Showing papers on "Continuous wavelet transform published in 2014"

Application of Cross Wavelet Transform for ECG Pattern Analysis and Classification

Abstract: In this paper, we use cross wavelet transform (XWT) for the analysis and classification of electrocardiogram (ECG) signals. The cross-correlation between two time-domain signals gives a measure of similarity between two waveforms. The application of the continuous wavelet transform to two time series and the cross examination of the two decompositions reveal localized similarities in time and frequency. Application of the XWT to a pair of data yields wavelet cross spectrum (WCS) and wavelet coherence (WCOH). The proposed algorithm analyzes ECG data utilizing XWT and explores the resulting spectral differences. A pathologically varying pattern from the normal pattern in the QT zone of the inferior leads shows the presence of inferior myocardial infarction. A normal beat ensemble is selected as the absolute normal ECG pattern template, and the coherence between various other normal and abnormal subjects is computed. The WCS and WCOH of various ECG patterns show distinguishing characteristics over two specific regions R1 and R2, where R1 is the QRS complex area and R2 is the T-wave region. The Physikalisch-Technische Bundesanstalt diagnostic ECG database is used for evaluation of the methods. A heuristically determined mathematical formula extracts the parameter(s) from the WCS and WCOH. Empirical tests establish that the parameter(s) are relevant for classification of normal and abnormal cardiac patterns. The overall accuracy, sensitivity, and specificity after combining the three leads are obtained as 97.6%, 97.3%, and 98.8%, respectively.

The fourier-based synchrosqueezing transform

Abstract: The short-time Fourier transform (STFT) and the continuous wavelet transform (CWT) are extensively used to analyze and process multicomponent signals, i.e. superpositions of modulated waves. The synchrosqueezing is a post-processing method which circumvents the uncertainty relation inherent to these linear transforms, by reassigning the coefficients in scale or frequency. Originally introduced in the setting of the CWT, it provides a sharp, concentrated representation, while remaining invertible. This technique received a renewed interest with the recent publication of an approximation result related to the application of the synchrosqueezing to multi-component signals. In the current paper, we adapt the formulation of the synchrosqueezing to the STFT and state a similar theoretical result to that obtained in the CWT framework. The emphasis is put on the differences with the CWT-based synchrosqueezing with numerical experiments illustrating our statements.

Spectral estimation—What is new? What is next?

Abstract: Spectral estimation, and corresponding time-frequency representation for nonstationary signals, is a cornerstone in geophysical signal processing and interpretation. The last 10-15 years have seen the development of many new high-resolution decompositions that are often fundamentally different from Fourier and wavelet transforms. These conventional techniques, like the short-time Fourier transform and the continuous wavelet transform, show some limitations in terms of resolution (localization) due to the trade-off between time and frequency localizations and smearing due to the finite size of the time series of their template. Well-known techniques, like autoregressive methods and basis pursuit, and recently developed techniques, such as empirical mode decomposition and the synchrosqueezing transform, can achieve higher time-frequency localization due to reduced spectral smearing and leakage. We first review the theory of various established and novel techniques, pointing out their assumptions, adaptability, and expected time-frequency localization. We illustrate their performances on a provided collection of benchmark signals, including a laughing voice, a volcano tremor, a microseismic event, and a global earthquake, with the intention to provide a fair comparison of the pros and cons of each method. Finally, their outcomes are discussed and possible avenues for improvements are proposed.

Time-Frequency Analysis of Seismic Data Using Synchrosqueezing Transform

Abstract: Time-frequency analysis can provide useful information in seismic data processing and interpretation. An accurate time-frequency representation is important in highlighting subtle geologic structures and in detecting anomalies associated with hydrocarbon reservoirs. The popular methods, like short-time Fourier transform and wavelet analysis, have limitations in dealing with fast varying instantaneous frequencies, which is often the characteristic of seismic data. The synchrosqueezing transform (SST) is a promising tool to provide a detailed time-frequency representation. We apply the SST to seismic data and show its potential to seismic signal processing applications.

