Blind estimation of reverberation time by neural networks
Rodrigo L. PRATES∗ , Mariane R. PETRAGLIA† , Julio C. B. TORRES‡ , Antonio PETRAGLIA§
Program of Electrical Engineering, COPPE
Federal University of Rio de Janeiro, Brazil

ABSTRACTIn this paper we investigate a procedure for blind estimation of room reverberation time, that is, without apriori knowledge of the room impulse response. A neural network based method is proposed, which is robust
to noise and to abrupt variations over time of the acquired signal. The input features of the neural network
are calculated in the frequency domain, where training samples are generated in the Mel scale. A competent
network architecture (i.e., with appropriate number and type of hidden layers and number of neurons comprisingeach layer), as well as the best training algorithm and regularization technique, are investigated. The use ofcross-entropy error during training gives better results than those obtained by mean squared error. Comparative
results are presented, considering two previously proposed blind methods: a deep neural network technique anda spectral decay distribution method.

Keywords: Reverberation Time, Neural Network, Power Spectral Density

1

INTRODUCTION

The reverberation time (RT60 ) in a room is defined as the time the sound takes to decay 60 dB after theinterruption of the sound emission. Its estimation is an important task in the characterization of sound qualityof closed spaces. It contributes to the assessment of the quality and intelligibility of audio signals obtained
from reverberant environments, and to the improvement of audio processing algorithms and speech recognition
methods.
The reverberation time was initially calculated by Sabine [1], through the information of geometry of theenvironment and coefficients of absorption of the surfaces that compose the environment. If such information is
not available, a controlled test signal can be generated to estimate the RT60 based on the noise-canceling method[2], or by the Schoroeder integration curve method [3], which uses the measured Room Impulse Response(RIR). Since the RIR may not be available, and the test signal may be difficult to implement, other ways ofcomputing the RT60 have to be explored. Thus, in many applications it becomes necessary to determine theRT60 only from the recorded speech signal.
Several approaches have been proposed for the estimation of the RT60 , among which there are some methods
that use maximum likelihood (ML) to model the decay of the reverberant signal [4], [5] and others that apply
the reverberant signal decay distribution (Spectral Decay Distribution - SDD), calculated through the energy envelope of the RIR [6]. There are also techniques that use the frequency domain by modeling the power spectral
density (PSD) through an IIR filter, whose pole is related to the reverberation time [7]. Finally, some papers
use Machine Learning (ML) techniques, such as Deep Neural Networks (DNN) [8]. These techniques havealready demonstrated significant improvement in problem solving such as voice recognition, pattern recognition
in images and estimation of arrival direction [2].
In this work, the estimation of the reverberation time in a room is treated as a problem of mapping thereverberant signal to an estimate of the RT60 using DNN, based on the work reported in [2]. A classification
network is used to select the most likely RT60 , given an input vector formed by the concatenation of the Mel∗ rodrigolp01@gmail.com† mariane@pads.ufrj.br‡ julio@poli.ufrj.br§ antonio@pads.ufrj.br

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coefficients [9] of the reverberant signal. The reverberant signals were generated from simulated RIRs by theimage method [10], and the addition of Gaussian white noise with different signal-to-noise ratios (SNRs). The
results obtained with the implementation of the method based on DNN are compared to those achieved by
the algorithms considered state-of-the-art techniques. In this work the same RT60 is assumed for all frequency
bands, which is a simplification adopted for all implemented methods.

2

PROBLEM FORMULATION

A signal y(n) recorded in a room consists of a direct sound s(n), followed by reverberation x(n) and possibly
involved in noise v(n), which can be expressed asy(n) = s(n) + x(n) + v(n),(1)

where n is the discrete-time index. The reverberant signal x(n) can be expressed asx(n) = h(n) ∗ s(n),(2)

where ∗ is the convolution operator and h(n) represents the room impulse response (RIR). According to the
Polack model [2], [7], the RIR can be described as one realization of the stochastic processh(n) = b(n)e−ηn , n ≥ 0,

(3)

where b(n) is a zero mean Gaussian noise with variance σb2 , which defines the RIR structure modulated by an
exponential function with decay rate η. This rate is defined as [7]η=

3ln(10),
RT60 fs(4)

where fs is the sampling frequency.
The decay rate η can be estimated by applying a linear fit to the natural logarithm of the time-frequency energy envelope. In [6] the decay rate of the energy envelope is blindly estimated from the observed reverberation
speech signal in the short-time Fourier transform domain, using a property of the spectral decay distribution.
The method that applies neural networks also separates the signal into frames, but instead of using thisinformation directly, the frames are transformed through coefficients of the Mel frequency scale [2]. These
coefficients are used as input data for the neural network training, which will learn to estimate the reverberation
time associated with the frame. In this way, several frames are concatenated until they form a signal segment
large enough for the estimation to be performed.

