Signal-to-noise ratio in university lecture halls with low intelligibility
Dario D’ORAZIO(1) , Domenico DE SALVIO(2) , Laura ANDERLUCCI(3) , Massimo GARAI(4)(1) DIN, Department of Industrial Engineering, University of Bologna, Italy, dario.dorazio@unibo.it(2) DIN, Department of Industrial Engineering, University of Bologna, Italy, domenico.desalvio2@unibo.it(3) STAT, Department of Statistical Science, University of Bologna, Italy, laura.anderlucci@unibo.it(4) DIN, Department of Industrial Engineering, University of Bologna, Italy, massimo.garai@unibo.it

Abstract
Speech intelligibility plays a key role in determining the quality of verbal communication. It depends on the
acoustic characteristics of the room and the signal-to-noise ratio (SNR). Background noise has three main components: HVAC noise, anthropic noise (student activity) and external activities noise, each of them with different
noise spectra. In this work, measurements taken with a sound level meter during lectures in university classrooms are analysed using advanced statistical techniques in order to detect and separate the various components
which contribute to background noise. The same statistical techniques are used to characterize the speech leveltoo, i.e. the signal in the SNR. From the raw data collected with a sound level meter, an asymmetrical distribution
is built. Then four statistical techniques are applied: percentile levels, Gaussian mixture model based on peakdetection, blind Gaussian mixture model and blind k-means clustering. Results are compared and discussed,
highlighting the pros and cons of each technique.
Keywords: Speech intelligibility, Gaussian Mixture Model, Signal-to-noise ratio

1

INTRODUCTION

Good quality of oral communication is the crucial aspect for a learning space. A high speech intelligibility
allows increasing student’s concentration and decreasing teacher’s vocal effort [1, 2]. Conversely, a high background noise triggers the Lombard effect [8], the mechanism for which a person tends to increase the level of
his voice in order to listen himself. As all people experience the same effect, the signal-to-noise ratio (SNR)
remains almost constant during time [9]. The main factors affecting the speech intelligibility are the reverberation time and the signal-to-noise ratio. Thus, in order to achieve an high interaction between students andteachers, a deep knowledge of the sound sources affecting the background noise is essential. The best intelligibility in a certain space is reached when the signal-to-noise ratio is at least +15 dB [3, 4]. Often, lecture halls
are provided of a public address (PA) system to increase the SNR, but it changes the human noise behaviour
too; Peng et al. note that in the case of elementary school classrooms the correlation between SNR and theLombard effect is missed [10]. Background noise in a university lecture hall in occupied condition is formed
by HVAC system, external noise due to the nearby spaces and student activity (anthropic noise) [6]. Separatingthese background noise sources is not immediate when anthropic noise is considered; for example it may benecessary to measure the sound pressure levels during the pauses in the teacher’s speech [5]. Statistical techniques offer a viable method to separate the different contributions. However, the standard technique, based on
the percentile levels, doesn’t allow to obtain the anthropic component in a stable way since it looks for the
portion of time exceeded by a random phenomenon. That is why a statistical algorithm is needed to groupsound pressure levels recorded with a sound level meter in a more structured way. In this work four statisticaltechniques are compared to identify the anthropic noise due to students during thirteen university lectures inthree different rooms: percentile levels (PL), Gaussian Mixture based on peak detection (PD), blind Gaussian
Mixture Model (GMM) and blind k-means clustering (KC). Results are compared and discussed, highlighting
the pros and cons of each technique.

