Harmonic wavelet transform

About: Harmonic wavelet transform is a research topic. Over the lifetime, 9602 publications have been published within this topic receiving 247336 citations.

Evaluation of earthquake-induced structural damages by wavelet transform

Abstract: The dynamic behavior of inelastic structures during an earthquake is a complicated non-stationary process that is affected by the random characteristics of seismic ground motions. The conventional Fourier analysis describes the feature of a dynamic process by decomposing the signal into infinitely long sine and cosine series, which loses all time-located information. However, both time and frequency localizations are necessary for the analysis of an evolutionary spectrum of non-stationary processes. In this paper, an analytical approach for seismic ground motions is developed by applying the wavelet transform, which focuses on the energy input to the structure. The procedure of identification of the instantaneous modal parameters based on the continuous wavelet transform (CWT) is given in detail. And then, a novel method using the auto-regressive moving average (ARMA), called “prediction extension”, is presented to remedy the edge effect during the numerical computation of the CWT. The effectiveness of the method is verified by the use of the benchmark model developed by the American Society of Civil Engineers (ASCE). Finally, a scale model with three-storey reinforced concrete frame-share wall structure is made and tested on a shaking table to investigate the relation between the dynamic properties of structures and energy accumulation and its change rates during the earthquake. The results have shown that the wavelet transform is able to provide a deep insight into the identity of transient signals through time-frequency maps of the time variant spectral decomposition.

Dual-Tree Complex Wavelet Transform Based SAR Despeckling Using Interscale Dependence

Abstract: In this paper, a dual-tree complex wavelet transform (DTCWT) based despeckling algorithm is proposed for synthetic aperture radar (SAR) images, considering the significant dependences of the wavelet coefficients across different scales. The DTCWT has the advantage of improved directional selectivity, approximate shift invariance, and perfect reconstruction over the discrete wavelet transform. The wavelet coefficients in each subband are modeled with a bivariate Cauchy probability density function (PDF) which takes into account the statistical dependence among the wavelet coefficients. Mellin transform of two dependent random variables is utilized to estimate the dispersion parameter of the bivariate Cauchy PDF from the noisy observations. This method is faster and effective when compared to that of the earlier techniques on numerical integration. Within this framework, we propose a new method for despeckling SAR images employing a maximum a posteriori estimator. Experimental results show that the proposed method based on bivariate Cauchy prior achieves better performance in terms of equivalent number of looks, peak signal-to-noise ratio, and Pratt's figure of merit.

Pitch-synchronous wavelet representations of speech and music signals

Abstract: A new wavelet representation is explored. The transform is based on a pitch-synchronous vector representation and it adapts to the oscillatory or aperiodic characteristics of signals. Pseudo-periodic signals are represented in terms of an asymptotically periodic trend and aperiodic fluctuations at several scales. The transform reverts to the ordinary wavelet transform over totally aperiodic signal segments. The pitch-synchronous wavelet transform is particularly suitable to the analysis, rate-reduction coding and synthesis of speech signals and it may serve as a preprocessing block in automatic speech recognition systems. Feature extraction such as separation of voice from noise in voiced consonants is easily performed by means of partial wavelet expansions. A stochastic model of aperiodic fluctuations is proposed. >

Characterization of dispersive surface waves using continuous wavelet transforms

Abstract: In this paper, we propose a method of surface waves characterization based on the deformation of the wavelet transform of the analysed signal. An estimate of the phase velocity (the group velocity) and the attenuation coefficient is carried out using a model-based approach to determine the propagation operator in the wavelet domain, which depends nonlinearly on a set of unknown parameters. These parameters explicitly define the phase velocity, the group velocity and the attenuation. Under the assumption that the difference between waveforms observed at a couple of stations is solely due to the dispersion characteristics and the intrinsic attenuation of the medium, we then seek to find the set of unknown parameters of this model. Finding the model parameters turns out to be that of an optimization problem, which is solved through the minimization of an appropriately defined cost function. We show that, unlike time-frequency methods that exploit only the square modulus of the transform, we can achieve a complete characterization of surface waves in a dispersive and attenuating medium. Using both synthetic examples and experimental data, we also show that it is in principle possible to separate different modes in both the time domain and the frequency domain

Matching-pursuit for simulations of quantum processes

Abstract: The matching-pursuit algorithm is implemented to develop an extension of the split-operator Fourier transform method to a nonorthogonal, nonuniform and dynamically adaptive coherent-state representation. The accuracy and efficiency of the computational approach are demonstrated in simulations of deep tunneling and long time dynamics by comparing our simulation results with the corresponding benchmark calculations.