Enhanced Fourier Transform Using Wavelet Packet Decomposition

Many domains, including communication, signal processing, and image processing, use the Fourier Transform as a mathematical tool for signal analysis. Although it can analyze signals with steady and transitory properties, it has limits. The Wavelet Packet Decomposition (WPD) is a novel technique that we suggest in this study as a way to improve the Fourier Transform and get beyond these drawbacks. In this experiment, we specifically considered the utilization of Daubechies level 4 for the wavelet transformation. The choice of Daubechies level 4 was motivated by several reasons. Daubechies wavelets are known for their compact support, orthogonality, and good time-frequency localization. By choosing Daubechies level 4, we aimed to strike a balance between preserving important transient information and avoiding excessive noise or oversmoothing in the transformed signal. Then we compared the outcomes of our suggested approach to the conventional Fourier Transform using a non-stationary signal. The findings demonstrated that the suggested method offered a more accurate representation of non-stationary and transient signals in the frequency domain. Our method precisely showed a 12% reduction in MSE and a 3% rise in PSNR for the standard Fourier transform, as well as a 35% decrease in MSE and an 8% increase in PSNR for voice signals when compared to the traditional wavelet packet decomposition method.

Theoretical research on structural damage alarming of long-span bridges using wavelet packet analysis

The state equation and observation equation of the structural dynamic systems under various analysis scales are derived based on wavelet packet analysis. The time-frequency properties of structural dynamic response under various scales are further formulated. The theoretical analysis results reveal that the wavelet packet energy spectrum （WPES） obtained from wavelet packet decomposition of structural dynamic response will detect the presence of structural damage. The sensitivity analysis of the WPES to structural damage and measurement noise is also performed. The transfer properties of the structural system matrix and the observation noise under various analysis scales are formulated, which verify the damage alarming reliability using the proposed WPES with preferable damage sensitivity and noise robusticity.

Acoustic emission source identification based on harmonic wavelet packet and support vector machine

In order to solve the fatigue damage identification problem of helicopter moving components, a new approach for acoustic emission （AE） source type identification based on the harmonic wavelet packet （HWPT） feature extraction and the hierarchy support vector machine （H-SVM） classifier is proposed. After a four-level decomposition of the HWPT, the energy feature of AE signals in different frequency bands is extracted, which overcomes the shortcomings of the traditional wavelet packet including energy leakage, and inflexible frequency band selection and different frequency resolutions on different levels. The H-SVM classifier is trained with a subset of the experimental data for known AE source types and tested using the remaining set of data. The results of pressure-off experiments on the specimens of carbon fiber materials indicate that the proposed approach can effectively implement the AE source type identification, and has a better performance in terms of computational efficiency and identification accuracy than the wavelet packet （WPT） feature extraction.

Structural health monitoring of long-span suspension bridges using wavelet packet analysis

During the service life of civil engineering structures such as long-span bridges, local damage at key positions may continually accumulate, and may finally result in their sudden failure. One core issue of global vibration-based health monitoring methods is to seek some damage indices that are sensitive to structural damage, This paper proposes an online structural health monitoring method for long-span suspension bridges using wavelet packet transform （WPT）. The WPT- based method is based on the energy variations of structural ambient vibration responses decomposed using wavelet packet analysis. The main feature of this method is that the proposed wavelet packet energy spectrum （WPES） has the ability to detect structural damage from ambient vibration tests of a long-span suspension bridge. As an example application, the WPES-based health monitoring system is used on the Runyang Suspension Bridge under daily environmental conditions. The analysis reveals that changes in environmental temperature have a long-term influence on the WPES, while the effect of traffic loadings on the measured WPES of the bridge presents instantaneous changes because of the nonstationary properties of the loadings. The condition indication indices VD reflect the influences of environmental temperature on the dynamic properties of the Runyang Suspension Bridge. The field tests demonstrate that the proposed WPES-based condition indication index VD is a good candidate index for health monitoring of long-span suspension bridges under ambient excitations.

