speech enhancement and room acoustics.
r
Peter Svensson received a M.Sc. degree in engineering physics in 1987 and a Ph.D. degree in 1994, both from Chalmers University of Technology, Gothenburg, Sweden. He has held postdoctoral positions at Chalmers Univer- sity, University of Waterloo, Ontario, Canada, and Kobe University, Japan. Since 1999 he has been a professor in
electroacoustics at the Norwegian University of Science and Technology, Trondheim, Norway. His main research interests are auralization, especially computational room acoustics and sound reproduction techniques, measurement techniques, and perceived room acoustical quality.
Prof. Svensson has published 33 journal papers and more than 100 conference papers. He is currently vice president of the European Acoustics Association and a past president of the Norwegian Acoustical Society. He is an associate ed- itor in the field of electroacoustics for Acta Acustica united with Acustica. In 2001 he received a best paper award, together with Johan L. Nielsen, for authors 35 years or younger from the Journal of the Audio Engineering Soci-
ety and in 2009 a best paper award from the IEEE Workshop
on Applications of Signal Processing to Audio and Acous- tics (WASPAA), together with Haohai Sun and Shefeng Yan.