5882

2

METHODThe case studies are three university rooms in the School of Literature and Philosophy of the University of
Bologna. Hall I and Hall II have an amphitheater shape with plaster walls and wooden seats and benches,volume of 1000 and 900 m3 and a maximum capacity of 250 and 200 students. Hall III has a shoe-box shape,
plaster walls and movable plastic chairs, a volume of 850 m3 and a maximum capacity of 170 students.
At ﬁrst, in order to characterize the acoustics of the rooms, a measurements campaign according to ISO
3382 [11] and IEC 60268-16 [12] was carried out, using a calibrated sound source [14] with enough signal-tonoise ratio [15]. Reverberation time, STI (Speech Transmission Index) and C50 (Sound clarity) are considered
the relevant acoustic criteria for this study [16].
Subsequently, thirteen lessons were entirely recorded with two sound level meters located at mid distance between the speaker and the rear wall, near the lateral walls of the rooms and at least 1 m from any reﬂecting
surface. An observer detected the unforeseen extraneous sounds in order to delete their peaks in post-processing.
Time history were cut in correspondence of the pauses, focusing the analysis on the lectures. Short-term, Aweighted sound pressure levels were recorded with an interval time of a 100 ms. The HVAC system was
switched off during the acquisitions.Therefore, only two sound sources were present, labelled in the following
as Speech Level (SL) and Student Activity (SA).
The workﬂow of the post-processing was the following:
1 - the statistical distribution of A-weighted sound pressure levels was built and plotted;
Then, basing on the type of analyses needed:
2.1 - the percentile levels were extracted;
or
2.2 - the distribution of occurrences was ﬁtted by two normal-distribution curves or two clusters, basing on theused technique, to identify each source (SL and SA);Sound pressure level (dB)

3 - SNR is evaluated as the difference between the local maxima of SL and SA.
100

80

60
09:00

10:00

11:00

12:00
13:00
Time (h : m)

14:00

15:00

16:00

·104

Figure 1. Example: temporal history of three recorded lectures.
If the number of sound sources is known it is possible to "force" the number of clusters assembled by thealgorithms or let them to optimize it.
The techniques employed in this work can be divided in two types: with or without an observer during theacquisition. The percentile levels and peak detection are techniques of the ﬁrst kind. In fact, here the observer

5883

decides the percentile value or the number of geometrical peaks on the occurrences curve to take int account(the observer decides which extraneous noises to discard).
The blind Gaussian Mixture Model and k-means clustering are techniques of the second kind. In fact, theywork in a blind way and the operator can just select the number of clusters to obtain. In this study, for theblind techniques a number of 2 clusters was set up.
Table 1. Subdivision between statistical techniques and observer requirement.
Technique
Percentile levels (PL)Peak detection (PD)
Gaussian Mixture Model (GMM)
K-means clustering (KC)With/without observer
with
with
without
without

Table 2. Occupancy during lectures (N), gender of the teacher and recording time for each lesson under study.
LessonN

Hall

Teacher’s gender

Recording time
(h:m)

A
B
C
D
E
F
G
H
I
J
K
L
M

145
200
100
150
250
160
120
150
200
110
80
110
175

I
I
I
I
II
II
II
II
II
III
III
III
III

M
M
F
M
M
F
F
F
M
F
F
M
F

01:16
01:22
01:38
01:24
01:32
01:24
01:19
01:30
01:29
01:35
01:30
01:35
01:27

2.1 Percentile Levels
In acoustics a percentile level corresponds to a sound pressure level which is exceeded a certain percentage ofthe recording time. In this work, using this technique the teacher’s speech level is identiﬁed with the LA,eq of
the whole time history while the student activity is associated to the L90 , as in many previous studies [5, 7, 18].
Thus, the SNR is evaluated with their difference. The "acoustic" percentile level corresponds to the rank R ofa percentile in statistical terms (see 2.2).
2.2 Peak detection
Peak detection executes a Gaussian Mixture Model algorithm forcing manually the number of possible clusters.
This is established by the operator identifying the peaks on the occurrences curve of the recorded SPL. A
multi-peak analysis was made with OriginPro [13] software in order to identify the main starting points for theGaussian ﬁtting. The Gaussian Mixture Model algorithm is analysed in detail in the following subparagraph.
The same dataset can be seen in two different ways: through the cumulative distribution or through the occurrence curve (see ﬁg 3). So percentile levels and peak detection techniques are linked. In fact, evaluatinga percentile level means doing a backwards integration of the occurrence curve (see ﬁgure 3(b)) covering the5884

percentage of its area until the percentile required. For example, determining the acoustic percentile level L90
corresponds to the backwards integral until the 10th percentile of the occurrence curve.
In statistics, the rank r of a percentile q of N observations is deﬁned as:r(q) =q(N + 1)100(1)Consequently, the value of the acoustic percentile level Lq of a certain dataset is equal to the rank r of 100q. For a large number of observation, if the the occurrence curve is represented by f (x), the value q can be
expressed as:�∞r(100−q)

100

(2)