3

REVERBERATION TIME ESTIMATION BY NEURAL NETWORKSIn this section the blind and supervised method for estimating RT60 based on deep neural networks (DNN)
is presented. The method maps portions of an input signal into a value corresponding to the RT60 estimate.
A sorting network with multiple outputs is used, where each output represents a set of RT60 values. Thus,
given the input samples, the network selects one of the outputs as the most likely to be the class associatedwith the range of reverberation time values of the environment, and from the index of that output provides theestimated value of RT60 . The main motivation for using deep neural networks lies in their ability to generalize
the learning process, thereby efficiently modeling complex problems. The DNN architecture employed in thiswork comprises an input layer, three hidden layers, and an output layer. In this section, the input, output andtraining data of the deep neural network will be presented.

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3.1 Input Data
As input parameters, we used the coefficients obtained by passing the input signal through a filter bank on the
Mel scale (Log Mel Filterbank Energies- LMFBE) [2, 8, 6]. This choice is due to the property that the Mel
scale correctly represents the response of the human auditory system. The steps for generating the features, or
input data, are described below [2, 9]. It is assumed that the signals are all sampled at the rate of 16 kHz.
1. Initially a pre-emphasis filter is applied to the reverberant speech signal, with coefficient α = 0.97, thatis,y(n) = x(n) − αx(n − 1);
2. The signal is then divided into frames of 25ms, with 40% overlap;
3. The Hamming window
w(n) = 0.54 − 0.46cos(

2πn
),
N −1

is applied to each frame, where N is the window size;
4. The Fast Fourier Transform (FFT) of length 512 is applied to each frame in order to compute the power
spectrum by|FFT (xi )|2P=,N
where xi is the i-th frame of the signal x. Finally, a bank of 23 triangular filters T256x23 of 256 coefficients
is applied to the power spectrum of each frame. Turning each frame F1x23 into an array of 23 coefficients,that is,F1x23 = f1x256 × T256x23 .
Still with each frame, the base 10 logarithm is applied and the mean is removed for spectrum balancing
and improvement on the signal-to-noise ratio [9].
In order to obtain the mapping between the LMFBE coefficients and the RT60 , it is necessary to concatenate
a sufficient number of frames. Thus, a sequence of 51 continuous frames, proportional to the longer time to be
estimated, is created as the input vector for DNN.
3.2 Output Data
It is usual to treat the estimation as a regression problem. DNN can be trained to minimize the mean squared
error (MSE) between the predicted and the true RT60 of the training set. However, according to [2], such
regression solution tends to generate high estimation errors within the range where RT60 is estimated. Thus, thepredicted value is skewed around the center of the training reverberation time scale. This issue is a direct resultof the regression choice as a way of treating the problem, and of the use of the MSE as a cost function for
DNN training. To avoid this difficulty, we can treat the estimation as a classification problem, where we divide
the values of RT60 , on the scale from 0.1 s to 1.0 s, into 19 bins, one per class for each bin [2]. We then have,for example, the output vector y = [0 1 0 · · · 0]T in case the value 175 ms is the true RT60 .
3.3 Neural Network Training
With defined network input and output parameters, the DNN is trained to learn the best mapping from the input
values to the output values. For each hidden layer of the network, the data undergoes an affine transformation
through the weight matrix and the bias vector, and then by the sigmoid activation function. The last layer
generates the output vector of the DNN using the softmax function. In this way, the output vector is given by4619

p = [p1 (ot ), . . . , pN (ot )]T , where pi (ot ) is the a posteriori probability of the i-th bin given the input feature ot ,N is the number of RT60 classes/bins and t is the frame index. The value of RT60 is then estimated by [2]j+1ˆ 60 =
RT∑i= j−1 pi (ot )ci
j+1∑i= j−1 pi (ot ),(5)where ci is the center of the i-th bin.
There is a compromise between the width of the bin and the number of classes. The larger the bin width,
the more accurate the classification, but the worse the RT60 resolution. A total of 19 bins were used to cover
the interval from 0.2 s to 1.0 s, with a bin of 0.042 s width, according to [2].

