A digital impulse-weighting method for a sound level meter

Accepted Manuscript A digital impulse-weighting method for a sound level meter Haijun Lin, Qiu Tang, Jing Li, Zhaosheng Teng, Huan Chen PII: DOI: Reference:

S0263-2241(18)31207-7 https://doi.org/10.1016/j.measurement.2018.12.063 MEASUR 6197

To appear in:

Measurement

Received Date: Revised Date: Accepted Date:

3 November 2017 5 December 2018 17 December 2018

Please cite this article as: H. Lin, Q. Tang, J. Li, Z. Teng, H. Chen, A digital impulse-weighting method for a sound level meter, Measurement (2018), doi: https://doi.org/10.1016/j.measurement.2018.12.063

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A digital impulse-weighting method for a sound level meter Haijun Lin1, Qiu Tang2, Jing Li2, Zhaosheng Teng2, and Huan Chen2 (1.School of Engineering and Design, Hunan Normal University, Changsha, 410081, China; 2. School of Electrical and Information Engineering, Hunan University, Changsha, 410082, China)

Abstract—This paper presents a new digital impulse-weighting (I-weighting) method for sound level meter by using a peak detector with attenuator. Firstly, the decay rate of time-weighting algorithm is analyzed, and it is proved that the decay rates of the existing time-weighting models (i.e., the fast-time-weighting model and the slow-time-weighting model) cannot meet the requirements of the I-weighting algorithm of the sound level meter defined by the international standard IEC61672. A new digital I-weighting model is constructed by designing a peak detector with attenuator and amending the existing timeweighting model. Finally, the detailed digital I-weighting algorithm is given. The experimental results of this proposed Iweighting model show that the model’s detection behaviors and decay rates all meet the requirements of class 1 sound level meters defined by IEC61672. Keywords—sound measurement; sound level meter; digital impulse-weighting algorithm; decay rate

1 INTRODUCTION Noise is one of the main pollution sources which can adversely affect the people's normal work, rest, physical and mental health[1,2]. There are many types of noises, but impulse noise is more harmful than steady-state noise. For example, the impulse noise from the gunfire on the battlefield or the transient loud noise from the explosions will make people temporarily deaf or even deaf[3]. Considering the bad damage of impulse noises, some scholars have proposed some methods for assessing the related hearing loss. Patterson et al [4] used the impulse noise energy to evaluate the degree of hearing loss, which is defined as the ratio of the square integration of the instantaneous sound pressure to the air acoustic impedance. Price[5] found that the noises of howitzer and rifle would cause the offset of the temporary hearing threshold, but the energies of these two noises mentioned above are different. Therefore, Price believed that the noise energy should not be independently used as a criterion for hearing loss. Erdreich[6] and Hamernik[7] et al suggested that the Kurtosis coefficient was used to describe the "impulse degree" of impulsive noise, where, the Kurtosis coefficient is defined as the ratio of the fourth order central moment of the instantaneous sound pressure to the square of its variance. Lei et al [8] considered that the Kurtosis coefficient combined with the equivalent sound level could predict the hearing loss. These assessment methods mentioned above are all aimed at the characteristics of impulse noise itself. Price and Kalb[9] established the electro-acoustic model of human ear contour and internal structure, and then proposed an auditory hazard assessment algorithm for humans (AHAAH) based on the human auditory model. In AHAAH, the daily acceptable fully recoverable noise dose is 500 ARUs (auditory risk units). At present, AHAAH has been used to assess the hearing loss during airbags deployment by the American Association of Automotive Engineers[10]. The US Army Research Laboratory has developed a PC software based on AHAAH, which currently can be downloaded on www.arl.army.mil/ahaaah. A sound level meter is used to measure sounds such as road traffic, engines, the work environment, etc[11-15]. For different noise signals, the slow weighting (S), the fast weighting (F) and the impulse weighting (I) are recommended to measure the noises with different time weightings by IEC61672 [16]. In these three different cases, the S weighting is used to measure steady noises (time constant τ = 1s), and the F weighting is used to measure unsteady noises (e.g., the 

Corresponding author. Tel: +86-13077368836; E-mail: [email protected];

