1. INTRODUCTION

For many years, environmental noise has been evaluated in terms of the statistical sound pressure level (SPL), represented as L_x or L_eq, and its power spectrum measured by a monaural sound level meter. The SPL and power spectrum alone, however, do not provide a description that matches subjective evaluations of environmental noise. Descriptions of many subjective attributes such as preference and diffuseness, as well as primary sensations (loudness, pitch, and timbre), can be based on a model of the response of the human auditory-brain system to sound fields [1], and the predictions of that model have been found to be consistent with experimental results. The loudness of band-limited noise, for example, has recently been shown to be affected by the effective duration of the autocorrelation function (ACF), t_e, as well as by the SPL [2, 3]. When a fundamental frequency of complex tones is below about 1200 Hz, the pitch and its strength are indicated well by t₁ and f₁ respectively [4]. In particular, the ACF factors obtained at (t_e)_min are good indicators of differences in the subjective evaluation of the noise source and the noise field [5, 6].
The model consists of autocorrelators on the signals at two auditory pathways and an interaural crosscorrelator between then signals, and it takes into account the specialization of the cerebral hemispheres in humans. The ACF and interaural crosscorrelation function (IACF) of sound signals arriving at both ears are calculated. Orthogonal factors F(0), t_e, t₁, and f₁ are extracted from the ACF as described in detail in section 3 [7]. The factors LL, IACC, t_IACC, and W_IACC are extracted from the IACF.
A software system that can obtain the ACF and IACF factors for any noise sources has been developed [8], and this paper describes the analytical process used to extract these factors and also discusses the way they can be used to identify a noise source.

2. OUTLINE OF THE MEASUREMENT SYSTEM

The measurement system consists of two microphones arranged as a binaural pair, a laptop computer, and software that extracts the ACF and IACF factors from real-time noise data. The system can measure environmental noise automatically and simultaneously calculate the ACFs for the two signals and the IACF of the dual signal. Figure 1 is a flow chart of the method used to calculate the ACF and IACF factors. 


FIGURE 1. A flow chart of the system for measuring environmental noise. ACF and IACF factors are extracted through the process of automatic detection of the environmental noise (target). The noise is identified by using four ACF factors. (LPF: low-pass filter; PC: computational system.)
 

Dual-channel electrostatic microphones are used as the receiver, and a sphere between the microphones is used as a simple dummy head. Preliminary investigations comparing a human head, a dummy head, and a styrene foam sphere 20 cm in diameter revealed that the physical factors discussed here are not much affected by the shape of the head. The sampling frequency is usually 44.1 kHz and all the orthogonal factors are extracted from the ACF and IACF in real time. The noise source may then be identified by the use of ACF factors as described in section 4. The IACF factors mainly indicate the spatial information like the directivity or diffuseness in relation to the noise source. For further information for other aspects on the system, refer to our web site [9].

3. CALCULATION OF ORTHOGONAL FACTORS

3.1. PEAK-DETECTION OF ENVIRONMENTAL NOISE

A number of measurement sessions of the environmental noise to be analyzed are extracted by a peak-detection process. In order to automatically extract environmental noises or target noises from a continuous noise, a monoaural energy F_ll(0) or F_rr(0), which is energy at the left or the right ear entrance, respectively, is continuously analyzed. The peak-detection procedure is shown in Figure 2, and the conditions determined in this analysis are listed in Table 1. 

FIGURE 2. Procedure for extracting target noise for a single session. The concept of running integration interval is also presented. Running ACF and running IACF are conducted for every sessions to extract physical factors.

TABLE 1
Conditions to be determined in the detection process, the calculation of the running ACF and running IACF, and the extraction of t_e

