Time-frequency analysis (TFA) is widely used to describe local time-frequency (TF) features of seismic data. Among the commonly used TFA tools, sparse TFA (STFA) is an excellent one, which can obtain ...a TF spectrum with good readability. However, many STFA algorithms suffer from expensive calculation time and unavoidable prior knowledge, such as the iterative shrinkage-thresholding algorithm (ISTA) and the sparse reconstruction by separable approximation (SpaRSA). Inspired by the unrolled algorithm and its successful applications in signal processing, we propose a deep learning (DL)-based ISTA unrolled algorithm, which is named the sparse time-frequency analysis network (STFANet). The STFANet contains two parts, i.e., the sparse TF spectrum generator and the reconstruction module. The former learns how to transform a 1-D seismic signal from a large amount of unlabeled data into a 2-D sparse TF spectrum, which is implemented based on the proposed unrolled iterative dynamic shrinkage-thresholding (UIDST) algorithm. Note that the UIDST algorithm is carried out by using a simplified DL network. The latter serves as a physical constraint of model training to ensure that our generator obtains an accurate TF spectrum, which is actually an inverse TF transform. In this study, the traditional inverse short-time Fourier transform (STFT) is utilized in the reconstruction module. To test the effectiveness of the proposed model, we apply it to 3-D poststack field data. The results show that, compared with the traditional TFA tools, the STFANet can availably compute the TF spectrum with better readability, which benefits seismic attenuation delineation.
Although prior studies have evaluated the role of sampling errors associated with local and regional methods to estimate peak flow quantiles, the investigation of epistemic errors is more difficult ...because the underlying properties of the random variable have been prescribed using ad‐hoc characterizations of the regional distributions of peak flows. This study addresses this challenge using representations of regional peak flow distributions derived from a combined framework of stochastic storm transposition, radar rainfall observations, and distributed hydrologic modeling. The authors evaluated four commonly used peak flow quantile estimation methods using synthetic peak flows at 5,000 sites in the Turkey River watershed in Iowa, USA. They first used at‐site flood frequency analysis using the Pearson Type III distribution with L‐moments. The authors then pooled regional information using (1) the index flood method, (2) the quantile regression technique, and (3) the parameter regression. This approach allowed quantification of error components stemming from epistemic assumptions, parameter estimation method, sample size, and, in the regional approaches, the number of pooled sites. The results demonstrate that the inability to capture the spatial variability of the skewness of the peak flows dominates epistemic error for regional methods. We concluded that, in the study basin, this variability could be partially explained by river network structure and the predominant orientation of the watershed. The general approach used in this study is promising in that it brings new tools and sources of data to the study of the old hydrologic problem of flood frequency analysis.
Key Points
Synthetic peak flows are used to investigate the epistemic and sampling errors associated with local and regional methods to estimate PFQs
Error components stemming from epistemic assumptions, parameter estimation method, sample size, and the number of pooled sites are evaluated
The spatial variability of the skewness of the peak flows is partially explained by river network structure and orientation of the watershed
The automatic detection of epileptic seizures from electroencephalography (EEG) signals is crucial for the localization and classification of epileptic seizure activity. However, seizure processes ...are typically dynamic and nonstationary, and thus, distinguishing rhythmic discharges from nonstationary processes is one of the challenging problems. In this paper, an adaptive and localized time-frequency representation in EEG signals is proposed by means of multiscale radial basis functions (MRBF) and a modified particle swarm optimization (MPSO) to improve both time and frequency resolution simultaneously, which is a novel MRBF-MPSO framework of the time-frequency feature extraction for epileptic EEG signals. The dimensionality of extracted features can be greatly reduced by the principle component analysis algorithm before the most discriminative features selected are fed into a support vector machine (SVM) classifier with the radial basis function (RBF) in order to separate epileptic seizure from seizure-free EEG signals. The classification performance of the proposed method has been evaluated by using several state-of-art feature extraction algorithms and other five different classifiers like linear discriminant analysis, and logistic regression. The experimental results indicate that the proposed MRBF-MPSO-SVM classification method outperforms competing techniques in terms of classification accuracy, and shows the effectiveness of the proposed method for classification of seizure epochs and seizure-free epochs.
Time-frequency analysis (TFA) technique is an effective approach to capture the changing dynamic in a nonstationary signal. However, the commonly adopted TFA techniques are inadequate in dealing with ...signals having a strong nonstationary characteristic or multicomponent signals having close frequency components. To overcome this shortcoming, a new TFA technique applying a polynomial chirplet transform (PCT) in association with a synchroextracting transform (SET) is proposed in this paper. It is shown that the energy concentration of the time-frequency representation (TFR) of a strong frequency-modulated signal from a PCT transform can be further enhanced by an SET transform. The technique can also be employed to accurately extract the signal components of a multicomponent nonstationary signal with close frequency components by adopting an iterative process. It is found that the TFR calculated from the proposed technique matches well with the ideal TFR, which demonstrates the superiority of the current technique in dealing with nonstationary signals having rapidly changing dynamics. Results from the analysis of the experimental data under varying speed conditions confirm the validity of the proposed technique in dealing with nonstationary signals from practical sources.