1

traffic noises), (τ=125ms), while the I weighting is used to measure impulse noises (e.g., the noises from punch, hammer, etc), (τ=35ms). The digital models of S and F time-weighting algorithms currently have been implemented in sound level meters, which can perfectly meet the requirements of class 1 sound level meters. However, the I time weighting currently is implemented by analog circuits in sound level meters, and there is no a useful digital algorithm. The analog I timeweighting circuit has some drawbacks, such as large errors and difficult to compensate errors. The digital S-weighting model and the digital F-weighting model offer a reference model of I time weighting, but these two decay rates are too fast to meet the requirement of the I-weighting decay rate which is 2.9dB/s, which cannot effectively test and evaluate the responses of the human ear for impulse noises. Therefore, the existing S-weighting algorithm and the F-weighting algorithm are should be amended for the I weighting. In this paper, a new digital I-weighting model combined a peak detector with attenuator is proposed, and its performances are effectively improved. The remainder is organized as follows. In section II, we discuss the principle of the time-weighting algorithm. In section III, the digital I-weighting model is described in detail. The results of our experimental studies are explained in section IV. Finally, we conclude this paper with a brief summary in section V.

2

2 PRINCIPLE OF THE TIME-WEIGHTING ALGORITHM For different noise signals, the three time weightings, i.e., the S weighting, the F weighting and the I weighting, are respectively recommended by IEC61672 to measure different noises in sound level meters. Where, the S weighting is used to measure steady noises (the time constant τ=1s), and the F weighting is used to measure unsteady noises and traffic noises (τ=125ms), while the I weighting is used to measure impulse noises (τ=35ms). According to IEC61672[16], the time-weighting sound level is represented by 12 t     t   2 LA  t   20 lg  1    p A   e d     

  p0  , 

(1)

where, LAτ(t) is the time-weighting sound level with A weighting (A weighing is a frequency weighing); τ is the time constant of I (35ms), F (125ms) and S (1s), respectively; ξ is a dummy variable of integration which is indicated as (-∞, t ]; pA(ξ) is the A-weighting instantaneous sound pressure, and p0 is the reference sound pressure (p0=20μPa). According to IEC61672, the time-weighting sound level can be obtained by square operating, low-pass filtering (LPF), root square operating and logarithm operating. The time-weighing model is shown in Fig.1, where, LPF has a real pole at -1/τ. pA

 

LPF

2

 

20 lg  

LA

Fig.1. Time-weighting model 2.1 Response Time of Time Weighting 2

In Eq. (1), if e-(t-ξ)/τ is regarded as a weight of the square of the A-weighting sound pressure p A , we can get W 

e

t

  t   





d  1 .

(2)

From Eq. (2), we can find that the total weight of p A is constant to 1. Dividing PA2   2

2

1

1

e

  t   /  1

into two

2

components, i.e., one is the part before zero time p1A , and the other is the part after zero time p2 A , we can obtain some equations as follows:  t  /   2 0 e  1 2 d  P1 A   PA   1  .   t  /  e  1  2  t 2 d  P2 A 0 PA     1

（3）

2

According to Eq.(1), the sum of weight of p1A is given by W1  

0



e

  t   / 



d   et / .

（4）

From Eq.(4), we can find that the larger the measurement time t, and the closer the W1 will is to zero, which indicates that the effect of the excitation before zero time on the A-weighting sound level is smaller and smaller, i.e., the zeroinput response of the sound level meter is getting weaker and weaker. When t=5τ, W1=e-5≈0.0067. In this case, the response of the sound level meter will be ignored, i.e., the system is steady. For the F weighting, the steady time t=5τ=625ms, but it is 125ms for the I weighting. 3

2.2 Decay Rate of Time Weighting Assuming that an A-weighting instantaneous sound pressure is hA(t), and according to Eq.(1), the time-weighting sound level with A weighting at time t is described as 12 t   t     LA  t   20 lg  1    hA2   e  d   p0  .     

(5)

According to the testing requirements of IEC61672, after suddenly stopping inputting signals, the time-weighting sound level described as Eq.(5) during the time interval T is given by 12  t  T      t T  2  ˆ LA  t  T   20 lg  1    hA   e d     

  p0  , 

(6)

where,  t h (t ) . hˆA ( )   A t   t T  0

(7)

Considering Eqs. (5) and (6), we can obtain the decay D(T) of time-weighting algorithm when t<ξ
dD T  dT

  0.035



10



lg  e 

  0.035

 124.1dB .