The interval for the calculation of F(0) can be fairly long, say 1 s, when the noise is a continuous one such as aircraft noise or railway noise, but a shorter interval must be used when the noise is brief or intermittent. For the running calculation in equation (1) described below, however, it may be necessary to select an interval longer than the integration interval. Thus, this time interval must be determined according to the kind of the noise source. This enables F(0) to be determined more accurately than it can be determined when using a normal sound level meter with a long time constant. The peaks cannot be detected unless the trigger level L_trig is properly set in advance. The appropriate L_trig value also varies according to the kind of target noise, the distances between the target and the receiver, and atmospheric conditions. It must therefore be determined by means of a preliminary measurement. It is easy to determine the value of L_trig, when the distance between the target and the receiver is short and there is no interfering noise source near the receiver. The noise centered on its maximum F(0) is recorded on the system as a single session. The duration of one session for each target noise, t_s, should be selected so as to include F(0) peak after exceeding L_trig value. For normal environmental noise like aircraft noise and railway noise, the value of t_s can be about 10 s. This is different from steady state noise with longer duration or intermittent noise with shorter duration. Note that the present system cannot be used when there are interfering noises. As shown in Figure 2, the set of sessions {S₁(t), S₂(t), S₃(t), ..., S_N(t); N: the number of sessions, 0 < t< t_s} are stored on the system automatically.
The running ACF and running IACF for each session S_N(t) with duration t_s are analyzed as shown in the figure. Here we consider only a single session in order to explain the process of "running". Appropriate values for the integration interval 2T and running step t_step are determined before the calculation. As explained in reference [6], the recommended integration interval seems to be around 30 (t_e)_min, where (t_e)_min is the minimum value of the running series of values t_e, and can easily be found by preliminary measurement. This is found by the use of data of different kinds of environmental noises. In most cases, adjoining integration intervals overlap each other. The ACF and the IACF are calculated for every step (n = 1, 2, ..., M) within one session with the range of 2T which shifts in every t_step, as {(0, 2T), (t_step, t_step + 2T), (2t_step, 2t_step + 2T),..., ((M – 1)t_step, (M – 1)t_step + 2T)}. Physical factors are extracted from each step of the ACF and the IACF. Note that 2T must be sufficiently longer than the expected value of t_e. Also, it should be deeply related to an "auditory time-window" for sensation of each step. A 2T between 0.1 and 0.5 s may be appropriate for environmental noise [5], but a value near 2.5 s is recommended for music [6]. If 2T is less than this range, the (t_e)_min converges at a certain value. In most cases, the t_step is recommended around 0.1 s. If a more detailed activity of fluctuation is necessary, a shorter t_step should be selected.
As is well known, the ACF and the IACF are analyzed by using the FFT for the binaural signals and then using the inverse FFT. The A-weighting filter and frequency characteristics of microphones must be taken into consideration after the process of FFT.

3.2. ACF FACTORS

The ACFs at the left and right ears are, respectively, represented as F_ll (t) and F_rr (t). In discrete numbers, they are represented as F_ll⁽ⁱ⁾ and F_rr⁽ⁱ⁾ (1 < i < Tf ; f : sampling frequency (Hz); i : integer). In the calculation of F(0) for left and right values, F_ll⁽ⁱ⁾ and F_rr⁽ⁱ⁾ are averaged as follows:

.

(1)

An accurate value for the SPL is given by

SPL
		(2)

where F_ref(0) is the F(0) at the reference sound pressure, 20 mPa. The binaural listening level is the geometric mean of F_ll(0) and F_rr(0):

(3)

Since this F(0) is the denominator for normalization of the IACF, it can be considered to be calssified as one of the IACF factors: or the right hemispheric spatial factors [1].
The effective duration, t_e, is defined by the delay time at which the envelope of the normalized ACF becomes 0.1 (the 10 percentile delay: see Figure 3). 


FIGURE 3. An example of the calculation of the effective duration, t_e, from normalized ACF by linear fitting to the initial envelope of the ACF.

The normalized ACF for the left and right ears, f_ll,_rr (t), is obtained as

(4)

It is easy to obtain t_e if the vertical axis is transformed into the decibel (logarithmic) scale, because the linear decay for initial ACF is usually observed as shown in the figure. For the linear regression, the least mean square (LMS) method for ACF peaks which are obtained within each constant short time range Dt is used. The Dt is used for the detection of peaks in the ACF and must be carefully determined before calculation. In calculating t_e, the origin of the ACF ( = 0, at t = 0) is sometimes excluded if it is not in the regression line. As an extreme example, if the target noise consists of a pure tone and a white noise, rapid attenuation at the origin due to the white-noise components is observed, and the subsequent decay is kept flat because of the pure-tone component. In such a case, the envelope function of ACF must be figured out.
    As shown in Figure 4, t₁ and f₁ are, respectively, the delay time and amplitude of the first peak of the normalized ACF. The first maximum must be determined as a main peak avoiding local minor peaks. The factors t_n and f_n (n > 2) are excluded because they are usually related to t₁ and f₁.

FIGURE 4. Definitions of t₁ and f₁ for the normalized ACF.