Wavelet Packet Domain LMS Based Multi-User Detection

An improved wavelet packet domain least mean square （IWPD-LMS） based adaptive muhiuser detection algorithm is proposed. The algorithm employs the wavelet packet transform to rewhiten the input data, and chooses the best wavelet packet basis according to a novel convergence contribution function rather than the conventional Shannon entropy. The theoretic analyses show that the inadequacy of the eigenvalue spread of the tap-input correlation matrix is ameliorated, thus the convergence performance is improved greatly. The simulation result of convergence performance and bit error rate（BER） performance as a function of the signal power to noise power ratio（SNR） are presented finally to prove the validity of the proposed algorithm.

Performance of STBC-MC-CDMA system based on complex wavelet packet and turbo coding

On the basis of analyzing the principle of the space-time coding technique and the multi-carrier code division multiple access （MC-CDMA） technique, adopting the turbo codes as channel coding and the optimized complex wavelet packet as multi-carrier modulation, a novel space-time block coded the MC-CDMA system based on complex wavelet packet and turbo coding is proposed, and the system bit error rate （BER） performance in the Rayleigh fading channel is investigated. The system can make full use of space-time block codes＇ transmit diversity and turbo codes＇ good ability against fading channel to improve the BER performance significantly, and it can also avoid the decrease of spectrum efficiency of conventional MC-CDMA due to inserting cyclic prefix （CP） by utilizing superior characteristics of the optimized complex wavelet packet. Simulation results show that the proposed space-time block coded MC-CDMA system based on the complex wavelet packet performs better than the conventional space-time block coded MC-CDMA （STBC-MC-CDMA） system, and slightly outperforms the STBC-MC-CDMA with CP. Moreover, the application of the space-time block coding technique concatenated with turbo codes strengthens the system ability to combat various interferences in fading channel further.

Ignition Pattern Analysis for Automotive Engine Trouble Diagnosis Using Wavelet Packet Transform and Support Vector Machines

Engine spark ignition is an important source for diagnosis of engine faults.Based on the waveform of the ignition pattern,a mechanic can guess what may be the potential malfunctioning parts of an engine with his/her experience and handbooks.However,this manual diagnostic method is imprecise because many spark ignition patterns are very similar.Therefore,a diagnosis needs many trials to identify the malfunctioning parts.Meanwhile the mechanic needs to disassemble and assemble the engine parts for verification.To tackle this problem,an intelligent diagnosis system was established based on ignition patterns.First,the captured patterns were normalized and compressed.Then wavelet packet transform（WPT） was employed to extract the representative features of the ignition patterns.Finally,a classification system was constructed by using multi-class support vector machines（SVM） and the extracted features.The classification system can intelligently classify the most likely engine fault so as to reduce the number of diagnosis trials.Experimental results show that SVM produces higher diagnosis accuracy than the traditional multilayer feedforward neural network.This is the first trial on the combination of WPT and SVM to analyze ignition patterns and diagnose automotive engines.

FEATURE EXTRACTION OF VIBRATION SIGNALS BASED ON WAVELET PACKET TRANSFORM

A method is proposed for the analysis of vibration signals from components ofrotating machines, based on the wavelet packet transformation (WPT) and the underlying physicalconcepts of modulation mechanism. The method provides a finer analysis and better time-frequencylocalization capabilities than any other analysis methods. Both details and approximations are splitinto finer components and result in better-localized frequency ranges corresponding to each node ofa wavelet packet tree. For the punpose of feature extraction, a hard threshold is given and theenergy of the coefficients above the threshold is used, as a criterion for the selection of the bestvector. The feature extraction of a vibration signal is accomplished by computing thereconstruction signal and its spectrum. When applied to a rolling bear vibration signal featureextraction, the proposed method can lead to be very effective.

Influence of explosion parameters on wavelet packet frequency band energy distribution of blast vibration

Blast vibration analysis is one of the important foundations for studying the control technology of blast vibration damage. According to blast vibration live data that have been collected and the characteristics of short-time non-stationary random signals, the wavelet packet energy spectrum analysis for blast vibration signal has made by wavelet packet analysis technology and the signals were measured under different explosion parameters （the maximal section dose, the distance of blast source to measuring point and the section number of millisecond detonator）. The results show that more than 95% frequency band energy of the signals sl-s8 concentrates at 0-200 Hz and the main vibration frequency bands of the signals sl-s8 are 70.313-125, 46.875-93.75, 15.625-93.75, 0-62.5, 42.969-125, 15.625-82.031, 7.813-62.5 and 0-62.5 Hz. Energy distributions for different frequency bands of blast vibration signal are obtained and the characteristics of energy distributions for blast vibration signal measured under different explosion parameters are analyzed. From blast vibration signal energy, the decreasing law of blast seismic waves measured under different explosion parameters was studied and the wavelet packet analysis is an effective means for studying seismic effect induced by blast.

