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Purpose portable electroencephalogram (EEG) devices have grown in popularity in recent years. However, the artifacts in EEG while capturing occur mostly due to either external or physiological activities. Before clinically relevant data can be extracted, artifacts must be eliminated. Methods Different approaches have been proposed earlier for EEG artifact removal. However, the transform-based method and its modified variants have shown good results. Though large application of wavelet transform is there, still S-Transform is unique as it combines the frequency resolution of the time-frequency space with referenced local phase information. Also, it exhibits a frequency invariant amplitude response, in contrast to the wavelet transform. Further, due to symmetrical property of cosine function, it is used for smooth transition of the signal from one period to another and reduces the leakage effect. As the novelty application of stock-well transform (ST) and its variants are used, though its application for feature extraction and classification problem was performed. Further it is modified as functional S-Transform (FST) for improved result. Results For verification and comparison purpose, different transform techniques are used for experimentation along with variants of ST. The suggested strategy is compared to transform-based methods including the short temporal Fourier transform (STFT), the discrete cosine transforms (DCT), and the discrete wavelet transform (DWT). The evaluating parameters found mean square error (MSE) as1.1554 µV 2 , normalized mean square error (NMSE) as 0.8969µV, relative error (RE) as 0.693, gain in signal-to-artifact ratio (GSAR) as 9,8971dB, signal-to-noise ratio (SNR) as 69.035dB, and correlation coefficient (CC) as 91.55 %. Conclusions The efficacy of proposed method is verified, compared and shown in the result section. It is found that the functional S-Transform performs well with measurement of different performance measures as mentioned.

Abstract We propose synchroextracting adaptive S-transform (SEAST) by combining the adaptivity provided by the recently introduced ‘Sparse Adaptive S-transform’ (SAST) with the high resolution of synchroextracting spectral decomposition method. Traditional synchroextracting transforms are based on short-time Fourier transforms (STFTs) and their application is limited by having a fixed analysis window size for high and low frequencies and no multi-resolution features. The arbitrary window functions used in the SAST vary with frequency and amplitude, making it more suitable for non-stationary seismic signal analysis. The SEAST retains the multi-resolution advantages of adaptive S-transforms, while providing the strong time–frequency focus associated with synchroextracting transforms. The method was used to calculate seismic dispersion attributes and the resulting field data indicates that its time–frequency resolution and joint P-wave dispersion attributes can help to fine-tune identification of the location of oil and gas reservoirs.

This paper introduces a novel geometry-based synchrosqueezing S-transform (GSSST) for advanced gearbox fault diagnosis, designed to enhance diagnostic precision in both planetary and parallel gearboxes. Traditional time-frequency analysis (TFA) methods, such as the Synchrosqueezing S-transform (SSST), often face challenges in accurately representing fault-related features when significant mode closely spaced components are present. The proposed GSSST method overcomes these limitations by implementing an intuitive geometric reassignment framework, which reassigns time-frequency (TF) coefficients to maximize energy concentration, thereby allowing fault components to be distinctly isolated even under challenging conditions. The GSSST algorithm calculates a new instantaneous frequency (IF) estimator that aligns closely with the ideal IF, thus concentrating TF coefficients more effectively than existing methods. Experimental validation, including tests on simulated signals and real-world gearbox fault data, demonstrates that GSSST achieves high robustness and diagnostic accuracy across various types of gearbox faults even in the presence of noise. Moreover, unlike conventional reassignment method, GSSST supports partial signal reconstruction, a key advantage for applications requiring accurate signal recovery. This research highlights GSSST as a promising and versatile tool for diagnosing complex mechanical faults and provides new insights for the future development of TFA methods in mechanical fault analysis.

The study presents a differential scheme for microgrid protection using time-frequency transform such as S-transform. Initially, the current at the respective buses are retrieved and processed through S-transform to generate time-frequency contours. Spectral energy content of the time-frequency contours of the fault current signals are calculated and differential energy is computed to register the fault patterns in the microgrid at grid-connected and islanded mode. The proposed scheme is tested for different shunt faults (symmetrical and unsymmetrical) and high-impedance faults in the microgrid with radial and loop structure. It is observed that a set threshold on the differential energy can issue the tripping signal for effective protection measure within four cycles from the fault inception. The results based on extensive study indicate that the differential energy-based protection scheme can reliably protect the microgrid against different fault situations and thus, is a potential candidate for wide area protection.

In this paper an attempt has been made to generate certain transformation formulae involving various transform.

