Windowed Fourier Transform Research Articles

Production processes optimization through machine learning methods based on geophysical monitoring data

The purpose of the article is to create an effective method for low-delay monitoring of the operating state of a drill string and a drill bit without interfering with the proper drilling process. For the drilling process to be continuously controlled, an experimental setup that operates by utilizing the phase-metric method of control was developed. Any movement of the bit causes a change in the electrical characteristics of the probing signal. To obtain a stable signal from a bit immersion depth of up to 250 m, a frequency of probing electrical signals of 166 Hz and an amplitude of up to 500 V were used; the sampling rate of an analog-to-digital converter (ADC) was 10101 Hz. To identify the state of the drill string and the bit based on graphs of time-dependences of changes in the probing signal electrical characteristics, the present authors investigated a number of deep learning methods. Based on the results of the study, a series of capsular neural network methods ( CapsNet ) was chosen. The authors developed modifications of 2D-CapsNet: windowed Fourier transform (WFT) - 2D-CapsNet and frequency slice wavelet transform (FSWT) - 2D-CapsNet. Both of these methods showed a 99% accuracy in determining the transition between two layers of rocks with different properties, which is 2–3% higher than the currently used measurement-while-drilling (MWD) and logging-while-drilling (LWD) rock surveys. Both of these methods unambiguously reveal self-oscillations in the drill string. When determining a fully serviceable bit in the case of self-oscillations, the (FSWT) - 2D-CapsNet method showed an accuracy of 99%.

Fringe pattern analysis based on the two-dimensional synchrosqueezing transform.

Windowed Fourier transform (WFT) is used to analyze fringe patterns observed from optical measurements. The space-frequency resolution of the WFT is limited, which affects the analyzing performance. In this Letter, we propose to apply the two-dimensional synchrosqueezing transform (SST) for analyzing fringe patterns. The SST is a technique used to overcome the limitation of the space-frequency resolution of the WFT, which sharpens the WFT representation using the derivative of the WFT phase. Numerical experiments confirm the effectiveness of the SST in denoising the fringe pattern and estimating the local frequency from the observed fringe pattern.

A windowed fourier transform-based method of numerically analyzing phase shifts of SPR sensors

This study presents a simple and reliable method for numerical evaluation of the sensitivity of SPR systems. A Windowed Fourier Transform (WFT) based method is applied to extract shifts of SPR interferogram. By applying the WFT, the frequencies consisting of SPR interferogram are extracted, and phase shifts of relevant frequencies are also obtained. The normalized amplitude of the frequencies larger than 0.35 is regarded as the most prominent frequency. The summation of the phase shifts of the most prominent frequencies is regarded as an index to numerically analyzing phase shifts of SPR sensors. Through this method, the small change in the sensing surface can be monitored. By using a homemade SPR system with the proposed calculation method, it can detect the NaCl solutions ranging from 0.00003% to 0.03% (wt%), indicating its great promise for applications in fields such as medicine, food safety, and biotechnology.

Guided mode resonance based phase sensing with spectral interferometry

In photonic biosensor designs, the phase-detection methods offer better sensing capabilities and lower detection limits in contrast to other conventional interrogation schemes. However, this class of detection scheme is explored very limitedly for realizing compact biosensing detection schemes. Predominantly, complex experimental setups involving bulk optical components are required for the phase interrogation scheme, which constrains the practical applicability of phase detection apart from the laboratory environment. Here, we present a common-path spectral interferometric technique utilizing a birefringent crystal and spectrometer to evaluate the phase of the guided mode resonance (GMR) signal operating in transmission mode. The common path method offers better stability and constitutes a simple and compact detection modality that can be incorporated into the practical world. A Window Fourier Transform method is implemented to extract the phase of the GMR signal. From the proposed technique, a sensitivity of 103.4 rad/RIU and a limit of detection of 9.8 × 10−5 RIU could be obtained experimentally. This method provides an improved limit of detection as compared to the conventional wavelength interrogation techniques, which also use a spectrometer as the detection system. Hence, this proposed simple and compact detection system enables the realization of highly sensitive portable biosensors.

Application of Crossed Polarizer Method in the Measurement of Differential Group Delay of Optical Fibers

In this paper, we report the use of crossed polarizer technique to measure the differential group delay (DGD) of few-mode optical fiber (FMF). The windowed Fourier transform (WFT) is applied in the analysis of beat length measurement in the spectral domain to obtain the dependence of DGD as a function of wavelength. The birefringence of polarization-maintaining fiber (PMF) and the DGD of FMF are measured by applying our method. We discuss the noise background, the width of DGD peaks, and the possible errors introduced in the optical path in the modified crossed polarizer technique.