4

METHODOLOGY AND SIMULATIONSIn this section, the procedures for generating the network training and validation data, the methodology used
for network calibration, and the simulated experiments for the evaluation of the algorithms will be presented.
4.1 Database Generation
A set of data was generated for training and validation of the estimating algorithms of RT 60 through the
VCTK-Corpus database. For the generation of impulse responses (RIRs) we applied the image method, forwhich 7 parameters were used: sound velocity in m/s, sampling frequency in samples/s, receiver position,
source position and room dimension in [x, y, z] m, reverberation time in s, and number of samples.
A methodology was chosen so as to vary the parameters of the imaging method, and thus to generate
different RIRs. In this procedure, 3 different room sizes were defined: small room d = [4, 3, 4] m, average roomd = [6, 4, 4] m and large room d = [10, 7, 4] m. Two possible distances between source and receiver, that is,close (1.5m) and distant (3.0m), were adopted. For sound velocity and sampling frequency, the values c = 340
m/s and fs = 16 kHz, respectively, were set.
The positioning of both the source s and the receiver r were chosen to start at [2, 2, 2] m. Then, an orientation to be altered is chosen randomly, which may either be x or y. The distance between source and receiver
were randomly chosen as well. Finally, the displacement was applied to the position of the receiver, thereby
verifying the room size, so that the receiver would not remain at an invalid position.
For the generation of training and test data, 3 second voice frames were used, generating a total of 9,586
voice files of 152 different people. From this amount of files, approximately 5% (479 files) were used forgenerating the final results, which contained voice signals from people who participated in the training andfrom people who did not participate. Data from the remaining 9,107 files were used for network calibration,
separated into sets containing 70% for training, 15% for validation, and 15% for testing. The following steps
were applied in order to generate the network input data:
1. Resample the speech signal at the rate of 16 kHz, and obtain a 3 s segment, with the removal of theinitial silence part;2. Convolve the signal segment with the RIR generated by the image method to obtain the reverberant signal.
The RIR is generated by random selection of the following parameters: RT60 from 0.2 to 1.0 s, room sizeand distance between source and receiver;
3. Scale the signal to the range of [0, 1];
4. Add white Gaussian noise to the reverberant signal, whose level in dB is also chosen randomly among
the following values: [0, 5, 10, 30] dB for the training signals, and [−10, 0, 10, 20] dB for the test signals;
5. Generate the Mel coefficients as explained above, as well as the output vectors. This step is performed 5times on the same signal, in order to generate additional data for training and validation.

4620

This generation was made in such a way as to guarantee a data balance between classes. The methodology
applied to evaluate the results are presented below.
4.2 Training Procedures and Comparison among Models
In this work the following network architecture was adopted by means of exploring and proposing improvements
to the method presented in [2]: (1) number of neurons of the input layer equal to the size of the input vector;(2) update of the weights and bias by the backpropagation algorithm with momentum and adaptive learning rate;(3) MSE and cross-entropy cost functions; (4) learning rate, number of neurons (in the range of [25, 400]) andregularization values to be defined in the network calibration. Accordingly, the network calibration must provide
the optimal values of number of hidden layer neurons, cost function type, learning rate value and regularization
value. Comparison between MSE and cross-entropy networks was also performed, where the other parameters
were tested until the best configuration was obtained for each network model. The best result considered in thecalibration process corresponds to the one that generated the smallest mean square error, whereas comparisonswith the other models proposed in the literature correspond to the average absolute error (which are the metrics
available in the other works).
The following are the steps of the calibration process of the two network models:
1. Initially we sought the best learning rate lr from [10−1 , 10−2 , 10−3 , 10−4 ] for 5 different networks, varying
the number of neurons h among [25, 50, 100, 200, 400].
2. After obtaining lr, the regularization λ is included, with values among [10−1 , 10−2 , 10−3 , 10−4 ], using thebest 3 values of h.
3. At this point, for each type of cost function, there are 3 network settings. The best of each is selected,
obtaining a network configuration for each type.
4. The final comparison is performed by evaluating the absolute mean error for different room sizes, distance
between the source and the receiver, and noise levels.
The selected model was compared to SDD and DNN reference methods, for different room sizes and noiselevels. The RIRs were generated according to Eq. (3), where b(n) is a stochastic process with variance σb2 = 0.1.
The following 6 values of RT60 were used to generate the synthetic RIRs: [0.2, 0.33, 0.42, 0.6, 0.82, 1.0] s. Twovoice signals (one female and one male) sampled at 16 kHz and two SNR values (0 dB and 20 dB) were
employed.
The next section presents training results, generated from the methodology described above, and comparative
conclusions with the other methods.