6
Occurrences distribution

Percentile level

Fitted gaussians
Peak detected

75
50
25
0
30

f (x)dx

Cumulative distribution

Occurrence (%)

Percentage o f exceeded time (%)

q = P(x > Lq ) =

40
50
60
Sound pressure level (dB)70(a) Percentile Levels technique

Means SPL

4

2

0

40
80
60
Sound pressure level (dB)(b) Peak Detection techniqueFigure 2. Example of the two techniques with observer. In ﬁgure (a) the continuous line represent the cumulative distribution of the SPL recorded by a sound level meter. The example highlights the L50 percentile level,
which corresponds to an SPL of 48.5 dB. In ﬁgure (b) the continuous line represents the distribution of occurrences of the same measurement. The asymmetrical distribution was decomposed in two gaussian curves basing
on the peak detection (peaks are indicated with �). The means of gaussian curves indicated with ∗ correspondto different sound sources.
2.3 Gaussian Mixture Model
The Gaussian Mixture Model decomposes the original model data in a sum of gaussian curves. The clusters, represented by the gaussian curves, and their points are deﬁned via Maximum Likelihood method. With
Rstudio [23] is possible estimate via Expectation - Maximization (EM) [22] iterative algorithm the Maximum
Likelihood of the recorded SPL.
Let X be a set of independent observations, x1 , . . . , xn , drawn from a mixture of Gaussian distributions; thedensity f (xi ) can be written in the formKf (xi ; ψ) = ∑ πk fk (xi ; θk )k=1

i = 1, . . . , n,

ψ = {θ , π}

(3)

5885

6

8
Occurrences distribution

Cluster 1
Cluster 2

Occurrence (%)

Occurrence (%)

Fitted gaussians

4

2

0

6
4
2
0

40
80
60
Sound pressure level (dB)

��
40
60
Sound pressure level (dB)(a) Blind Gaussian Mixture Model(b) Blind k-means clustering

Figure 3. Example of the two techniques without observer. In ﬁgure (a) the continuous line represents the
distribution of occurrences of the recorded SPL while the dashed lines represent the gaussian curves found. In
ﬁgure (b) are highlighted two clusters of the recorded dataset.
where the fk (xi , θ )s are the Gaussian densities with parameter vector θk = {µk , σk2 ; k = 1 . . . , K} and πk are theso called mixing proportions, non-negative quantities that sum to one; that is, 0 ≤ πk ≤ 1 (k = 1, . . . , K) and∑Kk=1 πk = 1 [21]. The likelihood function for a mixture model with K univariate Normal components is:
n

K

n

K

L (ψ|x) = ∏ ∑ πk fk (xi |θk ) = ∏ ∑ πk √i=1 k=1i=1 k=1

1
2πσ 2

2

(x −µ )
− i 2k

e

2σ
k

(4)

2.4 K-means clustering
K-means clustering is an algorithm which distributes the data basing on their characteristics, generally the metricused is the distance. As the EM, it is iterative too and identify each cluster with a signiﬁcant parameter named
centroid. Its aim is minimize the intra-cluster variance arranging the centroids [19]. With Rstudio [23] it ispossible to run the algorithm.
Let X = {xi }, i=1, . . . ,n be the set of n points to be clustered into a set of K clusters, C = {ck ; k = 1, . . . , K}.
K-means algorithm ﬁnds a partition such that the squared Euclidean distance between the empirical mean of acluster and the points in the cluster is minimized. Let µk be the mean of cluster ck . The squared Euclidean
distance between µk and the points in cluster ck is deﬁned as
J(ck ) = ∑ ||xi − µk ||2(5)

xi ∈ckThe goal of K-means is to minimize the sum of the squared Euclidean distance over all K clusters, therefore
the objective function to be minimize is the following:
K

J(C) = ∑ ∑ ||xi − µk ||2
k=1 xi ∈ck

5886

(6)

3

PRELIMINARY RESULTS

The recorded data were analysed with four statistical techniques. Results are presented in table 3. For eachmethod student activity (SA), speech level (SL) and signal-to-noise ratio (SNR) are shown.
Table 3. Measured A-weighted values of student activity (SA), received speech level (SL) and corresponding signal-to-noise ratio (SNR) for Peak detection, Percentile levels, Gaussian mixture and K-means clustering
methods. Values are averaged over the two receiver positions selected for the measurements performed during
lessons. In the Equivalent levels method LA90 and LAeq represent the student activity and the speech level. Meanvalues don’t evaluate lesson L since was conducted without P.A. system. All values are in dB.
Lesson