3.3. IACF FACTORS

The IACF between sound signals at left and right ears is represented as F_lr(t) ( - 1 < t < + 1 (ms)). In the digital form, it is represented as F_lr⁽ⁱ⁾ ( - f / 10³ < i < f / 10³ ; i : integer, where negative values signify the IACF as the left channel is delayed). Thus, it is enough to consider only the range from - 1 to + 1 ms, which is the maximum possible delay between the ears. The IACC is a factor related to the subjective diffuseness. As shown in Figure 5, it is obtained as the maximum amplitude of the normalized IACF f_lr⁽ⁱ⁾ within the delay range. 

FIGURE 5. Definitions of the IACC, t_IACC, and W_IACC descriptors from the IACF.

Thus,

.

(5)

The normalized IACF is given by

.

(6)

The value of t_IACC is simply obtained at the time delay of the maximum amplitude. For example, if t_IACC is greater than zero (positive), the sound source is on the right side of the receiver or is perceived as if it were. As shown in Figure 5, the value of W_IACC is given by the width of the peak at the level 0.1 (IACC) below the maximum value. The coefficient 0.1 is approximately used as JND at IACC = 1.0.
The listening level LL is obtained by the manner represented in equation (2) upon replacing SPL with LL.
Thus, physical factors extracted from fine structures of the ACF and IACF are obtained for each integration interval as running values.

4. SOURCE IDENTIFICATION USING THE ACF FACTORS

As shown in Figure 1, noise sources are identified by using four ACF factors in the present stage. Since the F(0) varies according to the distance between the source and receiver, special attention is paid to the conditions for calculation if the distance is unknown. Even if the factor F(0) is not useful, the noise source can be identified by using the other three factors. Remaining IACF factors may be taken into account if the spatial information is changed. One of the guidelines to figure out the minimum t_e, (t_e)_min, which represents the most active part of the noise signal, is the fact that the piece is most deeply associated with subjective responses [10]. The distances between the values of each factor at (t_e)_min for the unknown target data (indicated by the symbol a in equations (7-10), and values for the template (indicated by the symbol b) are calculated. Here, "target" is used as an environmental noise as an object to be identified by the system. Template values of a set of typical ACF factors for a specific environmental noise are prepared, and these templates for comparison with an unknown noise.
    The distance D(x) (x: F(0), t_e, t₁, and f₁) is calculated in the following manner:

		(7)
		(8)
		(9)
		(10)

The total distance D of the target can be represented as the sum of the right-hand terms of equations (7)-(10), so

(11)

where W^(x) (x: F(0), t_e)_min, t₁, and f₁) signifies the weighting coefficient. The template with the nearest D can be taken as the identified noise source. The method used to compute the weighting coefficients is described in Appendix A.

APPENDIX A: COMPUTATION OF THE WEIGHT COEFFICIENT

Weighting coefficients W^(x) (x: F(0), t_e, t₁, and f₁) in equation (11) are obtained by using statistical values s₁⁽ⁱ⁾ and s₂⁽ⁱ⁾. As shown in Figure A1, s₁⁽ⁱ⁾ is the arithmetic mean of the standard deviations (SD) for all categories of the ACF factor. Here category means a set of data for the same kind of noise. s₂⁽ⁱ⁾ is the SD of the arithmetic means for each category. Values of W^(x) are given as after normalization by maximum values among factors . This square root processing is experiential and would be improved by introduction of a better function. The procedure is explained as follows. As a factor with larger SD between noise sources and with smaller SD among a certain source can distinguish the different kinds of noise, the weighting of such factor should be larger than that of the other factors. If the learning function toward the improvement of a template is given, a template is overwritten in order by average values of each ACF factor between the latest session and the previous data in the system.

FIGURE A1. The method to compute the weighting coefficients, W^(x) in equation (12).

5. REMARKS

This paper described the detection of environmental noise, the analysis of ACF and IACF factors, and a process for identifying unknown environmental noises. The computational system described here may be useful for characterizing environmental noises. Such a noise can be identified by using four factors extracted from the ACF: F(0), t_e, t₁, and f₁. Though the spatial factors extracted from the IACF (LL, IACC, t_IACC, and W_IACC) are not used for the identification in this paper, spatial information on the noise source including its degree of diffuseness and its direction from the receiver can be described by these spatial factors. Experimental results which include spatial factors from the IACF are demonstrated in references [11, 12] in this special issue.

ACKNOWLEDGMENTS

The authors would like to thank Mr. Shinichi Aizawa for his invaluable assistance with programming the software. This work was supported by the Research and Development Applying Advanced Computational Science and Technology Program of the Japan Science and Technology Corporation (ACT-JST), 1999.

REFERENCES