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Extraction of effective features plays a key role in pattern recognition. A large number of patterns, such as speech, radar signals, earthquake signals, handwriting, etc. are of non-stationary signals or exhibit time-varying behavior. The features of these patterns are often located in both the time and frequency domains. The traditional methods fail to extract such kind of features. Fortunately, wavelet packet transform (WPT) can provide an arbitrary time-frequency decomposition for the signals, because a wavelet packet (WP) library contains many WP bases, which can handle the different components of a signal. Therefore, by selecting a suitable basis, which is called "best basis", the effective features can be extracted. In this paper, three criteria are used to select the best WPT basis, namely: (1) distance criterion, (2) divergence criterion and (3) entropy criterion. Three algorithms to implement the above criteria are also provided. Experiments are conducted and the positive results are obtained.

Ultrasonic receiving wave can reflect physical properties and damage degree of coal samples. Therefore, it is of great significance to deeply study the parameters of ultrasonic. In this paper, time-domain characteristics of receiving wave are analyzed systematically, which present good correlation with stress. The frequency spectrum of receiving wave is obtained using Fast Fourier Transform (FFT), and peak frequency and centroid frequency are calculated. During the entire loading process, peak frequency fluctuates around 110kHz, but corresponding centroid frequency decreases obviously at the end stage of loading. According to multifractal theory, the multifractal spectrum of wavelet packet energy characteristics is calculated. The results show that wavelet packet energy distribution has obvious multifractal characteristics, and multifractal parameter $\mathrm{\Delta }\alpha$ presents downward trend before coal samples buckling failure. Based on damage process of the coal samples, the reason of change in $\mathrm{\Delta }\alpha$ value is related to damage degree of coal samples. This research is of great significance for understanding the deformation and failure process of coal samples using ultrasonic technology.

This paper presents a new on-line technique for denoising impulsive vibration signals in noisy environments using Wavelet Packets. The proposed algorithm is based on localizing the frequency subbands of the resonances embedded in impulsive vibration signals. The performance of the algorithm is evaluated in denoising real vibration signals measured from faulty bearings. The results compared to the theoretical values and those obtained by the HFD algorithm show the effectiveness of the proposed algorithm while the computational cost reduces to half.

The study presented in this paper is concerned with the analysis of the ultrasound Doppler signal of the arteries in the spectro-temporal domain using the wavelet packet transform. The spectro-temporal representation is obtained by the decomposition of the Doppler signal in frequency sub-band, using filter banks associated with a well chosen wavelet. It is shown that the decomposition level depends on the stationarity of the Doppler signal, and the best profile of blood flow velocity in arteries is obtained according to an appropriate choice of wavelet type.

Three types of wavelets have been tested on two Doppler signals previously recorded from the carotid and femoral arteries. The best representation is obtained when the frequency sub-bands of the filter bank associated with chosen wavelet are regularly distributed in the frequency domain and the level of decomposition is 7.

Filtering methods have been introduced in the early nineties, in 1988 by Farge et al. for a wavelet filtering, in 1987 by Benzi et al. and in 1994 by Borue for a direct cut-off filtering. The aim of these methods is to filter the velocity and/or the vorticity fields of two-dimensional turbulence experiments in order to enhance the various components of the fluid. Using this king of methods allows us to separate the vortices from the background essentially composed by vorticity filaments. We have also shown the ability of the wavelet packets in performing this filtering. However, we had underestimated, like Borue in 1994, the influence of the filtering process in the computation of the energy and/or enstrophy spectra. We will show in the present paper how the introduction of discontinuities due to the filtering process can subsequently modify the spectra.

A new method by combining wavelet packet transform with kernel learning algorithms is proposed to estimate the mental fatigue state in this paper. The first step of this method is to investigate the impact of long term mental arithmetic task on psychology and physiology of subjects by subjective self-reporting measures, action performance test, power spectral indices of HRV and wavelet packet parameters of EEG. The second step is to calculate the wavelet packet features of all EEG data segments, including relative wavelet packet energy parameters in four frequency bands, wavelet packet entropy and three ratio indices. Finally, kernel principal component analysis (KPCA) and support vector machine (SVM) are jointly applied to differentiate two mental fatigue states. The investigation suggests that the joint KPCA-SVM method is able to effectively reduce the dimensionality of the feature vectors, speed up the convergence in the training of SVM and achieve higher classification accuracy (88%) of the mental fatigue state. Hence KPCA-SVM could be a promising model for the estimation of mental fatigue.