Battery Internal Temperature Measurement Using LC Resonant Tank for Battery Management Systems

This paper suggests an embedded battery impedance measurement based on an Inductor Capacitor (LC) resonant tank to measure the battery’s internal temperature for battery management systems (BMS). The purpose of the BMS is to provide state-of-charge (SoC) balancing and the preheating mechanism at sub-zero temperatures. Battery Impedance Spectroscopy (BIS) for battery internal temperature measurement is achieved by an LC resonant tank connected to the batteries in parallel to induce created resonant current and voltage into the battery. The peaks of the voltage and current waveforms are measured and recorded. Then, the resistance of the battery can be calculated by comparing the peak voltage and current waveforms. Since the resistance of the battery is affected by the battery’s internal temperature, the internal temperature of the battery can be estimated. The benefit of using the LC tank for the battery’s internal temperature is to reduce data processing since no window and Fast Fourier Transform (FFT) is needed for this method. In addition, the proposed method measures the battery’s internal temperature without any internal or external temperature sensor. Power Simulation (PSIM) simulation software is used in this proposed method. Panasonic batteries 18650 and a dSPACE DS1104 are used for the experiment to verify the proposed method. The proposed method shows that the LC resonant tank can measure three batteries B1, B2, and B3 internal resistance with 17.87%, 18.14%, and 17.73% errors compared to the Frequency Response Analyzer (FRA). In addition, the total time needed for balancing is 400 s, and the total energy consumed by the preheating mechanism is 0.214%/°C to preheat the lithium-ion batteries (LIBs) from −5 °C to 10 °C.

A novel moving window-based power spectrum features for single-channel EEG classification using machine learning

Electroencephalogram (EEG) signal classification is a crucial and very difficult task. Meanwhile, extracting features that are representative and able to discriminate different types of EEG signals is a complex task. Such features are usually fed to machine learning algorithms to classify the EEG signals based on the extracted features. This paper proposed a highly accurate and real-time features extraction method that can be used to help physicians in detecting different types of seizures and states in EEG signals characterized by a set of features extracted from the power spectrum of the EEG window. This is achieved by applying the following four steps. First, the EEG signals dataset contains different classes of EEG signals: Normal Eye Closed, Normal Eye Opened, Focal Seizure, Non-Focal Seizure, and Ictal Seizure activities. Second, each EEG signal has a length of 4097 samples sampled with a sampling frequency of 173.6 Hz which resulted in 23.6 seconds in length, this signal will be truncated into windows (Sub-signals) with a length of 349 samples (Approximately 2 seconds) with a total number of 12 windows for each signal. Afterward, the Fourier Transform (FT) based power spectrum will be computed for each window, then a set of different features are extracted from each window's FT power spectrum, and these features are classified using different Machine Learning (ML) algorithms. The results showed that the proposed methodology yields around 98% accuracy for the five different classification scenarios using different ML algorithms. The suggested method is hence robust, fast, real-time, accurate, and simple.

Dual Window Fourier Transform (DWFT): A Tool to Analyze Non-stationary Signals

Dual Window Fourier Transform (DWFT): A Tool to Analyze Non-stationary Signals

Investigations into the Recognisability of Gear Damage Sizes in Vibration Signals and Calculation of Appropriate Digital Filter Limits

The present work investigates the size of gear damage required for significant recognisable change in the vibration signal and presents a method to determine digital filter limits in order to emphasise the vibration behaviour in the time domain. For this purpose, two gears are artificially damaged to four different degrees. The damage levels are determined by a tactile gear measurement and the gears are inserted into two intact gearboxes. Measurements at different speeds are used to generate a representative dataset. On the one hand, the recorded signals are examined via cross-correlation in the time domain. On the other hand, the occurring frequency components are examined using a windowed fast Fourier transformation. Based on the two observations, a statement is made about the recognisability of the damage levels of the two gears in the vibration signal. Furthermore, smoothed spectra are calculated via linear prediction coefficients (LPC) and an appropriate number of required coefficients is estimated via the Akaike information criterion. Subsequently, the calculated prediction coefficients are used as coefficients of an all-pole filter to calculate difference spectra. Based on the difference spectra, filter limits for a digital filter are derived to emphasise the damaged tooth meshing in the time domain.

