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where r = |X — X’| is the distance from the source to an arbitrary field point and c is the wave propagation speed.

Figure 2 where r = |X — X’| is the distance from the source to an arbitrary field point and c is the wave propagation speed.

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Figure 2: Delay-and-sum beamforming. Figure 1: Simple five microphone array, point monopole source.
Figure 2: Delay-and-sum beamforming. Figure 1: Simple five microphone array, point monopole source.
Figure 3: Frequency domain beamforming method. Other advanced techniques can be found in [5, 6, 7].
Figure 3: Frequency domain beamforming method. Other advanced techniques can be found in [5, 6, 7].
Figure 4: Virtual grid on vehicle’s sideline. The blur effect is caused by the constant change of angles in the integration time. The fluctuation of frequency and amplitude, are caused by the approaching and displacing of the sound source to array’s position. Due to this issue a de-dopplerization procedure was adopted (further informations could be consulted in Fonseca, 2009 [10]). The procedure consists in creating a virtual grid on vehicle’s sideline. This means the virtual grid moves with the vehicle and each grid point is a potential moving acoustic source, Figure 4.
Figure 4: Virtual grid on vehicle’s sideline. The blur effect is caused by the constant change of angles in the integration time. The fluctuation of frequency and amplitude, are caused by the approaching and displacing of the sound source to array’s position. Due to this issue a de-dopplerization procedure was adopted (further informations could be consulted in Fonseca, 2009 [10]). The procedure consists in creating a virtual grid on vehicle’s sideline. This means the virtual grid moves with the vehicle and each grid point is a potential moving acoustic source, Figure 4.
Figure 5: Beamforming data without de-dopplerization. In order to gain a better understanding of the de-dopplerization method, a comparison between two results for the same measurement at the same frequency is presented. The Figure 5 shows the result without correction of the Doppler effect, which is blurred and the amplitude does not express the real value of the pressure. Alternatively the Figure 6 shows the same result with de-dopplerization method applied.
Figure 5: Beamforming data without de-dopplerization. In order to gain a better understanding of the de-dopplerization method, a comparison between two results for the same measurement at the same frequency is presented. The Figure 5 shows the result without correction of the Doppler effect, which is blurred and the amplitude does not express the real value of the pressure. Alternatively the Figure 6 shows the same result with de-dopplerization method applied.
Figure 6: Beamforming data with de-dopplerization. The Figures 5 and 6 are from the same measurement. This measurement was performed with buzzer, this is the reason the Figure 6 has only one direct sound source and a part of the reflection on the ground.
Figure 6: Beamforming data with de-dopplerization. The Figures 5 and 6 are from the same measurement. This measurement was performed with buzzer, this is the reason the Figure 6 has only one direct sound source and a part of the reflection on the ground.
Figure 8: Magnitude: Microphones against Mic. #45. A total of 50 microphones were built. The Figure 8 shows the magnitude relative response and the Figure 9 the phase relative response. Analyzing these two Figures the 32 more similar microphones were selected for use. The unshaded area shows the selection criterion.
Figure 8: Magnitude: Microphones against Mic. #45. A total of 50 microphones were built. The Figure 8 shows the magnitude relative response and the Figure 9 the phase relative response. Analyzing these two Figures the 32 more similar microphones were selected for use. The unshaded area shows the selection criterion.
Figure 9: Phase: Microphones against Mic. #45. It is possible to notice that up to frequencies of 14k Hz the deviations inside the unshaded part are small, i. e., +2.5dB V in magnitude and +4° in phase. Some microphones were discarded by phase and some others by magnitude criterion.
Figure 9: Phase: Microphones against Mic. #45. It is possible to notice that up to frequencies of 14k Hz the deviations inside the unshaded part are small, i. e., +2.5dB V in magnitude and +4° in phase. Some microphones were discarded by phase and some others by magnitude criterion.
Figure 7: (a) Microphone model. (b) Tool for evaluation of relative microphone responses.
Figure 7: (a) Microphone model. (b) Tool for evaluation of relative microphone responses.
Figure 10: Microphone #45: Sensibility x Temperature. Measurements and Linear regression.
Figure 10: Microphone #45: Sensibility x Temperature. Measurements and Linear regression.
The array was built with an aluminum structure and its dimensions are 1.5 x 1.2 m. A spiral based geometry with diameter of 1.0 m was utilized in all the results presented in this work. The 32 microphones are mounted in this structure which can be considered acoustically transparent up to frequencies near 15k Hz. The Figure 11 shows the complete array. Figure 11: The 32 microphone spiral array.
The array was built with an aluminum structure and its dimensions are 1.5 x 1.2 m. A spiral based geometry with diameter of 1.0 m was utilized in all the results presented in this work. The 32 microphones are mounted in this structure which can be considered acoustically transparent up to frequencies near 15k Hz. The Figure 11 shows the complete array. Figure 11: The 32 microphone spiral array.
Figure 12: Data acquisition system. (a) NI-9233, 4 channels. (b) NI-cDAQ-9172 with 8 modules. The data acquisition system is based on National Instruments [16, 17] portable hardware which can acquire 32 channels simultaneously at a rate of 50k Hz, Figure 12. All the beamforming measurements were performed with this maximum rate.