Generator Coherency Using the Wavelet Phase Difference Approach

Abstract: In this paper, the wavelet phase difference (WPD) approach is applied for the identification of power system areas with coherent generator groups. This approach allows observation, at different frequency bands, of movement of low frequency electromechanical oscillations (LFEO), identified at different parts of the power system and the identification of the inter-area components that move or do not move together. An illustration of the applied approach was performed on the New England (NE) 39-bus test system. The interesting results of WPD application are also presented in a real wide-area measurement data from European interconnected power system. By using the discrete wavelet transform (DWT) and Hilbert-Huang transform (HHT), the validation of results from WPD approach is also given.

Phase Estimation in Optical Interferometry

Abstract: Fourier Fringe Demodulation Mitsuo Takeda INTRODUCTION PRINCIPLE OF THE GENERIC FTM FOR FRINGE DEMODULATION GENERAL FEATURES OF THE FTM APPLICATIONS OF FOURIER FRINGE DEMODULATION CONCLUSION REFERENCES Windowed Fourier Transforms Jingang Zhong and Jiawen Weng INTRODUCTION PHASE DEMODULATION BASED ON FOURIER TRANSFORM PHASE DEMODULATION BASED ON WINDOWED FOURIER TRANSFORM PHASE DEMODULATION BASED ON ADAPTIVE WINDOWED FOURIER TRANSFORM NUMERICAL ANALYSIS EXPERIMENTAL ANALYSIS EXAMPLE CONCLUSION REFERENCES Continuous Wavelet Transforms Lionel R. Watkins INTRODUCTION THE ONE-DIMENSIONAL CONTINUOUS WAVELET TRANSFORM WAVELET CENTERS AND BANDWIDTHS SCALOGRAMS RIDGE OF THE CONTINUOUS WAVELET TRANSFORM THE GRADIENT METHOD THE PHASE METHOD FOURIER APPROACH TO CWT EFFECT OF DISCONTINUITIES AT THE SIGNAL EDGE ONE-DIMENSIONAL WAVELET FUNCTIONS TWO-DIMENSIONAL CONTINUOUS WAVELET TRANSFORM CONCLUSIONS APPENDIX A RIDGE OF THE TWO-DIMENSIONAL CWT REFERENCES The Spiral Phase Transform Kieran G. Larkin INTRODUCTION THEORY IMPLEMENTATION WHEN TO USE THE SPIRAL PHASE TRANSFORM PRACTICAL DEMODULATION EXAMPLE SUMMARY REFERENCES Regularized Phase Estimation Methods in Interferometry Moises Padilla and Manuel Servin INTRODUCTION REGULARIZED LOW-PASS LINEAR FILTERING CONVOLUTION-BASED TEMPORAL PHASE-SHIFTING INTERFEROMETRY SPATIALLY REGULARIZED TEMPORAL LINEAR CARRIER INTERFEROMETRY CONVOLUTION-BASED SPATIAL-CARRIER INTERFEROMETRY REGULARIZATION IN GENERAL SPATIAL CARRIER INTERFEROMETRY TEMPORAL REGULARIZATION IN PHASE-SHIFTING INTERFEROMETRY REGULARIZED PHASE ESTIMATION OF SINGLE-IMAGE CLOSED-FRINGES INTERFEROGRAMS REGULARIZED SPATIAL INTERPOLATION-EXTRAPOLATION IN INTERFEROMETRY REGULARIZATION IN LATERAL SHEARING INTERFEROMETRY CONCLUSIONS REFERENCES Local Polynomial Phase Modeling and Estimation Gannavarpu Rajshekhar, Sai Siva Gorthi, and Pramod Rastogi INTRODUCTION DIGITAL HOLOGRAPHIC INTERFEROMETRY PRINCIPLE MAXIMUM LIKELIHOOD ESTIMATION CUBIC PHASE FUNCTION HIGH-ORDER AMBIGUITY FUNCTION PHASE-DIFFERENCING OPERATOR CONCLUSIONS REFERENCES Signal-Processing Methods in Phase-Shifting Interferometry Abhijit Patil, Rajesh Langoju, and Pramod Rastogi INTRODUCTION TEMPORAL TECHNIQUES LINEAR PHASE STEP ESTIMATION METHODS EVALUATION OF PHASE DISTRIBUTION DUAL PZT IN HOLOGRAPHIC MOIRE EVALUATION OF PHASE DISTRIBUTION IN HOLOGRAPHIC MOIRE NONLINEAR PHASE STEP ESTIMATION METHOD SUMMARY OF SIGNAL-PROCESSING METHODS REFERENCES Phase Unwrapping David R. Burton INTRODUCTION THE BASIC OPERATION OF PHASE UNWRAPPING PHASE UNWRAPPING: THE PRACTICAL ISSUES AND CHALLENGES PHASE UNWRAPPING AND DEFENSIVE PROGRAMMING PHASE-UNWRAPPING ALGORITHMS ONLINE SOURCES OF UNWRAPPING CODES CONCLUSION REFERENCES Uncertainty in Phase Measurements Erwin Hack INTRODUCTION INFLUENCE QUANTITIES QUANTIFICATION OF UNCERTAINTY CONTRIBUTIONS UNCERTAINTY CONTRIBUTIONS FOR IMAGING UNCERTAINTY CONTRIBUTIONS FOR LINEAR PHASE-STEPPING ALGORITHMS PHASE MEASUREMENT UNCERTAINTY FOR CARRE-TYPE ALGORITHMS PHASE MEASUREMENT UNCERTAINTY FOR SINGLE-FRAME ALGORITHMS SUMMARY REFERENCES Index

