On the need for bump event correction in vibration test profiles representing road excitations in automobiles

This paper presents an approach to the synthesis of compressed vibration test profiles representing much longer time histories obtained in road testing of ground vehicles. Vibration test profiles are defined as those related directly to operational testing on specific road surfaces and which summarise the input to the vehicle in the given conditions. The method extends classical Fourier transform technique by means of bump event correction in the background Fourier signal where the bump event term implies a high-amplitude transient event of the shock type. The orthogonal wavelet decomposition was used as a specific filtering tool facilitating bump event identification. Examples of seat guide vertical acceleration have been considered. Calculated probability density functions suggest the ability of the bump correction method to improve the statistical accuracy of the final vibration test profile with respect to the original road data. Test profiles obtained by means of Fourier transform synthesis with subsequent reinsertion of bump events from separated frequency bands were more accurate than those obtained by Fourier synthesis alone. Further developments led to advanced bump reinsertion with synchronisation of events occurring in different frequency bands at the same moment of time. Test profiles generated in this way have provided better accuracy compared to the non-synchronised algorithm

Phase Harmonic Correlations and Convolutional Neural Networks

A major issue in harmonic analysis is to capture the phase dependence of frequency representations, which carries important signal properties. It seems that convolutional neural networks have found a way. Over time-series and images, convolutional networks often learn a first layer of filters which are well localized in the frequency domain, with different phases. We show that a rectifier then acts as a filter on the phase of the resulting coefficients. It computes signal descriptors which are local in space, frequency and phase. The non-linear phase filter becomes a multiplicative operator over phase harmonics computed with a Fourier transform along the phase. We prove that it defines a bi-Lipschitz and invertible representation. The correlations of phase harmonics coefficients characterise coherent structures from their phase dependence across frequencies. For wavelet filters, we show numerically that signals having sparse wavelet coefficients can be recovered from few phase harmonic correlations, which provide a compressive representationComment: 26 pages, 8 figure

Construction of Hilbert Transform Pairs of Wavelet Bases and Gabor-like Transforms

We propose a novel method for constructing Hilbert transform (HT) pairs of wavelet bases based on a fundamental approximation-theoretic characterization of scaling functions--the B-spline factorization theorem. In particular, starting from well-localized scaling functions, we construct HT pairs of biorthogonal wavelet bases of L^2(R) by relating the corresponding wavelet filters via a discrete form of the continuous HT filter. As a concrete application of this methodology, we identify HT pairs of spline wavelets of a specific flavor, which are then combined to realize a family of complex wavelets that resemble the optimally-localized Gabor function for sufficiently large orders. Analytic wavelets, derived from the complexification of HT wavelet pairs, exhibit a one-sided spectrum. Based on the tensor-product of such analytic wavelets, and, in effect, by appropriately combining four separable biorthogonal wavelet bases of L^2(R^2), we then discuss a methodology for constructing 2D directional-selective complex wavelets. In particular, analogous to the HT correspondence between the components of the 1D counterpart, we relate the real and imaginary components of these complex wavelets using a multi-dimensional extension of the HT--the directional HT. Next, we construct a family of complex spline wavelets that resemble the directional Gabor functions proposed by Daugman. Finally, we present an efficient FFT-based filterbank algorithm for implementing the associated complex wavelet transform.Comment: 36 pages, 8 figure

TRUFAS, a wavelet based algorithm for the rapid detection of planetary transits

Aims: We describe a fast, robust and automatic detection algorithm, TRUFAS, and apply it to data that are being expected from the CoRoT mission. Methods: The procedure proposed for the detection of planetary transits in light curves works in two steps: 1) a continuous wavelet transformation of the detrended light curve with posterior selection of the optimum scale for transit detection, and 2) a period search in that selected wavelet transformation. The detrending of the light curves are based on Fourier filtering or a discrete wavelet transformation. TRUFAS requires the presence of at least 3 transit events in the data. Results: The proposed algorithm is shown to identify reliably and quickly the transits that had been included in a standard set of 999 light curves that simulate CoRoT data. Variations in the pre-processing of the light curves and in the selection of the scale of the wavelet transform have only little effect on TRUFAS' results. Conclusions: TRUFAS is a robust and quick transit detection algorithm, especially well suited for the analysis of very large volumes of data from space or ground-based experiments, with long enough durations for the target-planets to produce multiple transit events.Comment: 9 pages, 10 figures, accepted by A&

The Application of Continuous Wavelet Transform Based Foreground Subtraction Method in 21 cm Sky Surveys

We propose a continuous wavelet transform based non-parametric foreground subtraction method for the detection of redshifted 21 cm signal from the epoch of reionization. This method works based on the assumption that the foreground spectra are smooth in frequency domain, while the 21 cm signal spectrum is full of saw-tooth-like structures, thus their characteristic scales are significantly different. We can distinguish them in the wavelet coefficient space easily and perform the foreground subtraction. Compared with the traditional spectral fitting based method, our method is more tolerant to complex foregrounds. Furthermore, we also find that when the instrument has uncorrected response error, our method can also work significantly better than the spectral fitting based method. Our method can obtain similar results with the Wp smoothing method, which is also a non-parametric method, but our method consumes much less computing time.Comment: Accepted by Ap

Laser Ultrasound Inspection Based on Wavelet Transform and Data Clustering for Defect Estimation in Metallic Samples

Laser-generated ultrasound is a modern non-destructive testing technique. It has been investigated over recent years as an alternative to classical ultrasonic methods, mainly in industrial maintenance and quality control procedures. In this study, the detection and reconstruction of internal defects in a metallic sample is performed by means of a time-frequency analysis of ultrasonic waves generated by a laser-induced thermal mechanism. In the proposed methodology, we used wavelet transform due to its multi-resolution time frequency characteristics. In order to isolate and estimate the corresponding time of flight of eventual ultrasonic echoes related to internal defects, a density-based spatial clustering was applied to the resulting time frequency maps. Using the laser scan beam’s position, the ultrasonic transducer’s location and the echoes’ arrival times were determined, the estimation of the defect’s position was carried out afterwards. Finally, clustering algorithms were applied to the resulting geometric solutions from the set of the laser scan points which was proposed to obtain a two-dimensional projection of the defect outline over the scan plane. The study demonstrates that the proposed method of wavelet transform ultrasonic imaging can be effectively applied to detect and size internal defects without any reference information, which represents a valuable outcome for various applications in the industry. View Full-TextPeer ReviewedPostprint (published version

Blind Deconvolution of Ultrasonic Signals Using High-Order Spectral Analysis and Wavelets

Defect detection by ultrasonic method is limited by the pulse width. Resolution can be improved through a deconvolution process with a priori information of the pulse or by its estimation. In this paper a regularization of the Wiener filter using wavelet shrinkage is presented for the estimation of the reflectivity function. The final result shows an improved signal to noise ratio with better axial resolution.Comment: 8 pages, CIARP 2005, LNCS 377