On Hilbert transform, analytic signal, and modulation analysis for signals over graphs

Venkitaraman, Arun; Chatterjee, Saikat; Händel, Peter

doi:10.1016/j.sigpro.2018.10.016

Cited by 13 publications

(4 citation statements)

References 69 publications

(89 reference statements)

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“…VMD can get the optimal result of the variational model through continuous iterative processing, and can obtain the bandwidth and frequency center of each intrinsic mode function (IMF) by adaptively separating the components. Using VMD to decompose complex signals is actually the process of solving the sum of the smallest frequency bands by constructing multiple variation functions, a brief introduction of the VMD is as follows [36,37]:…”

Section: Variational Modal Decomposition (Vmd)mentioning

confidence: 99%

A Temperature Error Parallel Processing Model for MEMS Gyroscope based on a Novel Fusion Algorithm

Cao

Shen

2020

Electronics

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To deal with the influence of temperature drift for a Micro-Electro-Mechanical System (MEMS) gyroscope, this paper proposes a new temperature error parallel processing method based on a novel fusion algorithm. Firstly, immune based particle swarm optimization (IPSO) is employed for optimal parameters search for Variational Modal Decomposition (VMD). Then, we can get the optimal decomposition parameters, wherein permutation entropy (PE) is employed as the fitness function of the particles. Then, the improved VMD is performed on the output signal of the gyro to obtain intrinsic mode functions (IMFs). After judging by sample entropy (SE), the IMFs are divided into three categories: noise term, mixed term and feature term, which are processed differently. Filter the mixed term and compensate the feature term at the same time. Finally, reconstruct them and get the result. Compared with other optimization algorithms, IPSO has a stronger global search ability and faster convergence speed. After Back propagation neural network (BP) is enhanced by Adaptive boosting (Adaboost), it becomes a strong learner and a better model, which can approach the real value with higher precision. The experimental result shows that the novel parallel method proposed in this paper can effectively solve the problem of temperature errors.Electronics 2020, 9, 499 2 of 21 circuit design structure to reduce the damping coefficient, which is convenient and economical [15]. Yang et al. adopted a new concept whereby the on-chip temperature compensation of the MEMS gyroscope is realized by the on-chip sensor. In order to make the on-chip temperature of the micro gyroscope well controlled, the newly integrated serpentine micro heater is used to achieve this function [16]. Cui et al. analyzed the working principle of the gyroscope and adopted the vibration compensation of the drive mode, which has a good effect [17]. However, the hardware compensation cost is high and it is too difficult to implement.The second is through software compensation, it includes the removal of noise and temperature compensation. The software compensation method mainly establishes a model for the drift part and the noise part of the MEMS gyroscope to remove noise and compensate drift. For the establishment of the temperature drift model, the reference temperature and the corresponding temperature drift output obtained in advance are used as a set of training set data. The model is established after the learning and training of the algorithm. When the temperature value is input, the model can predict the output value as compensation. There are two main methods. The first one is serial processing, which first uses a filter to perform noise reduction on the signal and then uses a model to eliminate drift. The other one is parallel processing, which refers to extracting and processing noise components and drift components separately. Dominik uses a combination of experiments and numerical values to provide accurate ceramic acceleration at higher temperature [18]. Yang uses a sim...

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Section: Variational Modal Decomposition (Vmd)mentioning

confidence: 99%

A Temperature Error Parallel Processing Model for MEMS Gyroscope based on a Novel Fusion Algorithm

Cao

Shen

2020

Electronics

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“…Graph signal processing or signal processing over graphs deals with extension of several traditional signal processing methods while incorporating the graph structural information [30], [31]. This includes signal analysis concepts such as Fourier transforms [32], filtering [30], [33], wavelets [34], [35], filterbanks [36], [37], multiresolution analysis [38]- [40], denoising [41], [42], and dictionary learning [43], [44], and stationary signal analysis [45], [46]. Spectral clustering and principal component analysis approaches based on graph signal filtering have also been proposed recently [47], [48].…”

Section: Preliminaries On Graph Signal Processingmentioning

confidence: 99%

Gaussian Processes Over Graphs

Venkitaraman

Chatterjee

Händel

2020

ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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We propose Gaussian processes for signals over graphs (GPG) using the apriori knowledge that the target vectors lie over a graph. We incorporate this information using a graph-Laplacian based regularization which enforces the target vectors to have a specific profile in terms of graph Fourier transform coeffcients, for example lowpass or bandpass graph signals. We discuss how the regularization affects the mean and the variance in the prediction output. In particular, we prove that the predictive variance of the GPG is strictly smaller than the conventional Gaussian process (GP) for any non-trivial graph. We validate our concepts by application to various real-world graph signals. Our experiments show that the performance of the GPG is superior to GP for small training data sizes and under noisy training.

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“…Graph signal processing offers a consistent treatment of graphstructured data in a wide variety of applications, be it in social networks, traffic networks, or biological networks [3,4] As mentioned in the beginning of this Section, GSP literature may be classified into two groups: one of them being that which uses an apiori specified graph for signal processing tasks over graphs. This includes a wealth of techniques from harmonic and filterbank analysis [5,6,7,8], sampling [9,10,11], statistical analysis [12], non-parametric analysis [2,13,14], prediction and recovery [15,16] to the more recent graph neural networks [17]. The second group deals with the problem of graph estimation or discovery where the graph signals are used to arrive at an estimate of the graph or the connections among the nodes [18,19,20].…”

Section: Literature Surveymentioning

confidence: 99%

Recursive Prediction of Graph Signals With Incoming Nodes

Venkitaraman

Chatterjee

Wahlberg

2020

ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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Kernel and linear regression have been recently explored in the prediction of graph signals as the output, given arbitrary input signals that are agnostic to the graph. In many real-world problems, the graph expands over time as new nodes get introduced. Keeping this premise in mind, we propose a method to recursively obtain the optimal prediction or regression coefficients for the recently proposed Linear Regression over Graphs (LRG), as the graph expands with incoming nodes. This comes as a natural consequence of the structure of the regression problem, and obviates the need to solve a new regression problem each time a new node is added. Experiments with real-world graph signals show that our approach results in good prediction performance which tends to be close to that obtained from knowing the entire graph apriori.

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On Hilbert transform, analytic signal, and modulation analysis for signals over graphs

Cited by 13 publications

References 69 publications

A Temperature Error Parallel Processing Model for MEMS Gyroscope based on a Novel Fusion Algorithm

A Temperature Error Parallel Processing Model for MEMS Gyroscope based on a Novel Fusion Algorithm

Gaussian Processes Over Graphs

Recursive Prediction of Graph Signals With Incoming Nodes

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