5

RESULTS

5.1 Network Selection
The networks were trained with either 5000 or 10000 runs. If convergence had not yet been observed with
5000 runs, training was continued up to 10000 runs. Figure 1 shows the convergence behaviors for the MSE
and Cross-Entropy networks containing 200 neurons.
Tables 1 and 2 display the MSE values obtained after convergence for the MSE and Cross-Entropy networks,
respectively, for different values of lr. The highlighted values correspond to the 3 smallest MSEs obtained. The
term "tuned" refers to the automatic updating of the lr parameter.
Tables 3 and 4 show the MSE values obtained after convergence for the MSE and Cross-Entropy networks,
respectively, for different values of λ and employing the tuned lr values. The highlighted values correspond to
the smallest MSEs obtained.

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Figure 1. Convergence of MSE and Cross-Entropy networks for lr calibration.
Table 1. MSEs after convergence of the MSE network for different lr values.
lr# neurons
25
50
100
200
400

tuned
0.05580.05170.05540.05300.067310−1
0.08210.07510.07540.07260.080210−20.11570.09980.08530.08090.076210−30.0884
0.09730.08160.08590.089310−40.08880.13590.07360.08870.0642

Table 2. MSEs after convergence of the Cross-Entropy network for different lr values.
lr# neurons
25
50
100
200
400

tuned
0.04270.04130.04250.0511
0.054410−1
0.06910.07290.07330.06380.064310−20.08020.07870.07570.07490.076910−30.08200.08960.08010.08610.079910−40.21390.09570.07960.08050.0822

Table 3. MSEs after convergence of the MSE network for different λ values.
λ# neurons
50
100
200

10−1
0.0522
0.05300.058110−20.04880.05490.060510−30.05090.05630.060410−40.04940.06130.0534

Table 4. MSEs after convergence of the Cross-Entropy network for different λ values.
λ# neurons
25
50
100

10−1
0.04310.04080.049210−20.04280.04280.043310−30.03940.0441
0.043510−40.04270.0476
0.0438

Tables 5 and 6 contain the MAE values and the corresponding standard-deviations of the best MSE andCross-Entropy networks, respectively, for different room sizes, source-receiver distances, and noise levels. It

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Table 5. MAEs and their standard-deviation after convergence for the proposed MSE network.
ROOM

DIST

Close
Distant
Close
Average
Distant
Close
Large
Distant
Mean Noise
Small-10 dB
0.303 ± 0.177
0.294 ± 0.173
0.294 ± 0.175
0.293 ± 0.189
0.305 ± 0.176
0.282 ± 0.177
0.295 ± 0.177

0 dB
0.151 ± 0.101
0.176 ± 0.107
0.179 ± 0.113
0.202 ± 0.122
0.156 ± 0.099
0.160 ± 0.101
0.168 ± 0.106

SNR
10 dB
0.140 ± 0.093
0.129 ± 0.083
0.135 ± 0.085
0.126 ± 0.083
0.146 ± 0.098
0.129 ± 0.082
0.132 ± 0.087

20 dB
0.122 ± 0.072
0.125 ± 0.078
0.136 ± 0.088
0.126 ± 0.083
0.133 ± 0.086
0.111 ± 0.084
0.125 ± 0.082

30 dB
0.135 ± 0.086
0.105 ± 0.066
0.112 ± 0.078
0.124 ± 0.0811
0.133 ± 0.090
0.114 ± 0.081
0.117 ± 0.079