A novel internet traffic identification approach using wavelet packet decomposition and neural network

Internet traffic classification plays an important role in network management, and many approaches have been proposed to classify different kinds of internet traffics. A novel approach was proposed to classify network applications by optimized back-propagation (BP) neural network. Particle swarm optimization (PSO) algorithm was used to optimize the BP neural network. And in order to increase the identification performance, wavelet packet decomposition (WPD) was used to extract several hidden features from the time-frequency information of network traffic. The experimental results show that the average classification accuracy of various network applications can reach 97%. Moreover, this approach optimized by BP neural network takes 50% of the training time compared with the traditional neural network.

Classification using wavelet packet decomposition and support vector machine for digital modulations

To make the modulation classification system more suitable for signals in a wide range of signal to noise rate （SNR）, a feature extraction method based on signal wavelet packet transform modulus maxima matrix （WPTMMM） and a novel support vector machine fuzzy network （SVMFN） classifier is presented. The WPTMMM feature extraction method has less computational complexity, more stability, and has the preferable advantage of robust with the time parallel moving and white noise. Further, the SVMFN uses a new definition of fuzzy density that incorporates accuracy and uncertainty of the classifiers to improve recognition reliability to classify nine digital modulation types （i.e. 2ASK, 2FSK, 2PSK, 4ASK, 4FSK, 4PSK, 16QAM, MSK, and OQPSK）. Computer simulation shows that the proposed scheme has the advantages of high accuracy and reliability （success rates are over 98% when SNR is not lower than 0dB）, and it adapts to engineering applications.

Damage Detection Methods for Offshore Platforms Based on Wavelet Packet Transform

The wavelet packet transform is used for the damage detection of offshore platforms. When some damage occurs, the dynamic response parameters of the structure will shift subtly. However, in some cases, the dynamic parameters, such as dynamic response, are not sensitive, and it is very difficult to predict the existence of damage. The present paper aims to describe how to find small damage by the use of wavelet packet transform. As the wavelet packet transform can be used to quickly find the singularity of the response signal on different scales, the acceleration signal of a damaged offshore platform in the time domain is transformed through the wavelet packet. Experimental results show that the Daubechies 4 wavelet transform can be used to detect damage.

Radar Emitter Signal Recognition Using Wavelet Packet Transform and Support Vector Machines

This paper presents a novel method for radar emitter signal recognition. First, wavelet packet transform （WPT） is introduced to extract features from radar emitter signals. Then, rough set theory is used to select the optimal feature subset with good discriminability from original feature set, and support vector machines （SVMs） are employed to design classifiers. A large number of experimental results show that the proposed method achieves very high recognition rates for 9 radar emitter signals in a wide range of signal-to-noise rates, and proves a feasible and valid method.

Separation of closely spaced modes by combining complex envelope displacement analysis with method of generating intrinsic mode functions through filtering algorithm based on wavelet packet decomposition

One of the important issues in the system identification and the spectrum analysis is the frequency resolution, i.e., the capability of distinguishing between two or more closely spaced frequency components. In the modal identification by the empirical mode decomposition （EMD） method, because of the separating capability of the method, it is still a challenge to consistently and reliably identify the parameters of structures of which modes are not well separated. A new method is introduced to generate the intrin- sic mode functions （IMFs） through the filtering algorithm based on the wavelet packet decomposition （GIFWPD）. In this paper, it is demonstrated that the CIFWPD method alone has a good capability of separating close modes, even under the severe condition beyond the critical frequency ratio limit which makes it impossible to separate two closely spaced harmonics by the EMD method. However, the GIFWPD-only based method is impelled to use a very fine sampling frequency with consequent prohibitive computational costs. Therefore, in order to decrease the computational load by reducing the amount of samples and improve the effectiveness of separation by increasing the frequency ratio, the present paper uses a combination of the complex envelope displacement analysis （CEDA） and the GIFWPD method. For the validation, two examples from the previous works are taken to show the results obtained by the GIFWPD-only based method and by combining the CEDA with the GIFWPD method.