(9)

From Eqs. (8) and (9), we can find that the decay rate of the time-weighting algorithm is constant, and the Iweighting decay rate is about -124.1dB/s, which is far more than -2.9dB/s (the standard of the I-weighting decay rate defined by IEC 61672 is not more than -2.9dB/s). Therefore, it is necessary that a new I-weighting model is constructed to meet the requirement of IEC 61672.

3 DIGITAL I-TIME-WEIGHTING ALGORITHM For meeting the requirement of I-weighting decay rate defined by IEC61672, a peak detector with attenuator is added into the existing time-weighting model, which is shown in Fig.2. The peak detector with attenuator is mainly composed of a peak detector, an attenuator and a comparator. This peak detector is used to slowly attenuate the output of the lowpass filter and its time constant is 1500ms according to IEC61672. pA

 

2

 1 =35ms LPF

Peak detector with attenuator

p

2 A

attenuator Comparator

LA

20 lg  

p02

 

2 1

p

 2 =1500ms

p02

Fig.2. Model of I-weighting algorithm 3.1 Low-Pass Filter in I-Weighting Algorithm In I-weighting model, the structure of low-pass filter (LPF) is the same as the F-weighting model and S-weighting model, but the time constant of I-weighting model is 35ms. From Eq. (1), we can get the low-pass filter as follow: t

p A2  t   1    p A2   e t    d  , 

4

(10)

From Eq.(10), we can find that p A2 is essentially the convolution of the p A2 and p A2  t   p A2  t   1   e t   p A2  t   h  t  ,

1



e t  , i.e.,

(11)

where, h(t)=(1/τ)e-t/τ. According to the convolution theorem, the Laplace transform of Eq. (11) is represented by 1 1 , (12) PA2  s   PA2  s  H  s   PA2  s   s 1  i.e., PA2  s   PA2  s    sPA2  s  .

(13)

By Laplace inverse transform, Eq.(13) is rewritten as p A2  t   p A2  t   

dp A2  t  dt

.

(14)

After discretizing and simplifying, Eq.(14) is rewritten as follows: 1  / t 2 p 2A (n)  p A2  n   p (n  1) , 1   / t 1   / t A where, n=1,2,3…N, t is the sampling time, τ=35ms. Assuming that  

(15)

1 , Eq.(15) can be simplified as 1   / t p 2A (n)   p A2  n   (1   ) p 2A (n  1) .

(16)

Eq.(16) is the digital low-pass filter model in the I weighting algorithm. 3.2 Peak Detector with Attenuator An I weighting is usually performed by an analog circuit in sound level meter. In this paper, for implementing Iweighting algorithm, we firstly design an analog peak detector, and then propose a digital peak detector with attenuator by digitalization. According to requirements of I weighting defined by IEC61672, we can design an analog peak detector with attenuator, which is shown in Fig.3. In this circuit, R2 should be small so that C can quickly be charged, but R3 should be large, and R3>>R2 and R3C=τ1=1500ms. If p A2 (t )  U C (t ) , D1 will turn on. In this case, the capacitor C will be quickly charged, and its voltage Uc(t) is represented by t   U C  t   U C  0   U1  0   U C  0   1  e R2C  

 ,  

(17)

where, U1(0) and Uc(0) are respectively the initial values of U1 and Uc when D1 turns on. Because R2 is small, C is quickly charged, and Uc=U1, i.e., po2  t   U c (t )  U1 (t )  p A2  t  .

(18)

After discretizing, Eq. (18) is rewritten as po2  n   p A2  n  .

5

(19)

Fig.3. Circuit model of the peak detector with attenuator When p A2 (t )  U c (t ) , D1 will be turn-off, and the capacitor C will slowly discharge through R3, i.e., p02 (t )  U C  t   U C  0  e



t R3C

 p02  0  e



t

1

,

(20)

where, U C  0  is the initial voltage of U C when D1 is turn-off, po2 (0) is the initial value of po2 . Similarly, after discretizing, Eq.(20) is transformed into as follows: po2  n   po2 (0)e



nt

1

 po2 (n  1)e



t

1

  po2 (n  1) ,

(21)

where, po2 (n  1) is the value of po2 at n-1th time, Δt is the sampling time interval, t=nΔt, n is the number of sampling the sound signal, and   e



t

1

.