PD

PL

GMM

KC

SA

SL

SNR

LA,90

LA,eq

SNR

SA

SL

SNR

SA

SL

SNR

A
B
C
D
E
F
G
H
I
J
K
L
M

48.0
47.4
51.1
50.8
47.9
50.1
62.0
55.5
53.6
46.9
50.4
–
48.8

65.1
63.5
65.8
67.4
68.2
66.7
75.8
76.1
68.1
59.9
68.2
60.7
62.7

17.1
16.1
14.7
16.6
18.9
16.7
13.2
20.2
12.9
13.0
17.8
–
13.9

48.0
45.8
53.0
49.3
52.1
55.0
61.6
56.4
58.8
50.3
47.5
53.4
51.5

69.9
64.8
68.9
69.7
72.3
71.9
78.6
79.2
74.6
63.3
67.8
63.6
65.1

22.0
19.0
15.9
20.4
20.2
17.0
17.0
22.8
15.8
13.0
20.3
10.2
13.7

48.2
47.5
53.3
51.2
48.4
50.3
61.0
55.3
53.4
53.0
50.6
57.7
51.1

65.0
63.3
66.3
67.2
67.5
66.5
75.5
75.3
68.0
61.6
67.6
62.9
63.1

16.8
15.8
12.9
16.0
19.1
16.2
14.5
20.0
14.6
8.6
17.0
5.2
12.0

52.2
48.8
55.8
52.7
49.1
53.1
55.7
55.8
56.5
53.3
50.6
55.8
53.8

68.3
64.2
68.4
68.4
68.0
68.5
74.9
76.0
69.7
63.6
67.7
64.4
64.7

16.1
15.4
12.6
15.7
18.9
15.5
19.3
20.2
13.1
10.3
17.1
8.6
10.9

Mean

51.0

67.3

15.9

52.4

70.5

18.1

51.9

67.2

15.3

53.1

68.5

15.4

Results show that the differences between the methods decrease when the SNR increases; indeed the lesson "L"highlights this behaviour. This lesson was carried out without the PA system so, because of the Lombard effect,
the student activity is not visually appreciable. Thus, the PD technique doesn’t succeed in the ﬁtting while othertechniques give very different results. The density of the data doesn’t permit to have a coherent clustering. The
most similar values are obtained by the PD and GMM, since they use the same algorithm but in a different
initial conditions. More in general, PL overestimates SNR values compared to the other techniques.
Measurements give further insights into the mechanism of the Lombard effect. Students and teachers create an
acoustical environment with an SNR of +15 dB as a consequence of the Lombard effect to reach the maximum
possible speech intelligibility in the rooms as indicated by previous studies [17, 9]. As shown in ﬁgure 4 SL
increases of 0.56 dB for each dB of increase of SA as suggested by literature [24, 25]. The intercept (37.4)
takes into account the combined effect of the source-receiver distance and the PA gain.

4

CONCLUSIONSThe present work has investigated a statistical analysis of the acoustic ﬁeld during university lessons. After ameasurement campaign carried out with two sound level meters, statistical analysis were conducted with four
different techniques: percentile levels, Gaussian Mixture model based on peak detection, blind Gaussian Mixture
Model and blind k-means clustering. Results show how the percentile levels overestimate, unlike the othertechniques, the value of the background noise during university lectures. Furthermore the reciprocity between
the student activity and the speech level highlights how Lombard effect works maintaining a costant SNR.

5887

80

Measured values
Regression line

R2 =0.26

SL (dB)75

y = 0.56x + 37.4

70
65
60
45

50

55
SA (dB)

60

65

Figure 4. Relationship between SA and SL. The regression line shows the increase of 0.56 dB/dB as suggested
by literature.