Figure 12: Data acquisition system. (a) NI-9233, 4 channels. (b) NI-cDAQ-9172 with 8 modules. The data acquisition system is based on National Instruments [16, 17] portable hardware which can acquire 32 channels simultaneously at a rate of 50k Hz, Figure 12. All the beamforming measurements were performed with this maximum rate.
Figure 14: Phase: Channel 1, module | against all 31 channels. The Figure 13 shows the magnitude and the Figure 14 shows the phase between the channel 1 of the module | against all the 31 others channels. All the deviations evaluated are below the manufacturer specifications.
Figure 14: Phase: Channel 1, module | against all 31 channels. The Figure 13 shows the magnitude and the Figure 14 shows the phase between the channel 1 of the module | against all the 31 others channels. All the deviations evaluated are below the manufacturer specifications.
Figure 15: Pass-by Noise Test, standard layout [19]. The Pass-by Noise Test is a standardized test described in the standard ISO 362-1:2007 [19]. This test evaluates the sound pressure level of two microphones positioned 7.5 m far from the central line of the car’s path, Figure 15. Every vehicle has to pass this test and satisfy the limits to join the vehicles market.
Figure 15: Pass-by Noise Test, standard layout [19]. The Pass-by Noise Test is a standardized test described in the standard ISO 362-1:2007 [19]. This test evaluates the sound pressure level of two microphones positioned 7.5 m far from the central line of the car’s path, Figure 15. Every vehicle has to pass this test and satisfy the limits to join the vehicles market.
Figure 13: Mag.: Channel 1, module | against all 31 channels.
Figure 13: Mag.: Channel 1, module | against all 31 channels.
Figure 17: Pass-by Noise Test, beamforming layout. 3D View.
Figure 17: Pass-by Noise Test, beamforming layout. 3D View.
Figure 16: Pass-by Noise Test, beamforming layout. The procedures of acceleration and displacement were preserved the same as described in the ISO362-1:2007. The array positioning was the same as the single microphone position in the standardized test, i.e., 7.5 m from the central line with its center 1.2 m from the ground. The data used in the post processing were cut and de-dopplerized from -5.0 m to +5.0 m, considering the array’s central line, Figures 16 and 17.
Figure 16: Pass-by Noise Test, beamforming layout. The procedures of acceleration and displacement were preserved the same as described in the ISO362-1:2007. The array positioning was the same as the single microphone position in the standardized test, i.e., 7.5 m from the central line with its center 1.2 m from the ground. The data used in the post processing were cut and de-dopplerized from -5.0 m to +5.0 m, considering the array’s central line, Figures 16 and 17.
Figure 18: H3 Silver: LR, 1.3k Hz, 1/12 octave band. Two different models of Hummer H3 were measured and some of their results are presented from Figure 18 to Figure 21. The differences between these models include engine and exhaust system.
Figure 18: H3 Silver: LR, 1.3k Hz, 1/12 octave band. Two different models of Hummer H3 were measured and some of their results are presented from Figure 18 to Figure 21. The differences between these models include engine and exhaust system.
Figure 19: H3 Yellow: LR, 1.3k Hz, 1/12 octave band. It is possible to observe in the case of LR that the overall noise is quite the same, however the prominent sources are different. The engine noise is dominant in relation to the exhaust system, this is more evident in the Figure 19 than the Figure 18.
Figure 19: H3 Yellow: LR, 1.3k Hz, 1/12 octave band. It is possible to observe in the case of LR that the overall noise is quite the same, however the prominent sources are different. The engine noise is dominant in relation to the exhaust system, this is more evident in the Figure 19 than the Figure 18.
Figure 21: H3 Yellow: RL, 1.3k Hz, 1/12 octave band. Figure 20: H3 Silver: RL, 1.3k Hz, 1/12 octave band.
Figure 21: H3 Yellow: RL, 1.3k Hz, 1/12 octave band. Figure 20: H3 Silver: RL, 1.3k Hz, 1/12 octave band.
Now in the case of RL the end of the exhaust system has a greater contribution than the LR, Figures 20 and 21.
Now in the case of RL the end of the exhaust system has a greater contribution than the LR, Figures 20 and 21.
Figure 22: Gol: LR, 1k Hz, 1/12 octave band. A Volkswagen Gol was measured and it is important to know that its engine, suspension and exhaust system are not the originals. This vehicle has a very characteristic noise, two results are presented, Figures 22 and 23.
Figure 22: Gol: LR, 1k Hz, 1/12 octave band. A Volkswagen Gol was measured and it is important to know that its engine, suspension and exhaust system are not the originals. This vehicle has a very characteristic noise, two results are presented, Figures 22 and 23.
Figure 23: Gol: RL, 1k Hz, 1/12 octave band. This vehicle has only two strong sources, the engine and the end of the exhaust system, one in each side of the vehicle. All the others possible sources are not able to identify due to its modified characteristics. Its “purr” noise is very strong and even in other frequencies only these two sources are noticed.
Figure 23: Gol: RL, 1k Hz, 1/12 octave band. This vehicle has only two strong sources, the engine and the end of the exhaust system, one in each side of the vehicle. All the others possible sources are not able to identify due to its modified characteristics. Its “purr” noise is very strong and even in other frequencies only these two sources are noticed.
Related topics:
InstrumentationMicrophone ArraysPass-by Noise
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