Solution of the Problem of Classification of Hydroacoustic Signals Based on Harmonious Wavelets and Machine Learning
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Solution of the Problem of Classification of Hydroacoustic Signals Based on Harmonious Wavelets and Machine Learning D. M. Klionskiia,*, D. I. Kapluna,**, A. S. Voznesenskya,***, S. A. Romanova,****, A. B. Levina a,*****, D. V. Bogaevskiya,******, V. V. Geppenera,*******, and N. V. Razmochaevaa,******** a
St. Petersburg Electrotechnical University “LETI”, St. Petersburg, 197376 Russia * e-mail: [email protected] ** e-mail: [email protected] *** e-mail: [email protected] **** e-mail: [email protected] ***** e-mail: [email protected] ****** e-mail: [email protected] ******* e-mail: [email protected] ******** e-mail: [email protected]
Abstract—Two types of real hydroacoustic signals of whales are classified based on the harmonic wavelet transform (HWT) coefficients (fast implementation), windowed Fourier transform (FT) (spectrogram), and conventional FT using the k-NN algorithm. The accuracy of the classification is estimated for various signal-to-noise ratios (SNRs). In order to reduce the dimension of the feature space during classification using the k-NN algorithm, the use of the modulo N reduction method is proposed. The efficiency of the use of harmonic wavelets in the classification of complex nonstationary signals is experimentally proved. The applicability of speech processing methods for the classification of underwater bioacoustic signals is confirmed. The discussed methods are initially developed taking into account the characteristics of human speech, but, nevertheless, showed good results even without being tuned to the characteristics of the classified signals. The problem of classifying two types of whales by the sounds they make using a neural network is solved.
Keywords: harmonic wavelets, classification, k-NN algorithm, neural networks, machine learning, Fourier transform, windowed Fourier transform, wavelet transform, spectrogram DOI: 10.1134/S1054661820030128
INTRODUCTION
HARMONIC WAVELETS
Classification is one of the tasks of signal processing. The quality of the classification depends on the noise level, the volume of the training and test samples, and the classification algorithm. Also the selection of classification features and the determination of the dimension of the feature space are important aspects. A classification attribute is the property or characteristic of an object by which it is classified. In the case of the classification of real nonstationary signals, it is important that the signs of classification are as informative as possible. Such signs are, among other things, wavelet coefficients.
We will consider the basis based on harmonic wavelets whose spectra are rectangular in the given frequency band [1].
Received December 25, 2018; revised December 26, 2018; accepted April 4, 2020
By definition, harmonic wavelets are defined in the frequency domain: Wavelet function (mother wavelet):
1 , 2π ≤ ω < 4π Ψ(ω) = 2π ⇔ ψ( x) 0, ω < 2π, ω ≥ 4π ∞
=
Ψ(ω)e
i ωx
dω = e
−∞
i 4 πx
−e i 2πx
(1.1)
i 2πx
.
Figure 1 shows the Fourier transform (FT) of the wavelet func
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