In summary, the output of the digital peak detector with attenuator is given by  p 2 (n), if p 2A (n)   po2 (n  1);  po2  n    2A 2 2    po (n  1), if p A (n)   po (n  1).

(22)

3.3 Implementation of the Digital I-Weighting Algorithm The major steps of the digital I-weighting algorithm can be summarized as follows: Step 1: Calculating A-weighting sound pressure p A (n) . We can firstly obtain the sound pressure p(n) by sampling the sound signal p from microphone, and then get the A-weighting result p A (n) by using an A-weighting filter. This filter is defined by IEC 61672. Step 2: Obtaining square of p A (n) , which is p 2 (n) ; A

Step 3: Filtering p (n) by using Eq.(16) and obtaining p A2  n  , where, p A2  0  =0; 2 A

Step 4: Detecting the peak of p A2  n  by using Eq.(22), and then obtaining the result of the I-weighting algorithm po2  n  ;

Step 5: Solving the root and the logarithm, and then obtaining the I-weighting sound pressure level LAI(t).

4 EXPERIMENTAL STUDY 4.1 I-Weighting Experimental Platform For verifying the I-weighting algorithm, we developed an experimental platform with a digital sound level meter (DSLM). The hardware diagram of DSLM is shown in Fig.4. The external noise sound pressure is transformed into a voltage signal by the electret capacitor microphone, and then the digital voltage signal will be obtained by matching impedance, amplifying signal and analog-digital converter (ADC). Where, ADC uses PCM1804, which is a 24-bit dualchannel professional audio processing chip. The digital voltage signal is processed by microprocessor STM32F407 with frequency-weighing algorithm, time-weighting algorithm, root operation and logarithm operation, and then the 6

sound pressure level is obtained. SD Card

E2PROM

USB

LCD

Keyboard

Signal Processing Unit (STM32F407) Microphone Impedance matching

Signal conditioning circuit

ADC (PCM1804)

Fig.4. Hardware diagram of the sound level meter According to IEC61672[16], the toneburst signals with frequency of 4 kHz are needed to test the I-weighting algorithm, where, the toneburst signals are transient sinusoidal electrical signals with one or more complete cycles and they are generated by special toneburst instruments. The I-weighting experimental platform is shown in Fig.5, which is mainly including a standard signal generator, an adjustable attenuator, a sound level meter, etc. The signal generator can provide stable sinusoidal electrical signals and the transient toneburst signals. The attenuator can attenuate the testing signals with 1dB as step.

Fig.5. Experimental platform of I-weighting algorithm 4.2 Testing the Decay Rate of I-Weighting Algorithm We can test the decay rate of the peak detector of this proposed digital I-weighting algorithm by using the 4kHz sinusoidal electrical signals. The experimental procedure is described as follows: (1) Inputting the stable 4kHz sinusoidal electrical signals and adjusting their amplitude to the upper limit (i.e., 130dB); (2) Suddenly interrupting the input signals after the indication of the sound level meter is steady; (3)Storing the I-weighting sound level LAI at the intervals of 1s until the indication of this sound level is close to the lower bound. The testing results of the decay rates of this proposed digital I-weighting algorithm are given in Table. 1. Table.1 Testing results of I-weighting decay rates Time indication Time indication Time Indication (seconds) (dB) (seconds) (dB) (seconds) (dB) 1 127.5 12 95.7 23 63.8 2

