Traditional Fourier-based Methods Research Articles

Spectral Decomposition of Seismic Data With Variational Mode Decomposition-Based Wigner–Ville Distribution

Wigner–Ville distributions (WVDs), which provide superior time-frequency resolution and energy distribution concentration relative to other traditional Fourier-based or wavelet-based seismic time-frequency methods, are an important tool for spectral decomposition and have the potential to yield better seismic interpretations for highlighting geophysical responses in particular frequency bands. However, the existence of cross-term interference in WVDs limits their application. To effectively suppress the cross-term interference in a WVD without reducing the time-frequency resolution and energy aggregation, we propose a variational mode decomposition (VMD) based WVD approach. VMD is first used to decompose the multicomponent seismic data into a series of narrow band limited intrinsic mode functions (IMFs). Next, we calculate the WVDs of these IMFs. Finally, the maximum amplitude volume above the average amplitude and the peak frequency volume are extracted from these WVDs for seismic interpretation. A synthetic data example demonstrates the effectiveness of the VMD-based WVD approach and its superiority comparison to the WVD, smoothed pseudoWVD and empirical mode decomposition based WVD approaches. Real seismic data applications show that spectral decomposition with VMD-based WVD has a strong ability to highlight hydrocarbon-related information.

Fast reconstruction of two-wavelength off-axis multiplexed holograms using division-multiplexing and critical sampling

Abstract Benefiting from two-wavelength information multiplexed into one hologram, two-wavelength off-axis holography can perform simultaneous quantitative phase imaging in an extended thickness range. However, its present phase processing still adopts the traditional Fourier-based method at the expense of the reconstruction speed. Hence, we propose a fast approach by combining critical sampling with division multiplexing. In our approach, the critical sampling is used to remove the redundant data, and the division multiplexing is developed to eliminate the redundant calculation processes. Experimental results illustrate that our approach can yield faster reconstruction with frame rates up to 46 fps even for one megapixel multiplexed holograms at two wavelengths on a single-core personal computer.

Incremental update of electrostatic interactions in adaptively restrained particle simulations

The computation of long-range potentials is one of the demanding tasks in Molecular Dynamics. During the last decades, an inventive panoply of methods was developed to reduce the CPU time of this task. In this work, we propose a fast method dedicated to the computation of the electrostatic potential in adaptively restrained systems. We exploit the fact that, in such systems, only some particles are allowed to move at each timestep. We developed an incremental algorithm derived from a multigrid-based alternative to traditional Fourier-based methods. Our algorithm was implemented inside LAMMPS, a popular molecular dynamics simulation package. We evaluated the method on different systems. We showed that the new algorithm's computational complexity scales with the number of active particles in the simulated system, and is able to outperform the well-established Particle Particle Particle Mesh (P3M) for adaptively restrained simulations. © 2018 Wiley Periodicals, Inc.

Nonsinusoidal Beta Oscillations Reflect Cortical Pathophysiology in Parkinson's Disease.

Oscillations in neural activity play a critical role in neural computation and communication. There is intriguing new evidence that the nonsinusoidal features of the oscillatory waveforms may inform underlying physiological and pathophysiological characteristics. Time-domain waveform analysis approaches stand in contrast to traditional Fourier-based methods, which alter or destroy subtle waveform features. Recently, it has been shown that the waveform features of oscillatory beta (13-30 Hz) events, a prominent motor cortical oscillation, may reflect near-synchronous excitatory synaptic inputs onto cortical pyramidal neurons. Here we analyze data from invasive human primary motor cortex (M1) recordings from patients with Parkinson's disease (PD) implanted with a deep brain stimulator (DBS) to test the hypothesis that the beta waveform becomes less sharp with DBS, suggesting that M1 input synchrony may be decreased. We find that, in PD, M1 beta oscillations have sharp, asymmetric, nonsinusoidal features, specifically asymmetries in the ratio between the sharpness of the beta peaks compared with the troughs. This waveform feature is nearly perfectly correlated with beta-high gamma phase-amplitude coupling (r = 0.94), a neural index previously shown to track PD-related motor deficit. Our results suggest that the pathophysiological beta generator is altered by DBS, smoothing out the beta waveform. This has implications not only for the interpretation of the physiological mechanism by which DBS reduces PD-related motor symptoms, but more broadly for our analytic toolkit in general. That is, the often-overlooked time-domain features of oscillatory waveforms may carry critical physiological information about neural processes and dynamics.SIGNIFICANCE STATEMENT To better understand the neural basis of cognition and disease, we need to understand how groups of neurons interact to communicate with one another. For example, there is evidence that parkinsonian bradykinesia and rigidity may arise from an oversynchronization of afferents to the motor cortex, and that these symptoms are treatable using deep brain stimulation. Here we show that the waveform shape of beta (13-30 Hz) oscillations, which may reflect input synchrony onto the cortex, is altered by deep brain stimulation. This suggests that mechanistic inferences regarding physiological and pathophysiological neural communication may be made from the temporal dynamics of oscillatory waveform shape.