Application of the wavelet packet and its energy spectrum to identify nugget splash during the aluminum alloys spot welding

Nugget splash during aluminum alloys spot welding has a detrimental effect on weld nugget integrity, strength and durability of the welded joints. This investigation is performed to identify nugget splash from voltage signals because these are easily accessible on-line. In the present work, we propose a novel method based on the wavelet packet transform and its energy spectrum for pattern recognition of splash signal. The result demonstrates that this novel method is more accuracy and a useful way of monitoring the spot welding quality.

Motion Classification of EMG Signals Based on Wavelet Packet Transform and LS-SVMs Ensemble

This paper presents an effective method for motion classification using the surface electromyographic (sEMG) signal collected from the forearm. Given the nonlinear and time-varying nature of EMG signal, the wavelet packet transform (WPT) is introduced to extract time-frequency joint information. Then the multi-class classifier based on the least squares support vector machine (LS-SVM) is constructed and verified in the various motion classification tasks. The results of contrastive experiments show that different motions can be identified with high accuracy by the presented method. Furthermore, compared with other classifiers with different features, the performance indicates the potential of the SVM techniques combined with WPT in motion classification.

A NOVEL ALGORITHM OF MULTI-SENSOR IMAGE FUSION BASED ON WAVELET PACKET TRANSFORM

In order to enhance the image information from multi-sensor and to improve the abilities of the information analysis and the feature extraction, this letter proposed a new fusion approach in pixel level by means of the Wavelet Packet Transform (WPT). The WPT is able to decompose an image into low frequency band and high frequency band in higher scale. It offers a more precise method for image analysis than Wavelet Transform (WT). Firstly, the proposed approach employs HIS (Hue, Intensity, Saturation) transform to obtain the intensity component of CBERS (China-Brazil Earth Resource Satellite) multi-spectral image. Then WPT transform is employed to decompose the intensity component and SPOT (Systeme Pour I'Observation de la Therre ) image into low frequency band and high frequency band in three levels. Next, two high frequency coefficients and low frequency coefficients of the images are combined by linear weighting strategies. Finally, the fused image is obtained with inverse WPT and inverse HIS. The results show the new approach can fuse details of input image successfully, and thereby can obtain a more satisfactory result than that of HM (Histogram Matched)-based fusion algorithm and WT-based fusion approach.

HYBRID WAVELET PACKET-TEAGER ENERGY OPERATOR ANALYSIS AND ITS APPLICATION FOR GEARBOX FAULT DIAGNOSIS

Based on wavelet packet decomposition （WPD） algorithm and Teager energy operator （TEO）, a novel gearbox fault detection and diagnosis method is proposed. Its process is expatiated after the principles of WPD and TEO modulation are introduced respectively. The preprocessed sigaaal is interpolated with the cubic spline function, then expanded over the selected basis wavelets. Grouping its wavelet packet components of the signal based on the minimum entropy criterion, the interpolated signal can be decomposed into its dominant components with nearly distinct fault frequency contents. To extract the demodulation information of each dominant component, TEO is used. The performance of the proposed method is assessed by means of several tests on vibration signals collected from the gearbox mounted on a heavy truck. It is proved that hybrid WPD-TEO method is effective and robust for detecting and diagnosing localized gearbox faults.

A SCHEME OF M-ARY MULTI-CARRIER SPREAD SPECTRUM BASED ON WAVELET PACKET

A novel scheme of M-ary multi-carrier spread spectrum based on wavelet packet is proposed. Its performance is investigated for a multipath, slow Rayteigh fading channel. The performance advantages of the system over that based on DFT are demonstrated by both analytical and simulation methods.

Application of wavelet packet decomposition and its energy spectrum on the coal-rock interface identification

The theory and method of wavelet packet decomposition and its energy spectrum dealing with the coal rock Interface Identification are presented in the paper. The characteristic frequency band of the coal rock signal could be identified by wavelet packet decomposition and its energy spectrum conveniently, at the same time, quantification analysis were performed. The result demonstrates that this method is more advantageous and of practical value than traditional Fourier analysis method.