Wavelet Theory: Applications of the Wavelet

In this Chapter, continuous Haar wavelet functions base and spline base have been discussed. Haar wavelet approximations are used for solving of differential equations (DEs). The numerical solutions of ordinary differential equations (ODEs) and fractional differential equations (FrDEs) using Haar wavelet base and spline base have been discussed. Also, Haar wavelet base and collocation techniques are used to approximate the solution of Lane-Emden equation of fractional-order showing that the applicability and efficacy of Haar wavelet method. The numerical results have clearly shown the advantage and the efficiency of the techniques in terms of accuracy and computational time. Wavelet transform studied as a mathematical approach and the applications of wavelet transform in signal processing field have been discussed. The frequency content extracted by wavelet transform (WT) has been effectively used in revealing important features of 1D and 2D signals. This property proved very useful in speech and image recognition. Wavelet transform has been used for signal and image compression.

Enhanced ACFM detection performance by multi-parameter synergy analysis

A procedure for the enhancement of alternating current field measurement (ACFM) detection performance is proposed based on a multi-parameter synergy analysis (MPSA) algorithm. Firstly, to gain the maximised ACFM signal characteristics, wavelet base property matching is adopted to choose the favourable wavelet bases. To this aim, the following six base properties should be considered: orthogonality, compact support, symmetry, discrete wavelet transform (DWT), vanishing moment and regularity. It is found that the applicable wavelet bases are Haar, Daubechies (DbN), Symlets (SymN) and Coiflets (CoifN). Secondly, the MPSA method is applied to select the optimal mother wavelet candidates. The candidate with the largest MPSA index value is regarded as the optimum wavelet base. Finally, the proposed MPSA denoising strategy is demonstrated using an ACFM experiment. The results indicate that wavelets Db4 with decomposition level (DL)9 and Sym7 with DL8 are most appropriate for x- and z-axis ACFM signal denoising, respectively. The enhanced ACFM detection performance is experimentally verified and it is found that the signal-to-noise ratio (SNR) is increased by 33.8 dB and 26.7 dB for the x- and z-axis signal, respectively.

A Common Spatial Pattern and Wavelet Packet Decomposition Combined Method for EEG-Based Emotion Recognition

To effectively reduce the day-to-day fluctuations and differences in subjects’ brain electroencephalogram (EEG) signals and improve the accuracy and stability of EEG emotion classification, a new EEG feature extraction method based on common spatial pattern (CSP) and wavelet packet decomposition (WPD) is proposed. For the five-day emotion related EEG data of 12 subjects, the CSP algorithm is firstly used to project the raw EEG data into an optimal subspace to extract the discriminative features by maximizing the Kullback-Leibler (KL) divergences between the two categories of EEG data. Then the WPD algorithm is used to decompose the EEG signals into the related features in time-frequency domain. Finally, four state-of-the-art classifiers including Bagging tree, SVM, linear discriminant analysis and Bayesian linear discriminant analysis are used to make binary emotion classification. The experimental results show that with CSP spatial filtering, the emotion classification on the WPD features extracted with bior3.3 wavelet base gets the best accuracy of 0.862, which is 29.3% higher than that of the power spectral density (PSD) feature without CSP preprocessing, is 23% higher than that of the PSD feature with CSP preprocessing, is 1.9% higher than that of the WPD feature extracted with bior3.3 wavelet base without CSP preprocessing, and is 3.2% higher than that of the WPD feature extracted with the rbio6.8 wavelet base without CSP preprocessing. Our proposed method can effectively reduce the variance and non-stationary of the cross-day EEG signals, extract the emotion related features and improve the accuracy and stability of the cross-day EEG emotion classification. It is valuable for the development of robust emotional brain-computer interface applications.

Determination of the Optimum Wavelet Basis Function for Indonesian Vowel Voice Recognition

Nowadays, wavelet has been widely applied in extracting features of the signal for automatic speech recognition system. Wavelets have many families that are determined by their mother function and order. The use of different wavelets to analyze the same signal would bring different results. In many cases, a trial and error procedure is used to select the optimal wavelet family. That is because there are no particular wavelet basis functions that can be applied to the entire speech signals. Therefore, it is necessary to analyze the similarity between the speech signal and the wavelet base function. One of the methods that can be used is cross-correlation. In this study, the degree of correlation is determined between wavelet base function and Indonesian vowels. The influence of gender and consistencies of the results are also used in the analysis. The results show that db45 and db44 are most similar to male and female vowels utterance, respectively. For consistencies, only vowel e gives a consistent result. Overall, db44 is most similar to all Indonesian vowels utterance.

A novel compound data classification method and its application in fault diagnosis of rolling bearings

Purpose The purpose of this paper is to provide a fault diagnosis method for rolling bearings. Rolling bearings are widely used in industrial appliances, and their fault diagnosis is of great importance and has drawn more and more attention. Based on the common failure mechanism of failure modes of rolling bearings, this paper proposes a novel compound data classification method based on the discrete wavelet transform and the support vector machine (SVM) and applies it in the fault diagnosis of rolling bearings. Design/methodology/approach Vibration signal contains large quantity of information of bearing status and this paper uses various types of wavelet base functions to perform discrete wavelet transform of vibration and denoise. Feature vectors are constructed based on several time-domain indices of the denoised signal. SVM is then used to perform classification and fault diagnosis. Then the optimal wavelet base function is determined based on the diagnosis accuracy. Findings Experiments of fault diagnosis of rolling bearings are carried out and wavelet functions in several wavelet families were tested. The results show that the SVM classifier with the db4 wavelet base function in the db wavelet family has the best fault diagnosis accuracy. Originality/value This method provides a practical candidate for the fault diagnosis of rolling bearings in the industrial applications.