K-SVD Meets Transform Learning: Transform K-SVD

Abstract: Recently there has been increasing attention directed towards the analysis sparsity models. Consequently, there is a quest for learning the operators which would enable analysis sparse representations for signals in hand. Analysis operator learning algorithms such as the Analysis K-SVD have been proposed. Sparsifying transform learning is a paradigm which is similar to the analysis operator learning, but they differ in some subtle points. In this paper, we propose a novel transform operator learning algorithm called as the Transform K-SVD, which brings the transform learning and the K-SVD based analysis dictionary learning approaches together. The proposed Transform K-SVD has the important advantage that the sparse coding step of the Analysis K-SVD gets replaced with the simple thresholding step of the transform learning framework. We show that the Transform K-SVD learns operators which are similar both in appearance and performance to the operators learned from the Analysis K-SVD, while its computational complexity stays much reduced compared to the Analysis K-SVD.

Wavelet-Based Method for Generating Nonstationary Artificial Pulse-Like Near-Fault Ground Motions

Abstract: A method to generate a suite of artificial near-fault ground motion time histories for specified earthquakes is presented. A wavelet-based nonstationary (WB-NS) model has been employed to effectively capture the time-varying frequency content of a particular acceleration record and continuous wavelet transform has been used to simulate the largest velocity pulse. Furthermore, an iterative procedure using discrete wavelet transform is utilized to modify an earthquake ground motion and generate energy-compatible ground motion. Eventually, the artificial near-fault accelerogram is achieved via the superposition of a coherent extracted velocity pulse with a random acceleration record corresponding to a WB-NS model and multiplied by a time-modulating envelope function. The effectiveness of the method is demonstrated by comparing the spectral response and Arias intensity curves of the simulated accelerograms with those of the real records.

Analysis of multicomponent LFM signals by Teager Huang-Hough transform

Abstract: A novel detection approach of linear FM (LFM) signals, with single or multiple components, in the time-frequency plane of Teager-Huang (TH) transform is presented. The detection scheme that combines TH transform and Hough transform is referred to as Teager-Huang-Hough (THH) transform. The input signal is mapped into the time-frequency plane by using TH transform followed by the application of Hough transform to recognize time-frequency components. LFM components are detected and their parameters are estimated from peaks and their locations in the Hough space. Advantages of THH transform over Hough transform of Wigner-Ville distribution (WVD) are: 1) cross-terms free detection and estimation, and 2) good time and frequency resolutions. No assumptions are made about the number of components of the LFM signals and their models. THH transform is illustrated on multicomponent LFM signals in free and noisy environments and the results compared with WVD-Hough and pseudo-WVD-Hough transforms.