In this paper, we introduce a new multidimensional fractional S transform S ϕ , α , λ using a generalized fractional convolution ⋆ α , λ and a general window function ϕ satisfying some admissibility condition. The value of S ϕ , α , λ f is also written in the form of inner product of the input function f with a suitable function ϕ t , u α λ . The representation of S ϕ , α , λ f in terms of the generalized fractional convolution helps us to obtain the Parseval’s formula for S ϕ , α , λ using the generalized fractional convolution theorem. Then, the inversion theorem is proved as a consequence of the Parseval’s identity. Using a generalized window function in the kernel of S ϕ , α , λ gives option to choose window function whose Fourier transform as a compactly supported smooth function or a rapidly decreasing function. We also discuss about the characterization of range of S ϕ , α , λ on L 2 ( R N , C ) . Finally, we extend the transform to a class of quaternion valued functions consistently.

As a critical component in industrial systems, timely and accurate fault diagnosis of rolling bearings is closely related to reliability and safety. Since the equipment usually operates in normal conditions with few fault samples, unbalanced data distribution problems lead to poor fault diagnosis ability. To address the above problems, a two-channel convolutional neural network (TC-CNN) model is proposed. Firstly, the frequency spectrum of the vibration signal is extracted using the Fast Fourier Transform (FFT), and the frequency spectrum is used as the input to the one-dimensional convolutional neural network (1D-CNN). Secondly, the time-frequency image of the vibration signal is extracted using generalized S-transform (GST), and the time-frequency image is used as the input to the two-dimensional convolutional neural network (2D-CNN). Then, feature extraction in the convolution and pooling layers is performed in the above two CNN channels, respectively. The feature vectors obtained from the two CNN models are stitched together in the fusion layer, and the fault classes are identified using an SVM classifier. Finally, using the rolling bearing experimental dataset of Case Western Reserve University (CWRU), the fault diagnosis effect of the proposed TC-CNN model under various data imbalance conditions is verified. In comparison with other related works, the experimental results demonstrate the better fault diagnosis results and robustness of the method.

The S-transform is a fundamental time–frequency (T-F) domain analysis method in ground penetrating radar (GPR) data processing and can be used for identifying targets, denoising, extracting thin layers, and high-resolution imaging. However, the S-transform spectrum experiences energy leakage near the instantaneous frequency. This phenomenon causes frequency components to erroneously spread over a wider range, impacting the accuracy and precision of GPR data processing. Synchrosqueezing is an effective method to prevent spectrum leakage. In this work, we introduce the synchrosqueezing generalized phase-shifting S-transform (SS-GPST). Initially, it resolves the compatibility issue between the S-transform and the synchrosqueezing strategy through phase-shifting. Subsequently, the SS-GPST accomplishes spectral energy focusing and resolution enhancement via a generalized parameter and synchrosqueezing. A synthetic signal test shows that the SS-GPST excels over other methods at focusing degree, spectral resolution, and signal reconstruction accuracy and speed. In actual GPR tunnel detection data processing, we assess the adaptability of the SS-GPST from three aspects: spectral energy distribution, thin layer identification, and data denoising. The results indicate: (1) compared to other methods, the SS-GPST accurately expresses spectral components with a strong focusing degree and fewer interference components; (2) high-frequency slices of the SS-GPST accurately detect the top and bottom interfaces of a 3.0–3.5 cm reinforcement protection layer; and (3) due to fewer interference components in the SS-GPST spectrum, reconstructing GPR profiles through the SS-GPST inverse transform is an efficient denoising technique. The SS-GPST demonstrates adaptability to different data processing purposes, offers high-resolution T-F spectra, and shows potential to supersede the S-transform.

In this work, we introduce the quaternion linear canonical S-transform, which is a generalization of the linear canonical S-transform using quaternion. We investigate its properties and seek the different types of uncertainty principles related to this transformation. The obtained results can be looked as an extension of the uncertainty principles for the quaternion linear canonical transform and the quaternion windowed linear canonical transform.

The synchrosqueezing transform (SST) is an advanced post-processing method to sharpen the time–frequency representation (TFR). However, it still processes the signal in frequency domain. Therefore, it cannot effectively analyze signals whose energy is not well concentrated in frequency domain. The fractional S-transform (FrST) inherits the merits of the short-time fractional Fourier transform and the continuous wavelet transform, processing signals in fractional frequency domain. In this paper, a novel non-stationary signal processing tool, synchrosqueezing fractional S-transform (SSFrST) has been proposed, which combines the advantages of SST and FrST. First, we introduce a novel FrST and derive its fundamental properties. Second, based on the novel FrST, we propose SSFrST and discuss its reconstruction formula and implementation. It can not only improve time–frequency resolution, but also process signals in the time-fractional–frequency plane. Finally, we provide several applications to validate the effectiveness of our methods, including chirp signal parameters estimation, signal separation, filtering and noise separation.