124.6

13

92.8

24

60.9

3

121.7

14

89.9

25

58.0

4

118.8

15

87.0

26

55.1

5

115.9

16

84.1

27

52.2

7

6

113.0

17

81.2

28

49.3

7

110.1

18

78.3

29

46.4

8

107.2

19

75.4

30

43.5

9

104.3

20

72.5

31

40.6

10

101.4

21

69.6

11 98.5 22 66.7 From Table.1, we can find that some conclusions as follows: (1) The total attenuation is 86.9dB in 30s (the first and the last is 127.5dB and 40.6dB, respectively, and the total attenuation is that 127.5-40.6=86.9dB), and the average decay rate is about 2.90dB/s, which meets the requirements of the I-weighting decay rate defined by IEC61672. In IEC61672, the decay rate is required 2.9dB/s. (2) The average error of the decay rate is about 0.0dB in 30s (i.e., the difference of the average decay rate and the decay rate specified by IEC 61672), which is far less than the requirement error (0.8dB/s) of decay rate defined by IEC 61672. (3) The attenuation (i.e., the difference) between adjacent two indications is 2.9dB/s except that between the 11th second and 12th second (shown as the gray area in Tab.1, the attenuation is that 98.5-95.7=2.8dB/s). Therefore, this digital I-weighting algorithm has a good linear attenuation, and its linear error of the maximum decay rate is 0.1dB/s (i.e., 2.9dB/s-2.8dB/s=0.1dB/s), which is far smaller than the requirement error (0.8dB/s) defined by IEC 61672. 4.3 Testing I-Weighting Algorithm by Single Toneburst Signal This proposed digital I-weighting algorithm is tested by using a single toneburst signal. In this experiment, considering the distribution of the linear errors, we respectively use the toneburst signal with 60dB, 80dB, 100dB, 120dB and 130dB amplitudes to test the I weighting. The experimental procedure is described as follows: Step 1: Setting the parameters of toneburst signal source: the frequency of the toneburst signal is 4kHz, the number of repeating the toneburst signal is 1, the duration time of outputting the toneburst signal is 20ms, the amplitude of the toneburst signal is 130dB, the attenuation of the attenuator is 0, then we record the I-weighting sound level LAI; Step 2: Gradually increasing the attenuation of the attenuator, i.e., the attenuations are 10dB, 30dB, 50dB, 70dB, respectively. Therefore, the amplitudes of input signal in the sound level meter are 120dB, 100dB, 80dB, 60dB, respectively, and then we write the corresponding I-weighting sound level LAI Step 3: Respectively setting the duration time of the toneburst signal are 5ms and 2ms, and go to the step 1 and step 2. The results of testing the digital I-weighting algorithm by using single toneburst signal are shown in Table.2. From this table, we can find that the I-weighting errors with single toneburst signal all are 0.0dB when duration time is 2ms and 20ms, and the I-weighting errors are 0.1dB when the amplitudes of the signal is less than 100dB and the duration time is 5ms, which are far less than those of the class 1 sound level meters defined by IEC 61672(±1.8dB、±2.3dB). Therefore, the performance of this proposed digital I-weighting algorithm is advantageous. Table. 2 Results of testing I weighting by using single toneburst signal Difference between the maximum Tolerant error toneburst response Duration Input of Indications Errors and the steady time signals class 1 sound (dB) (dB) response (dB) (ms) (dB) level meter (dB) Testing Target errors errors 130.0 126.4 -3.6 0.0 20 120.0 116.4 -3.6 -3.6 0.0 ±1.8 100.0 96.4 -3.6 0.0 8

5

2

80.0

76.4

-3.6

0.0

60.0

56.4

-3.6

0.0

130.0

121.2

-8.8

0.0

120.0

111.2

-8.8

0.0

100.0

91.3

-8.7

80.0

71.3

-8.7

0.1

60.0

51.3

-8.7

0.1

130.0

117.4

-12.6

0.0

120.0

107.4

-12.6

0.0

100.0

87.4

-12.6

80.0

67.4

-12.6

0.0

60.0

47.4

-12.6

0.0

-8.8

-12.6

0.1

0.0

±2.3

±2.3

4.4 Testing I-Weighting Algorithm by Continuous Toneburst Signals We set the duration time of the sinusoidal toneburst signals is 5ms, and then repeat the experimental steps described in Section 4.3, where, the number of repeating the toneburst signals FM is 100, 20 and 2, respectively. The results of testing I-weighting algorithm by continuous toneburst signals are written in Table.3. It can be found that the maximum I-weighting errors are -0.1dB when FM are 100 and 20, respectively, which are far less than those of the class 1 sound level meters defined by IEC61672 (the tolerant errors are 1.3dB and 2.3dB, respectively). Similarly, when FM is 2, the maximum I-weighting error is -0.7dB, and it is also less than that of class 1 sound level meters (±2.3dB). Table.3 Result of testing I weighting by continuous toneburst signals Difference between the maximum Tolerant tonebursts response error of FM Input signal Indications Errors and the steady class 1 (Hz) (dB) (dB) (dB) response (dB) sound level meter (dB) Testing Target errors errors 130.0 127.2 -2.8 -0.1 120.0 117.3 -2.7 0.0 100 100.0 97.3 -2.7 -2.7 0.0 ±1.3 80.0 77.3 -2.7 0.0 60.0 57.3 -2.7 0.0