Time-frequency (TF) analysis (TFA) plays an important role in seismic hydrocarbon reservoir identification, which is attributed to its ability to effectively identify the oil and gas seismic response ...characteristics of geological bodies in different frequency bands. In this letter, we introduce a novel TFA method termed high-order synchroextracting transform (SET) and apply it to the high-precision identification of gas-bearing reservoirs. Under the premise of short-time Fourier transform (STFT), this method defines a new synchroextracting operator (SEO) based on high-order approximations of signal amplitude and phase. Furthermore, only the TF information highly correlated with the TF characteristics of the signal is extracted from the STFT spectrum by using the SEO. Therefore, for a wider variety of the nonstationary signal, a highly energy-concentrated TF representation can be effectively obtained. The application of STFT and different-order SET on 1-D synthetic signal and field seismic data verifies the effectiveness of the proposed method.
As a generalization of the classical Fourier transform (FT), the fractional Fourier transform (FRFT) has proven to be a powerful tool for signal processing and analysis. However, it is not suitable ...for processing signals whose fractional frequencies vary with time due to a lack of time localization information. A simple method to overcome this limitation is the short-time FRFT (STFRFT). There exist several different definitions of the STFRFT in the literature. Unfortunately, these existing definitions do not well generalize the classical result of the conventional short-time FT (STFT), which can be interpreted as a bank of FT-domain filters. The objective of this paper is to propose a novel STFRFT that preserves the properties of the conventional STFT and can be implemented easily in terms of FRFT-domain filter banks. We first present the novel STFRFT and then derive its inverse transform and basic properties. The time-fractional-frequency analysis of this transform is also presented. Moreover, the implementation of the proposed STFRFT is discussed. Finally, we provide several applications for the proposed STFRFT.
Time-frequency (TF) analysis (TFA) method is an important tool in industrial engineering fields. However, restricted to Heisenberg uncertainty principle or unexpected cross terms, the classical TFA ...methods often generate blurry TF representation, which heavily hinder its engineering applications. How to generate the concentrated TF representation for a strongly time-varying signal is a challenging task. In this paper, we propose a new TFA method to study the nonstationary features of strongly time-varying signals. The proposed method is based on synchrosqueezing transform and employs an iterative reassignment procedure to concentrate the blurry TF energy in a stepwise manner, meanwhile retaining the signal reconstruction ability. Two implementations of the discrete algorithm are provided, which show that the proposed method has limited computational burden and has potential in real-time application. Moreover, we introduce an effective algorithm to detect the instantaneous frequency trajectory, which can be used to decompose monocomponent modes. Numerical and real-world signals are employed to validate the effectiveness of the proposed method by comparing with some advanced methods. By comparisons, it is shown that the proposed method has the better performance in addressing strongly time-varying signals and noisy signals.
Understanding the physical properties and scattering mechanisms contributes to synthetic aperture radar (SAR) image interpretation. For single-polarized SAR data, however, it is difficult to extract ...the physical scattering mechanisms due to lack of polarimetric information. Time-frequency analysis (TFA) on complex-valued SAR image provides extra information in frequency perspective beyond the "image" domain. Based on TFA theory, we propose to generate the subband scattering pattern for every object in complex-valued SAR image as the physical property representation, which reveals backscattering variations along slant-range and azimuth directions. In order to discover the inherent patterns and generate a scattering classification map from single-polarized SAR image, an unsupervised hierarchical deep embedding clustering (HDEC) algorithm based on TFA (HDEC-TFA) is proposed to learn the embedded features and cluster centers simultaneously and hierarchically. The polarimetric analysis result for quad-pol SAR images is applied as reference data of physical scattering mechanisms. In order to compare the scattering classification map obtained from single-polarized SAR data with the physical scattering mechanism result from full-polarized SAR, and to explore the relationship and similarity between them in a quantitative way, an information theory based evaluation method is proposed. We take Gaofen-3 quad-polarized SAR data for experiments, and the results and discussions demonstrate that the proposed method is able to learn valuable scattering properties from single-polarization complex-valued SAR data, and to extract some specific targets as well as polarimetric analysis. At last, we give a promising prospect to future applications.
Time−frequency analysis (TFA) is regarded as an efficient technique to reveal the hidden characteristics of the oscillatory signal. At present, the traditional TFA methods always construct the signal ...model in the time domain and assume the instantaneous features of the modes to be continuous. Thus, most of these approaches fail to tackle some specific kinds of impulselike signal, including shock and vibration waves, damped tones, or marine mammals. This article introduces a new method called generalized horizontal synchrosqueezing transform (GHST) to process the transient signal. A signal model defined in the frequency domain is used to deduce the GHST. Next, the new synchrosqueezing operator termed as group delay (GD) is proposed based on high-order Taylor expansions of the signal model. Finally, the modulus around ridge curves is rearranged from the original position to the estimated GD. Numerical results of a simulated signal demonstrate the precision of the GHST in terms of both readability of the time−frequency representation and reconstruction accuracy. Additionally, the proposed method is implemented to diagnose the fault in a rotary machine by analyzing the vibration signal. The validation demonstrates that the GHST performs better than other traditional TFA methods, and it is qualified for the online condition monitoring of the industrial mechanical system.
Temporally modulated metamaterials have attracted significant attention recently due to their nonreciprocal and frequency converting properties. Here, a transparent, time-modulated metasurface, which ...functions as a serrodyne frequency translator, is reported at <inline-formula> <tex-math notation="LaTeX">X </tex-math></inline-formula>-band frequencies. With a simple biasing architecture, the metasurface provides electrically tunable transmission phase that covers 360°. A sawtooth waveform is used to modulate the metasurface, allowing Doppler-like frequency translation. Modal analysis of an analogous time-modulated medium is performed to gain insight into the operation of the metasurface-based serrodyne frequency translator. Two such metasurfaces can be cascaded together to achieve magnetless devices that perform either phase or amplitude nonreciprocity.
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