ISAR Imaging by Two-Dimensional Convex Optimization-Based Compressive Sensing

A novel 2D convex optimization-based compressive sensing (CS) method is presented for inverse synthetic aperture radar (ISAR) imaging. The method deals directly with the 2D signal model for the image reconstruction based on solving a convex optimization problem. The superiority of this method is that the memory usage and the computational complexity are much lower than those of the 1D CS-based ISAR imaging method. Especially, the method belongs to a convex optimization problem. Convex functions do not suffer from local minima assuring that the achieved solution always happens to be the optimal. Simulation and experimental results are provided to demonstrate the performance of the proposed method with comparisons to the traditional Fourier-based method and to the smoothed L0-norm-based method, which proves that the proposed method is an effective way to solve the ISAR imaging problem.

Spurious cross-frequency amplitude–amplitude coupling in nonstationary, nonlinear signals

Recent studies of brain activities show that cross-frequency coupling (CFC) plays an important role in memory and learning. Many measures have been proposed to investigate the CFC phenomenon, including the correlation between the amplitude envelopes of two brain waves at different frequencies — cross-frequency amplitude–amplitude coupling (AAC). In this short communication, we describe how nonstationary, nonlinear oscillatory signals may produce spurious cross-frequency AAC. Utilizing the empirical mode decomposition, we also propose a new method for assessment of AAC that can potentially reduce the effects of nonlinearity and nonstationarity and, thus, help to avoid the detection of artificial AACs. We compare the performances of this new method and the traditional Fourier-based AAC method. We also discuss the strategies to identify potential spurious AACs.

Near-Field Radar Imaging via Compressive Sensing

A novel two-dimensional (2-D) compressive sensing (CS) based method is presented for near-field radar imaging. First, an accurate near-field approximation is proposed, based on which the circular wavefront curvature of spherical waves can be compensated by mapping the images to a rectified new grid. More importantly, the near-field approximation makes the two dimensions of the scattered data separable for the range and cross-range directions, which makes it possible to solve the 2-D reflectivity matrix for the image reconstruction directly. Then, a 2-D proximal subgradient algorithm for near-field radar imaging based on a fast iterative shrinkage/thresholding algorithm (FISTA) is introduced to resolve the memory usage and computation time issues. Simulation and experimental results are provided to demonstrate the performance of the proposed method with comparisons to the traditional Fourier-based method and to the conjugate gradient (CG) based method, which proves that the proposed method is an effective way to solve the near-field radar imaging problem.

Adaptive fixed-point iterative shrinkage/thresholding algorithm for MR imaging reconstruction using compressed sensing

Recently compressed sensing (CS) has been applied to under-sampling MR image reconstruction for significantly reducing signal acquisition time. To guarantee the accuracy and efficiency of the CS-based MR image reconstruction, it necessitates determining several regularization and algorithm-introduced parameters properly in practical implementations. The regularization parameter is used to control the trade-off between the sparsity of MR image and the fidelity measures of k-space data, and thus has an important effect on the reconstructed image quality. The algorithm-introduced parameters determine the global convergence rate of the algorithm itself. These parameters make CS-based MR image reconstruction a more difficult scheme than traditional Fourier-based method while implemented on a clinical MR scanner. In this paper, we propose a new approach that reveals that the regularization parameter can be taken as a threshold in a fixed-point iterative shrinkage/thresholding algorithm (FPIST) and chosen by employing minimax threshold selection method. No extra parameter is introduced by FPIST. The simulation results on synthetic and real complex-valued MRI data show that the proposed method can adaptively choose the regularization parameter and effectively achieve high reconstruction quality. The proposed method should prove very useful for practical CS-based MRI applications.

