The optimal fractional Gabor transform based on the adaptive window function and its application

We designed the window function of the optimal Gabor transform based on the time-frequency rotation property of the fractional Fourier transform. Thus, we obtained the adaptive optimal Gabor transform in the fractional domain and improved the time-frequency concentration of the Gabor transform. The algorithm first searches for the optimal rotation factor, then performs the p-th FrFT of the signal and, finally, performs time and frequency analysis of the FrFT result. Finally, the algorithm rotates the plane in the fractional domain back to the normal time-frequency plane. This promotes the application of FrFT in the field of high-resolution reservoir prediction. Additionally, we proposed an adaptive search method for the optimal rotation factor using the Parseval principle in the fractional domain, which simplifies the algorithm. We carried out spectrum decomposition of the seismic signal, which showed that the instantaneous frequency slices obtained by the proposed algorithm are superior to the ones obtained by the traditional Gabor transform. The adaptive time frequency analysis is of great significance to seismic signal processing.

Effects of Gabor transform parameters on signa time-frequency resolution

In this paper, it is described that the time-frequency resolution of geophysical signals is affected by the time window function attenuation coefficient and sampling interval and how such effects are eliminated effectively. Improving the signal resolution is the key to signal time-frequency analysis processing and has wide use in geophysical data processing and extraction of attribute parameters. In this paper, authors research the effects of the attenuation coefficient choice of the Gabor transform window function and sampling interval on signal resolution. Unsuitable parameters not only decrease the signal resolution on the frequency spectrum but also miss the signals. It is essential to first give the optimum window and range of parameters through time-frequency analysis simulation using the Gabor transform. In the paper, the suggestions about the range and choice of the optimum sampling interval and processing methods of general seismic signals are given.

Gabor Order Tracking Filtering Technology in Rotary Machinery

Order analysis is one of the most important technique means of condition monitoring and fault diagnosis for rotary machinery.The traditional order analyses usually employ the Vold-Kalman filtering,however this method is confined to the expensive hardware equipments.This paper starts from Gabor transform and applies the Gabor time-frequency filtering to vibration signal.The order component＇s time-frequency coefficients are extracted by mask operation.The order component is reconstructed from the obtained coefficients.The following four key technologies,such as smoothing rotary speed curve,defining filtering band width,constructing the mask operation matrix and reconstructing signal component,are also deeply discussed.Moreover,the technique to smooth the rotary speed curve based on polynomial approximation,the method to determine filtering band width,the arithmetic to constitute mask array and the iterative algorithm to reconstruct signal based on minimum mean square error are specifically analyzed.The 4th order component is successfully gained by using the methods that Gabor time-frequency filter,and the validity and feasibility of this method are approved.This method can solve the problem of order tracking filter technologies which used to depend on hardware and efficiently improve the accuracy of order analysis.

Analysis of frequency shifting in seismic signals using Gabor-Wigner transform

A hybrid time-frequency method known as Gabor-Wigner transform (GWT) is introduced in this paper for examining the time-frequency patterns of earthquake damaged buildings. GWT is developed by combining the Gabor transform (GT) and Wigner-Ville distribution (WVD). GT and WVD have been used separately on synthetic and recorded earthquake data to identify frequency shifting due to earthquake damages, but GT is prone to windowing effect and WVD involves ambiguity function. Hence to obtain better clarity and to remove the cross terms (frequency interference), GT and WVD are judiciously combined and the resultant GWT used to identify frequency shifting. Synthetic seismic response of an instrumented building and real-time earthquake data recorded on the building were investigated using GWT. It is found that GWT offers good accuracy for even slow variations in frequency, good time-frequency resolution, and localized response. Presented results confirm the efficacy of GWT when compared with GT and WVD used separately. Simulation results were quantified by the Renyi entropy measures and GWT shown to be an adequate technique in identifying localized response for structural damage detection.