Image fusion is an important concept in remote sensing. Earth observation satellites provide both high-resolution panchromatic and low-resolution multispectral images. Pansharpening is aimed on fusion of a low-resolution multispectral image with a high-resolution panchromatic image. Because of this fusion, a multispectral image with high spatial and spectral resolution is generated. This paper reports a new method to improve spatial resolution of the final multispectral image. The reported work proposes an image fusion method using wavelet packet transform (WPT) and principal component analysis (PCA) methods based on the textures of the panchromatic image. Initially, adaptive PCA (APCA) is applied to both multispectral and panchromatic images. Consequently, WPT is used to decompose the first principal component of multispectral and panchromatic images. Using WPT, high frequency details of both panchromatic and multispectral images are extracted. In areas with similar texture, extracted spatial details from the panchromatic image are injected into the multispectral image. Experimental results show that the proposed method can provide promising results in fusing multispectral images with high-spatial resolution panchromatic image. Moreover, results show that the proposed method can successfully improve spectral features of the multispectral image.

How to find a powerful method of feature representation and extraction is constantly a key issue in 1-D or 2-D signal recognition, such as face recognition. Wavelet Packet(WP) is a potential technique in this regard. However, we face the problems on how to find the optimal WP decomposition and extract the discriminant features. In this paper, we propose a fuzzy c-means shaped membership function in the evaluation of the classification abilities of WP sub-spaces or WP coefficients for seeking the optimal WP decomposition and extracting discriminant features. The classification is performed by Enhanced Fisher Linear Discriminant Model (EFM) and a conventional linear classifier. Experiments on typical Yaleface database are carried out. Compared with the well-known Principal Component Analysis(PCA), the face recognition rate of WP based method is higher than that obtained by PCA.

In view of the frequency spectrum characteristics of vibration signal of rotating machinery, the versatile model of pattern recognition and fault diagnosis of rotating machinery based on wavelet packet-neural network is presented. The abrupt change information of vibration signal can be obtained and the features related to the fault can be extracted by employing the multi-dimension and multi-resolution characteristics of wavelet to decompose and reconstruct the vibration signal. Energy of special frequency ranges is selected as feature vector and is put into ART2 neural network, then the trained neural network is able to perform real-time diagnosis of rotating machinery fault. The effectiveness of this method is proved by emulating rotating machinery failures.

This paper presents the method of multi-resolution analysis used in 2D image data to extract the curved edge features. The method is based on the combination of multi-resolution decomposition through Wavelet Packet and Prime Ridgelet transform. We call this combination Prime Wavelet Packet Contourlet Transform-PWPC. At each leave of Packet Wavelet Packet Tree, the prime ridgelet transform is applied on the band pass image or packet, which contains the high frequency data. The experiment shows that the PWPC coefficients are good approximations to curved edges. The speed of PWPC is faster than that of the basic Curvelet transform. This transform is very suitable to represent the noisy curved features that often exist in medicine or nano/micro images.

There are a series of advantages about the double involute gear with ladder shape of tooth. But whether the ladder-shaped of the double involute gear will cause the increase of the vibration or bring some other vibration components? This problem is especially concerned by people all the while. The essence of wavelet packet analysis is to make further decomposition of wavelet decomposed result, so the analysis will yield much better frequency localization. Duo to wavelet packet has agile and changeful characteristics in disposing signals, it can be used to analyzed and compared the vibration characteristics of common involute gear and double involute gear conveniently and exactly by decomposing and reconstructing signal components of correlative frequency components. The result shows that the double involute gear has lower noise, smaller vibration and better dynamics characteristic than common inlovute gear

A new algorithm for speech enhancement based on wavelet shrinkage method is presented in this paper. First, the noisy speech by the Bark-scaled Wavelet Packet (BS-WPD) is decomposed to simulate the human auditory characteristics. Then a new thresholding algorithm which has many advantages over soft and hard thresholdings put forward by D.L. Donoho and I.M. Johnstone is proposed. Simulation results indicate that this new method is very useful and efficient in the process of white noise reduction from speech, and the new thresholding algorithm gives better SNR improvement than other traditional thresholding algorithms.