Interest in parameterized time-frequency analysis for non-stationary signal processing is increasing steadily. An important advantage of such analysis is to provide highly concentrated time-frequency ...representation with signal-dependent resolution. In this paper, a general scheme, named as general parameterized time-frequency transform (GPTF transform), is proposed for carrying out parameterized time-frequency analysis. The GPTF transform is defined by applying generalized kernel based rotation operator and shift operator. It provides the availability of a single generalized time-frequency transform for applications on signals of different natures. Furthermore, by replacing kernel function, it facilitates the implementation of various parameterized time - frequency transforms from the same standpoint. The desirable properties and the dual definition in the frequency domain of GPTF transform are also described in this paper. One of the advantages of the GPTF transform is that the generalized kernel can be customized to characterize the time - frequency signature of non-stationary signal. As different kernel formulation has bias toward the signal to be analyzed, a proper kernel is vital to the GPTF. Thus, several potential kernels are provided and discussed in this paper to develop the desired parameterized time - frequency transforms. In real applications, it is desired to identify proper kernel with respect to the considered signal. This motivates us to propose an effective method to identify the kernel for the GPTF.
We consider in this article the analysis of multicomponent signals, defined as superpositions of modulated waves also called modes. More precisely, we focus on the analysis of a variant of the ...second-order synchrosqueezing transform, which was introduced recently, to deal with modes containing strong frequency modulation. Before going into this analysis, we revisit the case where the modes are assumed to be with weak frequency modulation as in the seminal paper of Daubechies et al. 8, to show that the constraint on the compactness of the analysis window in the Fourier domain can be alleviated. We also explain why the hypotheses made on the modes making up the multicomponent signal must be different when one considers either wavelet or short-time Fourier transform-based synchrosqueezing. The rest of the paper is devoted to the theoretical analysis of the variant of the second order synchrosqueezing transform 16 and numerical simulations illustrate the performance of the latter.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
•A novel gear fault diagnosis method based on the structured sparsity time-frequency analysis is proposed.•The different components of the signals can be extracted simultaneously.•The method is ...validated by simulations and practical tests.•The proposed method outperforms the traditional methods.
Over the last decade, sparse representation has become a powerful paradigm in mechanical fault diagnosis due to its excellent capability and the high flexibility for complex signal description. The structured sparsity time-frequency analysis (SSTFA) is a novel signal processing method, which utilizes mixed-norm priors on time-frequency coefficients to obtain a fine match for the structure of signals. In order to extract the transient feature from gear vibration signals, a gear fault diagnosis method based on SSTFA is proposed in this work. The steady modulation components and impulsive components of the defective gear vibration signals can be extracted simultaneously by choosing different time-frequency neighborhood and generalized thresholding operators. Besides, the time-frequency distribution with high resolution is obtained by piling different components in the same diagram. The diagnostic conclusion can be made according to the envelope spectrum of the impulsive components or by the periodicity of impulses. The effectiveness of the method is verified by numerical simulations, and the vibration signals registered from a gearbox fault simulator and a wind turbine. To validate the efficiency of the presented methodology, comparisons are made among some state-of-the-art vibration separation methods and the traditional time-frequency analysis methods. The comparisons show that the proposed method possesses advantages in separating feature signals under strong noise and accounting for the inner time-frequency structure of the gear vibration signals.
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The measured vibration signals of mechanical equipment with defects are generally non-stationary. Time–frequency analysis is an effective tool in processing non-stationary signals. However, the ...concentration of time–frequency representation will greatly affect the performance of feature extraction. Thus, a more concentrated time–frequency analysis method plays an important role in mechanical signal processing and fault diagnosis. A novel time–frequency analysis method, called synchrosqueezing extracting transform has been proposed in this study. The proposed method can not only well extract the time-varying information of the nonstationary signal then achieve a better-concentrated time–frequency representation, but also have better noise robustness and lower time-consuming than the traditional time–frequency analysis methods. The analysis of numerical signals verified the great performance of this method. Finally, synchrosqueezing extracting transform is used to process the bearing vibration signals under variable speed conditions. It has been demonstrated that the proposed method achieves better results than other state-of-art time–frequency analysis methods.
•SSET has been proposed in this work.•SSET can well achieve a better concentrated time–frequency representation.•SSET can successfully detect bearing faults under non-stationary conditions.
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Time‐frequency analysis based on Wigner‐Ville distribution (WVD) plays a significant role in analysing non‐stationary signals, but it is susceptible to interference from cross‐terms (CTs) for ...multi‐component signals. To address this issue, a novel WVD enhancement method based on generative adversarial networks (namely WVD‐GAN) is proposed, to achieve highly‐concentrated time‐frequency (TF) representation. Specifically, a deep feature extraction module is designed with multiple residual connections in the generator of WVD‐GAN to leverage the latent information encoded in the shallow representations. Meanwhile, a simple and effective attention module is introduced to enhance auto‐term features. Moreover, a multi‐scale discriminator is proposed based on dilated convolutions to guide the generator to reconstruct high‐resolution TF images by discriminating CT. Finally, a comparative analysis is provided to demonstrate the effectiveness and robustness of the proposed method on different simulated and real‐life datasets. Extensive experiments demonstrate that the proposed method outperforms several state‐of‐the‐art methods.