Compressive sampling and reconstruction in shift-invariant spaces associated with the fractional Gabor transform

In this paper,we propose a compressive sampling and reconstruction system based on the shift-invariant space associated with the fractional Gabor transform.With this system,we aim to achieve the subNyquist sampling and accurate reconstruction for chirp-like signals containing time-varying characteristics.Under the proposed scheme,we introduce the fractional Gabor transform to make a stable expansion for signals in the joint time-fractional-frequency domain.Then the compressive sampling and reconstruction system is constructed under the compressive sensing and shift-invariant space theory.We establish the reconstruction model and propose a block multiple response extension of sparse Bayesian learning algorithm to improve the reconstruction effect.The reconstruction error for the proposed system is analyzed.We show that,with considerations of noises and mismatches,the total error is bounded.The effectiveness of the proposed system is verified by numerical experiments.It is shown that our proposed system outperforms the other systems state-of-the-art.

Properties of an improved Gabor wavelet transform and its applications to seismic signal processing and interpretation

This paper presents an analytical study of the complete transform of improved Gabor wavelets （IGWs）, and discusses its application to the processing and interpretation of seismic signals. The complete Gabor wavelet transform has the following properties. First, unlike the conventional transform, the improved Gabor wavelet transform （IGWT） maps time domain signals to the time-frequency domain instead of the time-scale domain. Second, the IGW＇s dominant frequency is fixed, so the transform can perform signal frequency division, where the dominant frequency components of the extracted sub-band signal carry essentially the same information as the corresponding components of the original signal, and the sub- band signal bandwidth can be regulated effectively by the transform＇s resolution factor. Third, a time-frequency filter consisting of an IGWT and its inverse transform can accurately locate target areas in the time-frequency field and perform filtering in a given time-frequency range. The complete IGW transform＇s properties are investigated using simulation experiments and test cases, showing positive results for seismic signal processing and interpretation, such as enhancing seismic signal resolution, permitting signal frequency division, and allowing small faults to be identified.

GABOR ANALYSIS OF THE SPACES M(p,q,w)(R^d) AND S(p,q,r,w,ω)(R^d)

Let g be a non-zero rapidly decreasing function and w be a weight function. In this article in analog to modulation space, we define the space M（p, q, w）（Rd） to be the subspace of tempered distributions f ∈ S′（Rd） such that the Gabor transform Vg（f） of f is in the weighted Lorentz space L（p, q, wdμ） （R2d）. We endow this space with a suitable norm and show that it becomes a Banach space and invariant under time frequence shifts for 1 ≤ p, q ≤ ∞. We also investigate the embeddings between these spaces and the dual space of M（p, q, w）（Rd）. Later we define the space S（p, q, r, w, ω）（Rd） for 1 p ∞, 1 ≤ q ≤ ∞. We endow it with a sum norm and show that it becomes a Banach convolution algebra. We also discuss some properties of S（p, q, r, w, ω）（Rd）. At the end of this article, we characterize the multipliers of the spaces M（p, q, w）（Rd） and S（p, q, r, w, ω）（Rd）.

SAR target detection based on the optimal fractional Gabor spectrum feature

In this paper,an algorithm based on a fractional time-frequency spectrum feature is proposed to improve the accuracy of synthetic aperture radar(SAR)target detection.By extending the fractional Gabor transform(FrGT)into two dimensions,the fractional time-frequency spectrum feature of an image can be obtained.In the achievement process,we search for the optimal order and design the optimal window function to accomplish the two-dimensional optimal FrGT.Finally,the energy attenuation gradient(EAG)feature of the optimal time-frequency spectrum is extracted for high-frequency detection.The simulation results show the proposed algorithm has a good performance in SAR target detection and lays the foundation for recognition.

Global motion estimation with Gabor wavelet transform

A novel algorithm of global motion estimation is proposed. First, through Gabor wavelet transform （GWT）, a kind of energy distribution of image is obtained and checkpoints are selected according to a probability decision approach proposed. Then, the initialized motion vectors are obtained via a hierarcbal block-matching based on these checkpoints. Finally, by employing a 3-parameter motion model, precise parameters of global motion are found. From the experiment, the algorithm is reliable and robust.

Real-Valued Discrete Gabor Transform of Linear Time-Varying Systems: Exact Representation and Approximation

An efficient algorithm for the representation and approximation of linear time-varying systems is presented via the fast real-valued discrete Gabor transform. Compared with the existing algorithm based on the traditional complex-valued discrete Gabor transform, the proposed algorithm runs faster, can more easily be implemented in software or hardware, and leads to a more compact representation. Simulation results are given for demonstration.