A Wavelet-Based Assessment of Topographic-Isostatic Reductions for GOCE Gravity Gradients

Abstract: Gravity gradient measurements from ESA’s satellite mission Gravity field and steady-state Ocean Circulation Explorer (GOCE) contain significant high- and mid-frequency signal components, which are primarily caused by the attraction of the Earth’s topographic and isostatic masses. In order to mitigate the resulting numerical instability of a harmonic downward continuation, the observed gradients can be smoothed with respect to topographic-isostatic effects using a remove–compute–restore technique. For this reason, topographic-isostatic reductions are calculated by forward modeling that employs the advanced Rock–Water–Ice methodology. The basis of this approach is a three-layer decomposition of the topography with variable density values and a modified Airy–Heiskanen isostatic concept incorporating a depth model of the Mohorovicic discontinuity. Moreover, tesseroid bodies are utilized for mass discretization and arranged on an ellipsoidal reference surface. To evaluate the degree of smoothing via topographic-isostatic reduction of GOCE gravity gradients, a wavelet-based assessment is presented in this paper and compared with statistical inferences in the space domain. Using the Morlet wavelet, continuous wavelet transforms are applied to measured GOCE gravity gradients before and after reducing topographic-isostatic signals. By analyzing a representative data set in the Himalayan region, an employment of the reductions leads to significantly smoothed gradients. In addition, smoothing effects that are invisible in the space domain can be detected in wavelet scalograms, making a wavelet-based spectral analysis a powerful tool.

Reference-free damage detection for truss bridge structures by continuous relative wavelet entropy method

Abstract: This article proposes a continuous relative wavelet entropy–based reference-free damage detection algorithm for truss bridge structures. Advantages of the proposed method are that (1) there is no need to measure dynamic response of pristine structures, in other words, the method is reference-free; (2) it is suitable for highly nonlinear and nonstationary random response data due to the multiresolution signal analysis feature of the continuous wavelet transform; and (3) it is sensitive to slight damage extents (i.e. 5%–10%) for the tested damage type (i.e. loosening of bolts). In order to demonstrate consistency and sensitivity of the proposed method, multiple experimental tests using a laboratory-size truss structure were mainly conducted for various damage scenarios and progressive damage states. The proposed continuous relative wavelet entropy–based reference-free damage detection algorithm showed reliable damage localization capabilities, and it is proven as an effective method compared to other damage...

Reliable Fault Diagnosis of Multiple Induction Motor Defects Using a 2-D Representation of Shannon Wavelets

Abstract: This paper proposes an approach for a 2-D representation of Shannon wavelets for highly reliable fault diagnosis of multiple induction motor defects. Since the wavelet transform is efficient for analyzing non-stationary and non-deterministic vibration signals, this paper utilizes wavelet coefficients deduced from the Shannon mother wavelet function with varying dilation and translation parameters to create 2-D gray-level images. Using the resulting images and their associated texture characteristics, this paper extracts features by generating global neighborhood structure maps, which are used to extract global image features. The texture features are then used as inputs in one-against-all multi-class support vector machines to identify faults in the induction machine. To evaluate the performance of the proposed approach, it is compared with five conventional state-of-the-art algorithms in terms of classification accuracy. In addition, this paper explores the robustness of the proposed approach in noisy environments by adding white Gaussian noise to the acquired vibration signals. The experimental results indicate that the proposed approach outperforms conventional algorithms in terms of the classification accuracy. Moreover, the proposed approach achieves higher classification accuracy, even in noisy environments.

Hilbert–Huang Transform Time-Frequency Analysis in $\phi $ -OTDR Distributed Sensor

Abstract: Time-frequency analysis is a practical method to analyze the characteristics of vibration signals. We introduce the Hilbert–Huang transform (HHT) to the phase-sensitive optical time-domain reflectometer sensor system for time-frequency analysis. The Hilbert spectral analysis makes the instantaneous frequency meaningful, and acquires the high frequency resolution. Compared with other time-frequency analysis methods, such as the short-time Fourier transform and the continuous wavelet transform, HHT presents high frequency resolution for both stationary and nonstationary signals, and with much less time consuming.

Source location in plates based on the multiple sensors array method and wavelet analysis

Abstract: A new method for impact source localization in a plate is proposed based on the multiple signal classification (MUSIC) and wavelet analysis. For source localization, the direction of arrival of the wave caused by an impact on a plate and the distance between impact position and sensor should be estimated. The direction of arrival can be estimated accurately using MUSIC method. The distance can be obtained by using the time delay of arrival and the group velocity of the Lamb wave in a plate. Time delay is experimentally estimated using the continuous wavelet transform for the wave. The elastodynamic theory is used for the group velocity estimation.

