2023 RISP International Workshop on Nonlinear Circuits, Communications and Signal
Processing (RISP NCSP 2023), Feb. 28 - Mar. 3, 2023

Investigation of Sound Data with Three Types of Noise-Mixing
Effects by Neural Network Using Autocorrelation Function
Takuya Nakamura, Ryosuke Shimizu, Yoko Uwate and Yoshifumi Nishio
Dept. of Electrical and Electronic Engineering, Tokushima University
2-1 Minami-Josanjima, Tokushima 770-8506, Japan
E-mail: {takuya, shimizu, uwate, nisho}@ee.tokushima-u.ac.jp
Abstract
One-dimensional convolutional neural networks (1D-CNN)
are used for time series analysis. However, noise mixed in
the data can interfere with time series analysis. Therefore,
we compare the classification accuracy of two types of patterns. One is a pattern learned by mixing three kinds of noise(white noise, pink noise, and red noise) into the data, and theother is a pattern learned by replacing the original data with
an autocorrelation function (ACF).

disadvantage of being computationally expensive and timeconsuming since they are mainly used for image recognition[5]. Therefore, the use of 1D-CNN can reduce the computational cost. In addition, it is possible to automatically extract features through learning. The one-dimensional Residual Network (1d-ResNet) is used as the model for the NN.
This is a model proposed by He of Facebook AI Researchin 2015 [6]. This model can be used to prevent the gradientloss problem, which prevents learning from progressing in theNN.

1. Introduction
There are many phenomena in the world that have timeseries, such as temperature and seismic waves. In addition,audio and video can also be considered time series. Its features are difficult for the human eye to recognize and judge.
However, by using a neural network (NN), it is possible todiscriminate even the smallest details. The academic field of
NN was established in 1958, and much research has been conducted to date [1]. The advantage of NN is that it can learn
from input data and can be used for pattern recognition anddata classification. NN include well-known models such as
Recurrent neural networks (RNN) and Convolutional neuralnetworks (CNN) [2]. In recent years, many researcher havebeen investigated on time series analysis, in which neural network is trained to analyze and classify time series [3].
However, the data often contain information that is notneeded for analysis, called noise. If the amount of noise
mixed in the data is too large, time series analysis becomescomplicated and very troublesome. In this study, three typesof noise (white noise, pink noise, and red noise) are mixed
into the training data of speech, and the classification accuracy of the NN is investigated.
2. 1D-CNN

Figure 1: The example of image recognition using CNN.

3. Dataset
In this study, three sound data sets are used: fireworks,
thunderstorms, and vacuum cleaner. Table 1 shows the number of training and test data used in this study. These numbers
are performed under the same conditions for all three noises.
Table 1: Number of train data and test data.
Data
Train data
Test data

Original
1500
500

ACF
1500
500

Figures 2, 3, and 4 show examples of fireworks, thunderstorms, and vacuum cleaner sounds.

CNN is a type of NN with a convolution layer and a pooling layer added [4]. CNN is also used for natural language
processing and image recognition. Figure 1 shows the example of image recognition using CNN. However, CNN has the380

2023 RISP International Workshop on Nonlinear Circuits, Communications and Signal
Processing (RISP NCSP 2023), Feb. 28 - Mar. 3, 2023

4.1 Autocorrelation Function
The autocorrelation function (ACF) is defined as the product of time t and data shifted by k from t in time series data.
The correlation between the current data and the data shiftedby k in the past is examined. ACF measures the relationships
between a lagged version of itself over successive time intervals [7]. ACF is expressed by the following Eq. (1).

rk =Figure 2: The example of fireworks sound.

∑ni=k+1 (xt − x)(xt−k − x)∑n2i=1 (xt − x)(1)

n is the sampling number and k is the time lag. Figure 5
shows the example of the original data. Figure 6 shows ACFof the original data. These images also show amplitude on
the vertical axis and time on the horizontal axis.

Figure 3: The example of thunderstorms sound.

Figure 5: Original data.

Figure 4: The example of vacuum cleaner sound.

4. Proposed Method

Figure 6: The autocorrelation function (ACF).

In this study, the following method is used to confirm theaccuracy of the classification of noise in the data.Noises areadded to both the original data and ACF, and the accuracy ofthe original data is compared to the using ACF.
Step 1. The data to be trained is replaced with ACF from theoriginal data.
Step 2. ACF is trained on the 1D-CNN.
Step 3. ACF is trained on the 1d-ResNet.

4.2 Noise
In the field of time series analysis, noise refers to not necessary data that is not subject to analysis. The greater theamount of noise, the less accurate the analysis becomes. In
this case, we used three types of noise: white noise, pinknoise, and red noise. These noises are added to the training
data to train the 1d-ResNet.