Prestack nonstationary deconvolution based on variable-step sampling in the radial trace domain

The conventional nonstationary convolutional model assumes that the seismic signal is recorded at normal incidence. Raw shot gathers are far from this assumption because of the effects of offsets. Because of such problems, we propose a novel prestack nonstationary deconvolution approach. We introduce the radial trace （RT） transform to the nonstationary deconvolution, we estimate the nonstationary deconvolution factor with hyperbolic smoothing based on variable-step sampling （VSS） in the RT domain, and we obtain the high-resolution prestack nonstationary deconvolution data. The RT transform maps the shot record from the offset and traveltime coordinates to those of apparent velocity and traveltime. The ray paths of the traces in the RT better satisfy the assumptions of the convolutional model. The proposed method combines the advantages of stationary deconvolution and inverse Q filtering, without prior information for Q. The nonstationary deconvolution in the RT domain is more suitable than that in the space-time （XT） domain for prestack data because it is the generalized extension of normal incidence. Tests with synthetic and real data demonstrate that the proposed method is more effective in compensating for large-offset and deep data.

Intelligibility evaluation of enhanced whisper in joint time-frequency domain

Some factors influencing the intelligibility of the enhanced whisper in the joint time-frequency domain are evaluated. Specifically, both the spectrum density and different regions of the enhanced spectrum are analyzed. Experimental results show that for a spectrum of some density, the joint time-frequency gain-modification based speech enhancement algorithm achieves significant improvement in intelligibility. Additionally, the spectrum region where the estimated spectrum is smaller than the clean spectrum, is the most important region contributing to intelligibility improvement for the enhanced whisper. The spectrum region where the estimated spectrum is larger than twice the size of the clean spectrum is detrimental to speech intelligibility perception within the whisper context.

Analysis of pressure pulsation mechanism and dynamic characteristics of axial piston pump

The pressure pulsation of axial piston pump is not only an important cause of rotation speed fluctuation,vibration noise and output stability of the hydraulic system,but also the main information source for obtaining fault information.Hydraulic system is characterized by strong noise interference,which leads to low signal-to-noise ratio(SNR)of detection signals.Therefore,it is necessary to dig deep into the system operating state information carried by pressure signals.Firstly,based on flow loss mechanism of the plunger pump,the mapping relationship between flow pulsation and pressure pulsation is analyzed.After that,the pressure signal is filtered and reconstructed based on standard Gabor transform.Finally,according to the time-domain waveform morphology of pressure signal,four characteristic indicators are proposed to analyze the characteristics of pressure fluctuations under different working conditions.The experimental results show that the standard Gabor transform can accurately extract high-order harmonics and phase frequencies of the signal.The reconstructed time-domain waveform of pressure pulsation of the axial piston pump contains a wealth of operating status information,and the characteristics of pulsation changes under various working conditions can provide a new theoretical basis and a method support for fault diagnosis and health assessment of hydraulic pumps,motors and key components.

Dissolution rate determination of alumina in molten cryolite-based aluminum electrolyte

Determination of dissolution rate of alumina is one of the classical problems in aluminum electrolysis. A novel method which can measure the dissolution rate of alumina was presented. Effect of factors on dissolution rate of alumina was studied intuitively and roundly using transparent quartz electrobath and image analysis techniques. Images about dissolution process of alumina were taken at an interval of fixed time from transparent quartz electrobath of double rooms. Gabor wavelet transforms were used for extracting and describing the texture features of each image. After subsampling several times, the dissolution rate of alumina was computed using these texture features in local neighborhood of samples. Regression equation of the dissolution rate of alumina was obtained using these dissolution rates. Experiments show that the regression equation of the dissolution rate of alumina is y=-0.000 5x^3＋0.024 0x^2-0.287 3x＋ 1.276 7 for Na3AIF6-AIF3-Al2O3-CaF2-LiF- MgF2 system at 920 ℃.

