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As a fast and non-destructive spectroscopic analysis technique, Raman spectroscopy has been widely applied in chemistry. However, noise is usually unavoidable in Raman spectra. Hence, denoising is an important step before Raman spectral analysis. A novel spectral denoising method based on variational mode decomposition (VMD) was introduced to solve the above problem. The spectrum is decomposed into a series of modes (uk) by VMD. Then, the high-frequency noise modes are removed and the remaining modes are reconstructed to obtain the denoised spectrum. The proposed method was verified by two artificial noised signals and two Raman spectra of inorganic materials, i.e., MnCo ISAs/CN and Fe-NCNT. For comparison, empirical mode decomposition (EMD), Savitzky–Golay (SG) smoothing, and discrete wavelet transformation (DWT) are also investigated. At the same time, signal-to-noise ratio (SNR) was introduced as evaluation indicators to verify the performance of the proposed method. The results show that compared with EMD, VMD can significantly improve mode mixing and the endpoint effect. Moreover, the Raman spectrum by VMD denoising is more excellent than that of EMD, SG smoothing and DWT in terms of visualization and SNR. For the small sharp peaks, some information is lost after denoising by EMD, SG smoothing, DWT and VMD while VMD loses fewest information. Therefore, VMD may be an alternative method for Raman spectral denoising.

Variational Mode Decomposition (VMD) serves as an effective method for simultaneously decomposing signals into a series of narrowband components. However, its theoretical foundation, the classical Wiener filter, exhibits limited adaptability when applied to broadband signals. This paper proposes a novel Variable Filtered-Waveform Variational Mode Decomposition (VFW-VMD) method to address critical limitations in VMD, particularly in handling broadband and chirp signals. By incorporating fractional-order constraints and dynamically adjusting filter waveforms, the proposed algorithm effectively mitigates mode mixing and over-smoothing issues. The mathematical framework of VFW-VMD is formulated, and its decomposition performance is validated through simulations involving both synthetic and real-world signals. The results demonstrate that VFW-VMD exhibits superior adaptability in extracting broadband signals and effectively captures more rolling bearing fault features. This work advances signal processing techniques, enhancing capability and significantly improving the performance of practical bearing fault diagnostic applications.

Tunable open-access Fabry-Pérot microcavities enable the combination of cavity enhancement with high resolution imaging. To assess the limits of this technique originating from background variations, we perform high-finesse scanning cavity microscopy of pristine planar mirrors. We observe spatially localized features of strong cavity transmission reduction for certain cavity mode orders, and periodic background patterns with high spatial frequency. We show in detailed measurements that the localized structures originate from resonant transverse-mode coupling and arise from the topography of the planar mirror surface, in particular its local curvature and gradient. We further examine the background patterns and find that they derive from non-resonant mode coupling, and we attribute it to the micro roughness of the mirror. Our measurements and analysis elucidate the impact of imperfect mirrors and reveal the influence of their microscopic topography. This is crucial for the interpretation of scanning cavity images, and could provide relevant insight for precision applications such as gravitational wave detectors, laser gyroscopes, and reference cavities.

As a classical method to deal with nonlinear and nonstationary signals, the Hilbert–Huang transform (HHT) is widely used in various fields. In order to overcome the drawbacks of the Hilbert–Huang transform (such as end effects and mode mixing) during the process of empirical mode decomposition (EMD), a revised Hilbert–Huang transform is proposed in this article. A method called local linear extrapolation is introduced to suppress end effects, and the combination of adding a high-frequency sinusoidal signal to, and embedding a decorrelation operator in, the process of EMD is introduced to eliminate mode mixing. In addition, the correlation coefficients between the analyzed signal and the intrinsic mode functions (IMFs) are introduced to eliminate the undesired IMFs. Simulation results show that the improved HHT can effectively suppress end effects and mode mixing. To verify the effectiveness of the new HHT method with respect to fault diagnosis, the revised HHT is applied to analyze the vibration displacement signals in a rotor system collected under normal, rubbing, and misalignment conditions. The simulation and experimental results indicate that the revised HHT method is more reliable than the original with respect to fault diagnosis in a rotor system.

This paper proposes a framework combining the complementary ensemble empirical mode decomposition with both the independent component analysis and the non-negative matrix factorization for estimating both the heart rate and the respiratory rate from the photoplethysmography (PPG) signal. After performing the complementary ensemble empirical mode decomposition on the PPG signal, a finite number of intrinsic mode functions are obtained. Then, these intrinsic mode functions are divided into two groups to perform the further analysis via both the independent component analysis and the non-negative matrix factorization. The surrogate cardiac signal related to the heart activity and another surrogate respiratory signal related to the respiratory activity are reconstructed to estimate the heart rate and the respiratory rate, respectively. Finally, different records of signals acquired from the Medical Information Mart for Intensive Care database downloaded from the Physionet Automated Teller Machine (ATM) data bank are employed for demonstrating the outperformance of our proposed method. The results show that our proposed method outperforms both the digital filtering approach and the conventional empirical mode decomposition based methods in terms of reconstructing both the surrogate cardiac signal and the respiratory signal from the PPG signal as well as both achieving the higher accuracy and the higher reliability for estimating both the heart rate and the respiratory rate.