20

2

130.0

122.3

-7.7

-0.1

120.0

112.4

-7.6

0.0

100.0

92.4

-7.6

80.0

72.4

-7.6

0.0

60.0

52.3

-7.7

-0.1

130.0

120.5

-9.5

-0.7

120.0

110.5

-9.5

-0.7

100.0

90.6

-9.4

80.0

70.6

-9.4

-0.6

60.0

50.7

-9.3

-0.5

9

-7.6

-8.8

0.0

-0.6

±2.3

±2.3

5. CONCLUSIONS The existing digital algorithms of the F and S weightings can not meet the decay rates of I weighting, and a new digital I-weighting model with a peak detector is proposed in this paper. According to the IEC61672, we test this proposed I-weighting algorithm by using toneburst signals. The experimental results show that the I-weighting decay rates fully meet the requirements of class 1 sound level meters defined by IEC61672, and its performances of sound level meters are effectively improved.

ACKNOWLEDGMENT This work was supported by the National Natural Science Foundation of China [grant number 51775185]; and the  Natural Science Foundation of Hunan Province, China [grant number2018JJ2261]. REFERENCES [1] Hammer M S, Swinburn T K, and Neitzel R L, Environmental noise pollution in the United States: developing an effective public health response, Environ. Health. Perspect., 122 (5)(2014) 115-119. [2] C.Hansen, Noise Control: From concept to application, CRC Press, Boca Raton, USA, 2005. [3] Buck K, Hamery P, Mezzo SD, and Koenigstein F, Measurement of high level impulse noise for the use with different damage risk criteria, J. Acoust. Soc. Am., 138(3)(2015) 1774-1774. [4] Armements Terrestres D T, Recommendations on evaluating the possible harmful effects of noise on hearing, Technical Report AT-83/27/28, Establissement Technique de Bourges, 1983. [5] Price G R, Hazard from intense low-frequency acoustic impulses, J. Acoust. Soc. Am., 80(4)(1986) 1076-1086. [6] Erdreich J, A distribution based definition of impulse noise, J. Acoust. Soc. Am., 79(4)(1986) 990-998. [8] Lei S F, Ahroon W A, and Hamernik R P, The application of frequency and time domain kurtosis to the assessment of hazardous noise exposures, J. Acoust. Soc. Am., 96(3)(1994) 1435-1444. [9] Price G R, and Kalb J T, A new approach: the auditory hazard assessment algorithm (AHAA), in: International Conference on Biological Effects of Noise, Australia, 2(1998)725-728. [10] Price G R, Impulse noise hazard: From theoretical understanding to engineering solutions, Noise Control Eng. J., 60(3)( 2012)301-312. [11] Consolatina Liguori, Alessandro Ruggiero, Paolo Sommella, and Domenico Russo, Choosing Bootstrap Method for the Estimation of the Uncertainty of Traffic Noise Measurements. IEEE Trans. Instrum. Meas., 66(5)(2017) 869-878. [12] M E Nilsson, A-weighted sound pressure level as an indicator of short-term loudness or annoyance of road-traffic sound, J. Sound Vib., 302(1-2)(2007)197-207. [13] Conggan Ma, Chaoyi Chen, Qinghe Liu, Haibo Gao, Qing Li, Hang Gao, and Yue Shen, Sound Quality Evaluation of the Interior Noise of Pure Electric Vehicle Based on Neural Network Model, IEEE Trans. Ind. Electron., 2017(online), http://www.ieee.org /publications_standards/publications/rights/index.html. [14] M.Robinson, and C.Hopkins, Effects of signal processing on the measurement of maximum sound pressure levels, Appl. Acoust., 77(77)(2014) 11-19. [15] J Qin, PF Sun, and J Walker, Measurement of field complex noise using a novel acoustic detection system, in: IEEE Proc. Autotestcon, USA, (2014)177-182. [16] IEC 61672, Sound level meters-Part 1: Specifications, International Electrotechnical Commission, Switzerland, Geneva, 2003.

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Highlights 1) Propose a new digital I-weighting algorithm for a sound level meter. 2) Prove that the decay rates of the existing F weighting and the S weighting do not meet the requirements of the I weighting. 3) Develop a new sound level meter with this digital I-weighting algorithm and test its performances.

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