REFERENCES[1] Visentin C., Prodi N., Cappelletti F., Torresin S., Gasparella A., Using listening effort assessment in the
acoustical design of rooms for speech, Build. Environ., 136 (2018), 38–53.
[2] Puglisi G. E., Cutiva L. C., Pavese L., Castellana A., Bona M., Fasolis S., Astolﬁ A., Acoustic comfort in
high-school classrooms for students and teachers. Energy Procedia, 78 (2015), 3096–3101.
[3] Reich R., Bradley J., Optimizing classroom acoustics using computer model studies, Canadian Acoustics,
26(4) (1998), 15–21.
[4] Hodgson M., Experimental investigation of the acoustical characteristics of university classrooms, J. Acoust.
Soc. Am., 106(4) (1999), 1810–1819.
[5] Bottalico P., Astolﬁ A. (2012). Investigations into vocal doses and parameters pertaining to primary school
teachers in classrooms. The Journal of the Acoustical Society of America, 131(4), 2817-2827.
[6] Hodgson M., Rempel R., Kennedy S., Measurement and prediction of typical speech and background noise,
J. Acoust. Soc. Am., 105(1) (1999), 226–233.
[7] Shield B., Conetta R., Dockrell J., Connolly D., Cox T., Mydlarz C., A survey of acoustic conditions andnoise levels in secondary school classrooms in England, J. Acoust. Soc. Am., 137(1) (2015), 177–188.
[8] Lombard E., Le signe de l’elevation de la voix, Ann. Mal. de L’ Oreille et du Larynx XXXVII (1911),
101-119.
[9] Sato H., Bradley J., Evaluation of acoustical conditions for speech communication in working elementary
school classrooms, J. Acoust. Soc. Am., 123(4) (2008), 2064–2077.
[10] Peng J., Zhang H., Wang D., Measurement and analysis of teaching and background noise level in classrooms of Chinese elementary schools, Applied Acoustics, 131 (2018), 1-4.
[11] ISO 3382-2:2008, Acoustics - Measurement of room acoustic parameters - Part 2: Reverberation time inordinary rooms. Geneva: International Organization for Standardization.

5888

[12] IEC 60268-16:2011, Sound system equipment - Part 16: Objective rating of speech intelligibility by speechtransmission index. Geneva: International Electro-technical Commission.
[13] OriginPro 2017. OriginLab Corporation, 2016.
[14] D’Orazio, D., De Cesaris, S., Guidorzi, P., Barbaresi, L., Garai, M., Magalotti, R. Room acoustic measurements using a high-SPL dodecahedron (2016) 140th Audio Engineering Society International Convention
2016, AES 2016,[15] P. Guidorzi, L. Barbaresi, D. D’Orazio, M. Garai, Impulse responses measured with MLS or Swept- Sinesignals applied to architectural acoustics: an in-depth analysis of the two methods and some case studies ofmeasurements inside theaters, Energy Procedia, 78 (2015) 1611–1616.
[16] De Cesaris, S., F. Morandi, L. Loreti, D. D’Orazio, and M. Garai (2015). Notes about the early to latetransition in italian theatres. Proc. of ICSV22, Florence .
[17] Hodgson M., Nosal E., Effect of noise and occupancy on optimal reverberation times for speech intelligibility in classrooms, J. Acoust. Soc. Am., 111(2) (2002), 931–939.
[18] Titze, I. R., Hunter, E. J., Å vec, J. G. (2007). Voicing and silence periods in daily and weekly vocalizations of teachers. The Journal of the Acoustical Society of America, 121(1), 469-478.
[19] Jain, A. K. (2010). Data clustering: 50 years beyond k-means. Pattern Recognition Letters, 31(8), 651–666.
[20] Lloyd, S. (1982). Least squares quantization in pcm. IEEE Trans. Inf. Theor. 28 (2), 129–137.
[21] McLachlan, G. J. and D. Peel (2000). Finite Mixture Models. Wiley.
[22] Dempster, A. P., Laird, N. M., and Rubin, D. B. (1977), Maximum Likelihood for Incomplete Data via
the EM Algorithm (with discussion). Journal of the Royal Statistical Society, Ser. B, 39, 1–38.
[23] R Core Team. R: a language and environment for statistical computing. Vienna, Austria: R Foundation for
Statistical Computing; 2017.
[24] Rindel, J. H. (2010). Verbal communication and noise in eating establishments. Applied Acoustics, 71,
1156–1161.
[25] Lazarus, H. (1986). Prediction of verbal communication in noise–a review: part 1. Applied Acoustics, 19,
439–464.

5889