Empirical mode decomposition (EMD) is a widely used adaptive signal processing method, which has shown some shortcomings in engineering practice, such as sifting stop criteria of intrinsic mode function (IMF), mode mixing and end effect. In this paper, an improved sifting stop criterion based on the valid data segment is proposed, and is compared with the traditional one. Results show that the new sifting stop criterion avoids the influence of end effects and improves the correctness of the EMD. In addition, a novel AEMD method combining the analysis mode decomposition (AMD) and EMD is developed to solve the mode-mixing problem, in which EMD is firstly applied to dispose the original signal, and then AMD is used to decompose these mixed modes. Then, these decomposed modes are reconstituted according to a certain principle. These reconstituted components showed mode mixing phenomena alleviated. Model comparison was conducted between the proposed method with the ensemble empirical mode decomposition (EEMD), which is the mainstream method improved based on EMD. Results indicated that the AEMD and EEMD can effectively restrain the mode mixing, but the AEMD has a shorter execution time than that of EEMD.

The singular value decomposition package (SVDP) is often used for signal decomposition and feature extraction. At present, the general SVDP has insufficient feature extraction ability due to the two-row structure of the Hankel matrix, which leads to mode mixing. In this paper, an improved singular value decomposition packet (ISVDP) algorithm is proposed: the feature extraction ability is improved by changing the structure of the Hankel matrix, and similar signal sub-components are selected by similarity to avoid having the same frequency component signals being decomposed into different sub-signals. In this paper, the effectiveness of ISVDP is illustrated by a set of simulation signals, and it is utilized in fault diagnosis of bearing data. The results show that ISVDP can effectively suppress the model-mixing phenomenon and can extract the fault features in bearing vibration signals more accurately.

Background Ensemble Empirical Mode Decomposition (EEMD) has been popularised for single-channel Electromyography (EMG) signal processing as it can effectively extract the temporal information of the EMG time series. However, few papers examine the temporal and spatial characteristics across multiple muscle groups in relation to multichannel EMG signals. Experiment The experimental data was obtained from the Center for Machine Learning and Intelligent Systems, University of California Irvine (UCI). The data was donated by the Nueva Granada Military University and the Technopark node Manizales in Colombia. The databases of 11 male subjects from the healthy group were taken into the study. The subjects undergo three exercise programs, leg extension from a sitting position (sitting), flexion of the leg up (standing), and gait (walking), while four electrodes were placed on biceps femoris (BF), vastus medialis (VM), rectus femoris (RF), and semitendinosus (ST). Methods Based on the experimental data, a comparative study is provided by assessing the Empirical Mode Decomposition (EMD)-based approaches, EEMD, Multivariate EMD (MEMD), and Noise-Assisted MEMD (NA-MEMD). The outcomes from these approaches are then quantitatively estimated on the basis of three criterions, the number of Intrinsic Mode Functions (IMFs), mode-alignment and mode-mixing. Results Both MEMD and NA-MEMD methods (except EEMD) can guarantee equal numbers of IMFs. For mode-alignment and mode-mixing, NA-MEMD is optimal compared with MEMD and EEMD, and MEMD is merely better than EEMD. Conclusions This study proposes the NA-MEMD approach for multichannel EMG signal processing. This finding implies that NA-MEMD is effective for simultaneously analysing IMFs based frequency bands. It has a vital clinical implication in exploring the neuromuscular patterns that enable the multiple muscle groups to coordinate while performing the functional activities of daily living.

Gaussian filter (GF) is a commonly used linear filter in signal and image noise reduction. However, its limitation is that it cannot adapt parameters to deal with non-stationary noise that varies over time. To address this problem and improve the filtering effectiveness of GF in the face of non-stationary non-Gaussian (NSNG) noise, this paper proposes a new approach called adaptive Gaussian filter based on improved complete ensemble empirical mode decomposition (ICEEMDAN-AGF). The ICEEMDAN-AGF firstly uses the fusion information of the dispersion entropy (DE) and the power spectral entropy (PSE) to divide the intrinsic mode functions (IMFs) into two groups. One group is called guiding IMFs, which contains the high-frequency components of the NSNG noise, and the other group is called hybrid IMFs, which contains the low-frequency components of the NSNG noise and all the noise-free signals. Next, a method called multi-resolution local similarity (MRLS) is proposed to identify the mixed modes presented in the guiding IMFs. Then, the variance of the guiding IMFs is used to adjust the window width w and kernel parameter σ of GF. Finally, the adaptive Gaussian filter (AGF) obtained above is used to filter the hybrid IMFs. The experiments shows that ICEEMDAN-AGF performs better than other conventional algorithms on known signals.

Complex human activities consist of sequential, simple limb movements, acting as impulse responses from the motor system. In short-term human activity recognition (ST-HAR), the inherently brief observation window results in non-stationary signals and “information starvation,” breaking the time-translational symmetry of kinetic signals. Moreover, traditional Variational Mode Decomposition (VMD) and Hilbert Transform (HT) suffer from suboptimal decomposition levels (K) and spectral asymmetry. This paper proposes an improved VMD-HT framework to enhance feature extraction from short-term Inertial Measurement Unit (IMU) signals. First, an instantaneous-frequency-driven adaptive VMD method is developed to mitigate mode mixing by automatically determining the optimal K. Second, an information-enhanced instantaneous energy density (IEIE) feature is introduced. By fusing kinetic energy from both positive and negative frequency domains, this feature restores the spectral symmetry of the energy representation, precisely quantifying fine motion variations and compensating for information loss caused by the limited temporal span. Experimental results on PAMAP2, WARD, and a self-collected dataset, NOITOM, demonstrate the method’s effectiveness. With a 0.5 s window, the proposed model achieves outstanding recognition accuracies of 93.60%, 96.41%, and 97.22%, respectively, outperforming state-of-the-art approaches in capturing transient short-term information.