Fault-induced transient detection based on real-time analysis of the wavelet coefficient energy

Abstract: In the last years, wavelet-based methodologies have been proposed as a good alternative for real-time fault detection. However, these methodologies usually fail to detect faults with overdamped transients and they are highly influenced by the choice of the mother wavelet, presenting time delay in the real-time analysis. By using the discrete wavelet transform (DWT) or the maximal overlap discrete wavelet transform (MODWT), the wavelet coefficient energy has been also used for fault analysis and presents the same drawbacks of the wavelet coefficient analysis. However, this paper presents a novel wavelet-based methodology for real-time detection of fault-induced transients in transmission lines, where the wavelet coefficient energy takes into account the border effects of the sliding windows. As a consequence, the performance of the proposed energy analysis is not affected by the choice of the mother wavelet, presenting no time delay in real-time fault detection, and the fault detection is scarcely influenced to the fault inception angle, fault resistance, and fault location, even if in critical situations where there are no fault-induced transients. The performance of the proposed methodology was assessed by using actual and simulated data. Some records were reproduced to be analyzed in real-time with a digital signal processor (DSP).

Automatic baseline recognition for the correction of large sets of spectra using continuous wavelet transform and iterative fitting.

Abstract: A new algorithm for the automatic recognition of peak and baseline regions in spectra is presented. It is part of a study to devise a baseline correction method that is particularly suitable for the simple and fast treatment of large amounts of data of the same type, such as those coming from high-throughput instruments, images, process monitoring, etc. This algorithm is based on the continuous wavelet transform, and its parameters are automatically determined using the criteria of Shannon entropy and the statistical distribution of noise, requiring virtually no user intervention. It was assessed on simulated spectra with different noise levels and baseline amplitudes, successfully recognizing the baseline points in all cases but for a few extremely weak and noisy signals. It can be combined with various fitting methods for baseline estimation and correction. In this work, it was used together with an iterative polynomial fitting to successfully process a real Raman image of 40 000 pixels in about 2.5 h.

Diffraction phase microscopy: retrieving phase contours on living cells with a wavelet-based space-scale analysis

Abstract: We propose a two-dimensional (2-D) space-scale analysis of fringe patterns collected from a diffraction phase microscope based on the 2-D Morlet wavelet transform. We show that the adaptation of a ridge detection method with anisotropic 2-D Morlet mother wavelets is more efficient for analyzing cellular and high refractive index contrast objects than Fourier filtering methods since it can separate phase from intensity modulations. We compare the performance of this ridge detection method on theoretical and experimental images of polymer microbeads and experimental images collected from living myoblasts.

Wavelet transform-based feature extraction for ultrasonic flaw signal classification

Abstract: In this paper, we present automatic classification models for ultrasonic flaw signals acquired from carbon-fiber-reinforced polymer specimens. Different state-of-the-art strategies based on wavelet transform are utilized for feature extraction. Furthermore, a wavelet packet transform-based local energy feature extraction method is proposed to solve the deficiencies of the existing methods. Artificial neural networks and support vector machines are trained to validate the effectiveness of different feature extraction methods for flaw signal classification. Experimental results show that the proposed method can extract reliable features to effectively classify the different ultrasonic flaw signals with high accuracy.

Modeling and Simulation of Nonstationary Processes Utilizing Wavelet and Hilbert Transforms

Abstract: An approach is proposed for modeling and simulating nonstationary earthquake ground motions that utilizes stationary wavelet and Hilbert transforms. The proposed model is based on the time-frequency representation of a process, which is essential for capturing the nonstationary characteristics of earthquake ground motions. Stationary wavelet transform is first utilized to decompose a sample of a multicomponent nonstationary random process into a set of monocomponent signals. These signals are subsequently transformed to analytic signals using the Hilbert transform, which yields the instantaneous amplitudes and frequencies. Without the customary assumption of piecewise stationarity or reliance on an assumed modulation function, this approach is able to simulate nonstationary random processes, such as earthquake ground motion, based on a sample realization of the process and its instantaneous features. The method is extended to the simulation of multivariate random processes utilizing the proper ort...