Standard S-transform Research Articles

Power Quality Disturbances Recognition Using Modified S-Transform Based on Optimally Concentrated Window with Integration of Renewable Energy

To meet power quality requirements, it is necessary to classify and identify the power quality of the power grid connected with renewable energy generation. S-transform (ST) is an effective method to analyze power quality in time and frequency domains. ST is widely used to detect and classify various kinds of non-stationary power quality disturbances. However, the long taper and scaling criteria of the Gaussian window in standard ST (SST) will lead to poor time domain resolution at low frequency and poor frequency resolution at high frequency. To solve the discrete side effects, it is necessary to select the optimal window function to locate the time frequency accurately. This paper proposes a modified ST (MST) method. In this method, an improved window function of energy concentration in time-frequency distribution is introduced to optimize the shape of each window function. This method determines the parameters of Gaussian window to maximize the product of energy concentration in a time-frequency domain within a given time and frequency interval, so as to improve the energy concentration. The result shows that compared with the SST with Gaussian window, ST based on the optimally concentrated window proposed in this paper has better energy concentration in time-frequency distribution.

Radar Signal Emitter Recognition Based on Combined Ensemble Empirical Mode Decomposition and the Generalized S-Transform

Present radar signal emitter recognition approaches suffer from a dependency on prior information. Moreover, modern emitter recognition must meet the challenges associated with low probability of intercept technology and other obscuration methodologies based on complex signal modulation and must simultaneously provide a relatively strong ability for extracting weak signals under low SNR values. Therefore, the present article proposes an emitter recognition approach that combines ensemble empirical mode decomposition (EEMD) with the generalized S-transform (GST) for promoting enhanced recognition ability for radar signals with complex modulation under low signal-to-noise ratios in the absence of prior information. The results of Monte Carlo simulations conducted using various mixed signals with additive Gaussian white noise are reported. The results verify that EEMD suppresses the occurrence of mode mixing commonly observed using standard empirical mode decomposition. In addition, EEMD is shown to extract meaningful signal features even under low SNR values, which demonstrates its ability to suppress noise. Finally, EEMD-GST is demonstrated to provide an obviously better time-frequency focusing property than that of either the standard S-transform or the short-time Fourier transform.

High-Resolution Seismic Time–Frequency Analysis Using the Synchrosqueezing Generalized S-Transform

In this letter, a new method is introduced for a seismic time–frequency (TF) analysis. The proposed method is called synchrosqueezing generalized S-transform (SSGST), which belongs to a postprocessing procedure of the GST. The frequency-dependent Gaussian window used in the standard S-transform may be not suitable for real applications. In order to overcome this limitation, the frequency-dependent Gaussian window is replaced by a parameterized function containing three parameters. These three parameters result in flexibility in the variation of TF resolution. Then, the synchrosqueezing transform is employed to squeeze the TF coefficients of the GST to achieve an energy-concentrated TF representation. Synthetic examples and field data show that the SSGST achieves a high resolution and has the potential in highlighting geological structures with high precision.

Time–Frequency Analysis of Seismic Data Using a Three Parameters S Transform

The S transform (ST) is one of the most commonly used time–frequency (TF) analysis algorithms and is commonly used in assisting reservoir characterization and hydrocarbon detection. Unfortunately, the TF spectrum obtained by the ST has a low temporal resolution at low frequencies, which lowers its ability in thin beds and channels detection. In this letter, we propose a three parameters ST (TPST) to optimize the TF resolution flexibly. To demonstrate the validity and effectiveness of the TPST, we first apply it to a synthetic data and a synthetic seismic trace and then to a filed data. Synthetic data examples show that this TPST achieves an optimized TF resolution, compared with the standard ST and modified ST with two parameters. Field data experiments illustrate that the TPST is superior to the ST in highlighting the channel edges. The lateral continuity of the frequency slice produced by the TPST is more continuous than that of the ST.

Parameter estimation of frequency hopping signals based on the Robust S-transform algorithms in alpha stable noise environment

In many communication systems the noise is non-Gaussian and usually exhibits impulsive characteristics. The alpha stable distribution, which is the only distribution satisfies the generalized central-limit theorem and characterizes a range of behaviors from Gaussian to extremely impulsive signals, is appropriate to model this type of noise. Since the performance of the S-transform (ST) based frequency hopping (FH) signal parameter estimation methods, which are very effective in Gaussian noise, may deteriorate significantly in the presence of impulsive noise, two robust methods based on the ST, i.e., the fractional lower order ST (FLOST) and the iterative ST (IST), are proposed in this paper. Specifically, the FLOST is the combination of fractional lower order statistics and the ST, whereas the IST is the application of the minimax Huber's robust theory to the ST. Both robust ST algorithms exhibit higher time-frequency concentration in the presence of alpha stable noise. Simulation results show that the proposed algorithms are valid for FH signal parameter estimation, and they distinctively outperform the standard ST in impulsive noise environment.