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2023 RISP International Workshop on Nonlinear Circuits, Communications and Signal
Processing (RISP NCSP 2023), Feb. 28 - Mar. 3, 2023

4.2.1 White NoiseWhite is noise mixed into data such as voice, and its energy is uniformly mixed in all frequency bands. This noiseis added to the training data to train the 1d-ResNet. Figure 7
shows the example of White noise.

Figure 9: Red Noise.
data. In addition, a dropout layer is used to prevent overtraining. 1d-ResNet is used as the classification model. 1dResNet solves the gradient loss problem, which is a problem of multi-layer networks, by residual learning. Figure 10
shows the structure of ResNet. Convolution(1, 128) means
convolution layer with 1 filter and 128 channel.

Figure 7: White Noise.

4.2.2 Pink Noise
Pink noise is noise whose energy is inversely proportional
to its frequency, and is often represented by the sound of rain
or a television sandstorm. Figure 8 shows the example of Pink
noise.

Figure 8: Pink Noise.

4.2.3 Red NoiseFigure 10: Structure of 1d-ResNet.

6. Simulation Results

Red noise is also known as Brownian noise. A noise that isTables 2, 3 and 4 show the classification accuracy of ACF
strong in energy at low frequencies and becomes less power- and original data whose three kinds of noise rate is verified
ful at higher frequencies inversely proportional to the square from 0.0 to 0.5 in increments of 0.1. These Tables show thatof the frequency. Figure 9 shows the example of Red noise.
for white noise, the use of ACF increased the classification
accuracy for all rates. For pink noise, the classification accuracy is higher only at the rate of 0.0 and 0.4, and lower at
5. Verification Structureother rates. For red noise, the classification accuracy is lower
In this study, two types of classification accuracy are tested than the original data expect for noise rate of 0.3. From thewith each of the three types of noise using the original data above, it is found that the use of ACF to improve the classifor training data and using ACF, and the original data for test fication accuracy of data contaminated with noise is effective382

2023 RISP International Workshop on Nonlinear Circuits, Communications and Signal
Processing (RISP NCSP 2023), Feb. 28 - Mar. 3, 2023

for white noise, but not for pink and red noises.

in 1D-CNN , Journal of Shikoku-Section Joint Convention of the Institutes of Elecrical and Related Engineers,
no. 1-6, p.6, Sep. 2021.

Table 2: Test accuracy of original and ACF(White Noise).
Rate
0.0
0.1
0.2
0.3
0.4
0.5

Original[%]
85.33
75.80
73.41
67.08
63.52
62.04

ACF[%]
85.68
80.18
77.35
77.80
71.13
68.88

[4] M. Matsugu, K. Mori, Y. Mitari and Y. Kaneda, Subject
Independent Facial Expression Recognition with Robust
Face Detection Using a Convolutional Neural Network ,Neural Networks 16, vol.5, pp.555-559, 2003.
[5] Y. Lecun, L. Bottou, Y. Bengio and P. Haffner, GradientBased Learning Applied to Document Recognition ,Proceedings of the IEEE, vol.86, pp.2278-2324, Nov.
1998.

Table 3: Test accuracy of original and ACF(Pink Noise).
Rate
0.0
0.1
0.2
0.3
0.4
0.5

Original[%]
81.65
71.24
68.92
62.84
59.95
58.62

[6] K. He, X. Zhang, S. Ren and J. Sun, Deep Residual Learning for Image Recognition ,IEEE International
Conference on Computer Vision and Pattern Recognition,
arXiv:1512.03385, 10 Dec. 2015.

ACF[%]
83.00
71.44
64.53
59.11
61.52
56.48

[7] T. Furugaki, Y. Uwate and Y. Nishio, Time Series
Classification Using Autocorrelation Function as Training Data in 1D-CNN , Jouenal of Shikoku-Section Joint
Convention of the Institutes of Electrical and Related Engineers, 21, Sep. 2018.

Table 4: Test accuracy of original and ACF(Red Noise).
Rate
0.0
0.1
0.2
0.3
0.4
0.5

Original[%]
66.88
61.07
60.07
57.20
59.61
57.19

ACF[%]
57.04
55.57
58.68
57.76
54.09
55.02

7. Conclusions
In this study, 1d-ResNet is trained with training data containing white noise, pink noise, and red noise using an ACF.
The results showed that ACF is effective in increasing theclassification accuracy for white noise, while the use of ACF
decreased the classification accuracy for pink and red noise.
In future studies, We will seek ways to increase classification
accuracy even with pink and red noise.
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[2] A. Sehgal, N. Kehtarnavaz, A Convolutional Neural
Network Smartphone App for Real-Time Voice Activity
Detection , Access IEEE, vol. 6, pp.9017-9026, 2018.
[3] T. Frugaki, Y. Uwate and Y.Nishio, Time Series Classification Using Autocorrelation Function as Training Data383