Wavelet analysis of a large sample of AGN at high radio frequencies

Aims. We have studied the characteristic timescales of 80 AGNs at 22, 37 and 90 GHz examining the properties of the wavelet method and comparing them to traditional Fourier-based methods commonly used in astronomy. Methods. We used the continuous wavelet transform with the Morlet wavelet to study the characteristic timescales. We also gain information when the timescale is present in the flux curve and if it is persistent or not. Results. Our results show that the sources are not periodic and changes in the timescales over a long time are common. The property of wavelets to be able to distinguish when the timescale has been present is superior to the Fourier-based methods. Therefore we consider it appropriate to use wavelets when the quasi-periodicities in AGNs are studied.

Application of EMD method to friction signal processing

Due to measurement limitation, the measured friction signal often contains noise and other force components such as elastic forces. Traditional Fourier-based analysis methods are not suitable to process nonlinear and non-stationary signal. In this paper, the combination of median filter and empirical mode decomposition (EMD) method is used to analyze the measured friction signal. Median filter is a nonlinear process useful in reducing random noise, while EMD method has offered a powerful method for nonlinear and non-stationary data processing. The background noise and the noise arising from the measurement system in the measured friction signal are removed using median filter first. Then the other force components except the real friction force can be extracted from the measured friction signal using the EMD method. The residue after extracting can be taken as a relatively clean and real friction force. This method is compared with the traditional Fourier-based methods and wavelet decomposition method. The comparison results both in time domain and in Hilbert spectrum can show the superiority of the EMD method in dealing with the problem of friction signal processing.

Methods for Characterizing Flicker and its Applications

Flicker is an important power quality disturbance and has received an increasing concern from power system researchers. Interharmonics are the non-integral frequencies other than harmonic frequencies. Nowadays, research has shown that interharmonics and flicker seem to be closely related. To clarify this relationship, flicker is characterized in the frequency domain. The traditional Fourier-based methods have shown some drawbacks in representing non-stationary, non-periodic power signals and therefore other methods should be investigated for accomplishing this task. This paper introduces the most common signal processing approaches to assess the problem, power spectrum estimation methods and linear transforms. The wavelet transform has shown superior performance comparing to other methods and circumventing the problem time-frequency resolution.

Multiresolution approximation for volatility processes

We present an application of wavelet techniques to non-stationary time series with the aim of detecting the dependence structure which is typically found to characterize intraday stock index financial returns. It is particularly important to identify what components truly belong to the underlying volatility process, compared with those features appearing instead as a result of the presence of disturbance processes. The latter may yield misleading inference results when standard financial time series models are adopted. There is no universal agreement on whether long memory really affects financial series, or instead whether it could be that non-stationarity, once detected and accounted for, may allow for more power in detecting the dependence structure and thus suggest more reliable models. Wavelets are still a novel tool in the domain of applications in finance; thus, one goal is to try to show their potential use for signal decomposition and approximation of time-frequency signals. This might suggest a better interpretation of multi-scaling and aggregation effects in high-frequency returns. We show, by using special dictionaries of functions and ad hoc algorithms, that a pre-processing procedure for stock index returns leads to a more accurate identification of dependent and non-stationary features, whose detection results are improved compared with those obtained by other traditional Fourier-based methods. This allows generalized autoregressive conditional heteroscedastic models to be more effective for statistical estimation purposes.

Prediction of small drill bit breakage by wavelet transforms and linear discriminant functions

Though the discrete wavelet transform (DWT) has gained attention in the field of machining monitoring, the potential uses of DWT-based classification techniques have not yet been fully explored. In this paper, linear discriminant analysis is used to post-process DWT output for on-line prediction of the breakage of small drill bits. Bit failure is characterized by two types of transient (`sawtooth' and `screeching') in the cutting force signal. To detect these transients, instead of traditional Fourier-based methods the DWT is used, which is better suited to analysis of time-localized phenomena. Three index functions (`energy', `waviness' and `irregularity') are adopted to test for the presence of transients in the DWT expansion. The indices are used to perform linear discriminant analysis, thereby classifying the input signals by state (normal or prefailure). Experiments showed that the DWT-based linear discriminant analysis method can accurately identify impending breakage about one to three cycles prior to failure, even when the cutting conditions change.