A novel approach is presented for Wigner‐Ville distribution enhancement based on generative adversarial networks to achieve high‐resolution time‐frequency representation. The authors’ method utilises the Wigner‐Ville distribution method to generate time‐frequency images of non‐stationary signals. Then a Wigner‐Ville distribution enhancement model based generative adversarial networks is proposed to construct highly‐concentrated time‐frequency representations. Extensive experiments demonstrate that the proposed method achieves high‐resolution time‐frequency images and can effectively restore the instantaneous frequency trajectory of non‐stationary signals, while maintaining energy concentration.
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In this letter, we present a deep learning algorithm for channel estimation in communication systems. We consider the time-frequency response of a fast fading communication channel as a 2D image. The ...aim is to find the unknown values of the channel response using some known values at the pilot locations. To this end, a general pipeline using deep image processing techniques, image super-resolution (SR), and image restoration (IR) is proposed. This scheme considers the pilot values, altogether, as a low-resolution image and uses an SR network cascaded with a denoising IR network to estimate the channel. Moreover, the implementation of the proposed pipeline is presented. The estimation error shows that the presented algorithm is comparable to the minimum mean square error (MMSE) with full knowledge of the channel statistics, and it is better than an approximation to linear MMSE. The results confirm that this pipeline can be used efficiently in channel estimation.
Recurrent sequence-to-sequence models using encoder-decoder architecture have made great progress in speech recognition task. However, they suffer from the drawback of slow training speed because the ...internal recurrence limits the training parallelization. In this paper, we present the Speech-Transformer, a no-recurrence sequence-to-sequence model entirely relies on attention mechanisms to learn the positional dependencies, which can be trained faster with more efficiency. We also propose a 2D-Attention mechanism, which can jointly attend to the time and frequency axes of the 2-dimensional speech inputs, thus providing more expressive representations for the Speech-Transformer. Evaluated on the Wall Street Journal (WSJ) speech recognition dataset, our best model achieves competitive word error rate (WER) of 10.9%, while the whole training process only takes 1.2 days on 1 GPU, significantly faster than the published results of recurrent sequence-to-sequence models.
Functional magnetic resonance imaging studies have documented the resting human brain to be functionally organized in multiple large‐scale networks, called resting‐state networks (RSNs). Other brain ...imaging techniques, such as electroencephalography (EEG) and magnetoencephalography (MEG), have been used for investigating the electrophysiological basis of RSNs. To date, it is largely unclear how neural oscillations measured with EEG and MEG are related to functional connectivity in the resting state. In addition, it remains to be elucidated whether and how the observed neural oscillations are related to the spatial distribution of the network nodes over the cortex. To address these questions, we examined frequency‐dependent functional connectivity between the main nodes of several RSNs, spanning large part of the cortex. We estimated connectivity using band‐limited power correlations from high‐density EEG data collected in healthy participants. We observed that functional interactions within RSNs are characterized by a specific combination of neuronal oscillations in the alpha (8–13 Hz), beta (13–30 Hz), and gamma (30–80 Hz) bands, which highly depend on the position of the network nodes. This finding may contribute to a better understanding of the mechanisms through which neural oscillations support functional connectivity in the brain.
Functional magnetic resonance imaging studies have documented the resting human brain to be functionally organized in multiple large‐scale networks, called resting‐state networks (RSNs). We examined frequency‐dependent functional connectivity between the main nodes of several RSNs, spanning large part of the cortex. We observed that functional interactions within RSNs are characterized by a specific combination of neuronal oscillations in the alpha (8–13 Hz), beta (13–30 Hz), and gamma (30–80 Hz) bands, which highly depend on the position of the network nodes.
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Central banks have different objectives in the short and long run. Governments operate simultaneously at different timescales. Many economic processes are the result of the actions of several agents, ...who have different term objectives. Therefore, a macroeconomic time series is a combination of components operating on different frequencies. Several questions about economic time series are connected to the understanding of the behavior of key variables at different frequencies over time, but this type of information is difficult to uncover using pure time-domain or pure frequency-domain methods.
To our knowledge, for the first time in an economic setup, we use cross-wavelet tools to show that the relation between monetary policy variables and macroeconomic variables has changed and evolved with time. These changes are not homogeneous across the different frequencies.
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Data-driven time–frequency analysis Hou, Thomas Y.; Shi, Zuoqiang
Applied and computational harmonic analysis,
September 2013, 2013-09-00, 20130901, Volume:
35, Issue:
2
Journal Article
Peer reviewed
Open access
In this paper, we introduce a new adaptive data analysis method to study trend and instantaneous frequency of nonlinear and nonstationary data. This method is inspired by the Empirical Mode ...Decomposition method (EMD) and the recently developed compressed (compressive) sensing theory. The main idea is to look for the sparsest representation of multiscale data within the largest possible dictionary consisting of intrinsic mode functions of the form {a(t)cos(θ(t))}, where a∈V(θ), V(θ) consists of the functions smoother than cos(θ(t)) and θ′⩾0. This problem can be formulated as a nonlinear l0 optimization problem. In order to solve this optimization problem, we propose a nonlinear matching pursuit method by generalizing the classical matching pursuit for the l0 optimization problem. One important advantage of this nonlinear matching pursuit method is it can be implemented very efficiently and is very stable to noise. Further, we provide an error analysis of our nonlinear matching pursuit method under certain scale separation assumptions. Extensive numerical examples will be given to demonstrate the robustness of our method and comparison will be made with the state-of-the-art methods. We also apply our method to study data without scale separation, and data with incomplete or under-sampled data.
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