Modified S transform and ELM algorithms and their applications in power quality analysis

Modified S transform (MST) and Extreme Learning Machine (ELM) algorithms are developed and are applied to power quality (PQ) analysis. Two adjustable parameters are introduced in MST to control the Gaussian window width, free from the limitation of time–frequency resolution in the standard S-transform (ST) with an uncontrollable window. Compared with ST, MST provides more convenient means for achieving desired time–frequency resolution for various PQ disturbances signals. In order to optimize the adjustable parameters, three optimization indexes are introduced to make the optimization process more adaptively. Based on the time–frequency matrix of MST, four disturbance features are enough to construct the feature vector, solving the problem of the statistical feature redundancy. Compared with the algorithms such as Back Propagation Neural Network (BPNN) and the Support Vector Machine (SVM), ELM has the advantages of simple structure, fast training speed and high precision, more suitable for engineering application. The simulation experiments show that the MST-ELM algorithms, could provide higher classification accuracy, better anti-noise property, less computational cost and independent of training set.

A new optimized Stockwell transform applied on synthetic and real non-stationary signals

The aim of this paper is to improve the energy concentration of the Stockwell transform (S-transform) in the time–frequency domain. A modified S-transform is proposed with several parameters to control the width of a hybrid Gaussian window. A constrained optimization problem is proposed based on an energy concentration measure as objective function and inequalities constraints to define the bounds of the Gaussian window. An active-set algorithm is applied to resolve the optimization problem. The optimization of the energy concentration in the time–frequency plane can lead to more reliable applications for non-stationary signals. The simulation results show a significant improvement of the proposed methodology most notably in the presence of noise comparing with the standard S-transform and existing modified S-transform in the literature. Moreover, comparison with other known time–frequency transforms such as Short-time Fourier transform (STFT) and smoothed-pseudo Wigner–Ville distribution (SPWVD) is also performed and discussed. The proposed S-transform is tested also on real non-stationary signals through an example of split detection in heart sounds.

S-transform with maximum energy concentration: Application to non-stationary seismic deconvolution

The S-transform is known as an efficient method for analyzing seismic signals in the time–frequency (TF) domain. However, it provides a TF map with high energy diffusion due to inflexibility of the window function used in its analysis or synthesis formulas. In this paper, an optimization algorithm for S-transform is proposed to find the optimum Gaussian windows for providing a TF map with maximum energy concentration. Afterwards, we show the possibility of obtaining the desired TF map from two different perspectives: generating the TF map from a time-windowed signal or from a frequency-windowed signal. Through the optimization algorithm and by using an energy concentration measure (ECM), the optimum windows are selected instantaneously, for each time or frequency sample. Testing the proposed method on variety of signals shows its good performance to provide a well concentrated TF map, compared with other TF analysis methods. Application of the proposed method to perform non-stationary deconvolution of synthetic and field seismic data sets presents a better performance than short-time Fourier transform (STFT) and standard S-transform (SST) in improving the temporal resolution of the data.

Evaluation of the modified S-transform for time-frequency synchrony analysis and source localisation

This article considers the problem of phase synchrony and coherence analysis using a modified version of the S-transform, referred to here as the Modified S-transform (MST). This is a novel and important time-frequency approach to study the phase coupling between two or more different spatially recorded entities with non-stationary characteristics. The basic method includes a cross-spectral analysis to study the phase synchrony of non-stationary signals, and relies on some properties of the MST, such as phase preservation. We demonstrate the usefulness of the technique using simulated examples and real newborn EEG data. The results show the advantage of using the cross-MST in the study of the connectivity between different signals using the time-frequency coherence. The MST led to improvements in resolution of almost twofold over the standard S-Transform in the examples presented in the article.

Robust S-transform based on L-DFT

Time-frequency representations of signals obtained by the S-transform can be very sensitive to the presence of ?-stable noise. An algorithm for the robust S-transform is introduced. The proposed scheme is based on the L-DFT. The results of conducted numerical analysis show a significantly enhanced performance of the proposed scheme compared to the standard S-transform.

A Window Width Optimized S-Transform

Energy concentration of the S-transform in the time-frequency domain has been addressed in this paper by optimizing the width of the window function used. A new scheme is developed and referred to as a window width optimized S-transform. Two optimization schemes have been proposed, one for a constant window width, the other for time-varying window width. The former is intended for signals with constant or slowly varying frequencies, while the latter can deal with signals with fast changing frequency components. The proposed scheme has been evaluated using a set of test signals. The results have indicated that the new scheme can provide much improved energy concentration in the time-frequency domain in comparison with the standard S-transform. It is also shown using the test signals that the proposed scheme can lead to higher energy concentration in comparison with other standard linear techniques, such as short-time Fourier transform and its adaptive forms. Finally, the method has been demonstrated on engine knock signal analysis to show its effectiveness.