Bubble Size Distribution for Waves Propagating over A Submerged Breakwater

Experiments are carried out to study the characteristics of active bubbles entrained by breaking waves as these propagate over an abruptly topographical change or a submerged breakwater. Underwater sounds generated by the entrained air bubbles are detected by a hydrophone connected to a charge amplifier and a data acquisition system. The size distribution of the bubbles is then determined inversely from the received sound frequencies. The sound signals are converted from time domain to time-frequency domain by applying Gabor transform. The number of bubbles with different sizes are counted from the signal peaks in the time-frequency domain. The characteristics of the bubbles are in terms of bubble size spectra, which account for the variation in bubble probability density related to the bubble radius r. The experimental data demonstrate that the bubble probability density function shows a - 2.39 power-law sealing with radius for r 〉 0. 8 mm, and a- 1.11 power law for r 〈0.8 mm.

Joint Time-Frequency Analysis of Seismic Signals:A Critical Review

This paper presents an evaluation of time-frequency methods for the analysis of seismic signals.Background of the present work is to describe,how the frequency content of the signal is changing in time.The theoretical basis of short time Fourier transform,Gabor transform,wavelet transform,S-transform,Wigner distribution,Wigner-Ville distribution,Pseudo Wigner-Ville distribution,Smoothed Pseudo Wigner-Ville distribution,Choi-William distribution,Born-Jordan Distribution and cone shape distribution are presented.The strengths and weaknesses of each technique are verified by applying them to a particular synthetic seismic signal and recorded real time earthquake data.

Everything Is Timelessly Connected: Metaphysics, Physics, Consciousness, Spacetime Travel, DNA, and the Dry Bones Prophesy (Ezekiel Ch. 37)

This paper provides a perception that all things are connected. Starting with the perception of Metaphysics and how matter exists out of total void, complementary matter, or dark matter, the incompleteness of Einstein relativistic theory. Multi spacetime universes and the jump drive for jumping within and between spacetime universes. Warp drive for space travel. DNA as sequence of momentary frequencies and how it related to Ezekiel’s dry bones prophecy. The outcome of neural patterns as cords of consciousness, consciousness as the collection of all cords of consciousness and the lack of uniqueness of individual consciousness. Finally, all things are cords of consciousness.

Automatic Feature Extraction from Ocular Images

Ocular images processing is an important task in: i) biometrics system based on retina and/or sclera images, and ii) in clinical ophthalmology diagnosis of diseases like various vascular disorders. We presents a general framework for image processing of ocular images with a particular view on feature extraction. The method uses the set of geometrical and texture features and based on the information of the complex vessel structure of the retina and sclera. The feature extraction contains the image preprocessing, locating and segmentation of the region of interest (ROI). The image processing of ROI and the feature extraction are proceeded, and then the feature vector is determined for the human recognition and ophthalmology diagnosis.

Acoustic Emission Source Linear Localization Based on an Ultra-Short FBGs Sensing System

An acoustic emission （AE） linear location system was proposed, which employed fiber Bragg gratings （FBGs） as AE sensors. It was demonstrated that the FBG wavelength could be modulated as the static case when the grating length was much shorter than the AE wavelength. In addition, an improved AE location method based on the Gabor wavelet transform （WT） and threshold analysis was represented. The method was testified through AE linear location experiments based on a tunable narrow-band laser interrogation system using ultra-short FBG sensors as AE sensors. Results of the experiments showed that 86% of the linear location errors were less than 10mm.

Synthetic demand data generation for individual electricity consumers:Inpainting

In this contribution we deal with the problem of producing“reasonable”data,when considering recorded energy consumption data,which are at certain sections incomplete and/or erroneous.This task is important,when energy providers employ prediction models for expected energy consumption,which are based on past recorded consumption data,which then of course should be reliable and valid.In a related contribution Yilmaz(2022),GAN-based methods for producing such“artificial data”have been investigated.In this contribution,we describe an alternative and complementary method based on signal inpainting,which has been successfully applied to audio processing Lieb and Stark(2018).After giving a short overview of the theory of proximity-based convex optimization,we describe and adapt an iterative inpainting scheme to our problem.The usefulness of this approach is demonstrated by analyzing real-world-data provided by a German energy supplier.