Mean Error
0.175 ± 0.119
0.166 ± 0.114
0.164 ± 0.116
0.174 ± 0.122
0.159 ± 0.110
0.151 ± 0.110
0.164 ± 0.115

Table 6. MAEs and their standard-deviations after convergence for the Cross-Entropy network.
ROOM

DIST

Close
Distant
Close
Average
Distant
Close
Large
Distant
Mean Noise
Small-10 dB
0.238 ± 0.134
0.228 ± 0.132
0.243 ± 0.124
0.234 ± 0.134
0.244 ± 0.146
0.221 ± 0.125
0.235 ± 0.134

0 dB
0.156 ± 0.092
0.168 ± 0.099
0.170 ± 0.101
0.185 ± 0.103
0.144 ± 0.092
0.140 ± 0.087
0.159 ± 0.097

SNR
10 dB
0.132 ± 0.088
0.123 ± 0.087
0.132 ± 0.083
0.125 ± 0.082
0.143 ± 0.093
0.121 ± 0.088
0.128 ± 0.084

20 dB
0.126 ± 0.075
0.124 ± 0.080
0.138 ± 0.089
0.117 ± 0.088
0.129 ± 0.082
0.119 ± 0.079
0.122 ± 0.079

30 dB
0.131 ± 0.082
0.103 ± 0.068
0.107 ± 0.072
0.136 ± 0.086
0.133 ± 0.086
0.112 ± 0.071
0.116 ± 0.074

MEan Error
0.162 ± 0.106
0.152 ± 0.103
0.153 ± 0.101
0.162 ± 0.110
0.150 ± 0.100
0.140 ± 0.094
0.153 ± 0.108

can be observed that the lowest MAE values were obtained for the "Large Room and Distant Source-Receiver"scenario for both networks. The Cross-Entropy network resulted in the smallest errors in all scenarios. It canalso be noticed that the errors associated with the variation of noise level do not change abruptly, which isdue to the robustness of the methods that use spectral information. In view of the results, the Cross-Entropy
network model was chosen as the proposed model to be compared with the other blind and non-blind reference
procedures.
5.2 Comparative Results
Figure 2 presents the MAE values obtained with the proposed Cross-Entropy network, DNN reference network[2], and with the SDD technique. The Cross-Entropy network presented lowest average error for all config-

Figure 2. MAEs of SDD, proposed and reference DNN networks for different room sizes, source-receiver
distances and noise levels.
urations when compared to the SDD approach, but worse than those obtained by the reference network. No
information was provided in [2], such as number of neurons, use of regularization, algorithms for updating4623

weights and polarizations and the parameters used in the generation of RIRs by the image method. Therefore,
the comparison with this method may not be fair.

6

CONCLUSION

The present work aimed to investigate the possibility of using neural networks for the estimation of reverberation time, by comparing their results with those of the SDD method and another DNN network, whose
information was used to start the calibration of the proposed model. A methodology was created for the network calibration, where it was chosen to explore the use of cross-entropy cost function, commonly appliedin classification networks. In this context, several parameter values were obtained experimentally, such as thenumber of neurons, the weight and bias updating algorithm, and the use of regularization and preprocessing of
input data. The choice was made considering the smallest mean squared error. Regarding the model selection,
this choice was made after evaluating the architecture that had the lowest mean absolute error, so as to becompatible with the results of the reference methods, in several configurations of room sizes, source-receiver
distances, noise levels and ranges of RT60 . It was observed that, in almost all configurations, the cross-entropy
network was the one that generated the lowest values of MAE and was therefore chosen for comparison withthe other approaches. The network obtained in this study presented similar results as those of the SDD method,being higher in the average. In conclusion, the performed experiments confirmed the capacity of the neuralnetworks for the estimation of the reverberation time, in a range of 0.2 s to 1 s, for different room conditions
and signal-to-noise ratios. As future proposals we intend to explore new network topologies, such as recurrent
and convolutional, and estimate other parameters, such as Early Decay Time (EDT), Speech Clarity Index (SCI)
and Direct Reverberant Energy Ratio (DRR).

ACKNOWLEDGEMENTS
The authors thank the financial support of CAPES/DAAD PROBRAL Program for developing this work throughproject number 88881.198848/2018-01, and FAPERJ, Grant 202.844/2018.

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