Quadratic-phase wave packet transform

The quadratic-phase Fourier transform (QPFT) has gained much popularity in recent years because of its applications in image and signal processing. However, the QPFT is inadequate for localizing the quadratic-phase spectrum, which is required in some applications. In this paper, the quadratic-phase wave packet transform (QP-WPT) is proposed to address this problem, based on the wave packet transform (WPT) and QPFT. Firstly, we propose the definition of the QP-WPT and give its relation with windowed Fourier transform (WFT). Secondly, several notable inequalities and important properties of newly defined QP-WPT, such as boundedness, reconstruction formula, Moyal’s formula, reproducing kernel are derived. Finally, we formulate several classes of uncertainty inequalities, such as Leib’s uncertainty principle, logarithmic uncertainty inequality and the Heisenberg uncertainty inequality.

Toeplitz Operators Associated with the Deformed Windowed Fourier Transform

Toeplitz Operators Associated with the Deformed Windowed Fourier Transform

Nonlinear error correction for Terahertz FMCW System by a new beat frequency estimation method.

Terahertz (THz) frequency modulated continuous wave (FMCW) technology is a means of nondestructive testing. The signal's nonlinearity is an unavoidable problem in the daily application of THz FMCW technology. The signal's nonlinearity will lead to the spectrum broadening of the FMCW's beat frequency (BF) signal, which degrades the range resolution and result in distance-measuring error. Traditional methods require additional hardware or require a lot of computation, which are not conducive to the miniaturization of the system and real-time measurement. A novel method for correcting the nonlinear error of THz FMCW technology has been proposed and demonstrated in this article. In the proposed method, the windowed Fourier transform (WFT) is introduced to estimate the BF corresponding to the measured target, according to the linearity distribution of voltage-controlled oscillator (VCO). In this way, the measured target's BF can be accurately estimated from the unprocessed BF signal with a poor linearity. From the estimated BF of the reference target, the non-linear compensation coefficients are calculated. With the non-linear compensation coefficients, the non-linearity of the output BF signal can be calibrated. The results of simulations and experiments show that the proposed method allows the range resolution of an FMCW system to reach the theoretical limit.

Quantum Windowed Fourier Transform and its Application to Quantum Signal Processing

Quantum Windowed Fourier Transform and its Application to Quantum Signal Processing

Vibration Parameters Study of Ship Structures Using Wavelet Analysis of Vibrogram

The study of the vibration parameters of ship structures is important for developing measures to ensure their reliable operation on ships. The commonly used analysis of vibrograms using the Continuous Fourier Transform (CFT) to accurately represent non-stationary functions in general and noise source signals in particular is unsuitable due to a number of drawbacks. The problems of spectral analysis and time-limited signal synthesis can be partially solved by switching to the Window Fourier Transform (WFT). The disadvantage of the WFT is that its calculation uses a fixed window, which cannot be adapted to the local properties of the signal. In order to get rid of this shortcoming for the analysis of vibrogram you can use wavelet transform. It also solves a number of other problems related to the processing of a noise signal. The word “wavelet” means small waves following each other (some sources have introduced the concept of “splash”). In a narrow sense, wavelets are a family of functions obtained by scaling and shifting a single, parent function. In a broad sense, wavelets are functions with frequency localization, whose average value is zero. The article shows the signs of a wavelet. Examples of the most common wavelet functions are given. The use of wavelet functions is proposed not only on the basis of time, but also frequency transformations. The implementation of the algorithm for analyzing vibration measurement data is proposed. An example of vibration measurement data and the results of their processing based on frequency wavelet analysis are given

Vibration Parameters Study of Ship Structures Using Wavelet Analysis of Vibrogram

The study of the vibration parameters of ship structures is important for developing measures to ensure their reliable operation on ships. The commonly used analysis of vibrograms using the Continuous Fourier Transform (CFT) to accurately represent non-stationary functions in general and noise source signals in particular is unsuitable due to a number of drawbacks. The problems of spectral analysis and time-limited signal synthesis can be partially solved by switching to the Window Fourier Transform (WFT). The disadvantage of the WFT is that its calculation uses a fixed window, which cannot be adapted to the local properties of the signal. In order to get rid of this shortcoming for the analysis of vibrogram you can use wavelet transform. It also solves a number of other problems related to the processing of a noise signal. The word “wavelet” means small waves following each other (some sources have introduced the concept of “splash”). In a narrow sense, wavelets are a family of functions obtained by scaling and shifting a single, parent function. In a broad sense, wavelets are functions with frequency localization, whose average value is zero. The article shows the signs of a wavelet. Examples of the most common wavelet functions are given. The use of wavelet functions is proposed not only on the basis of time, but also frequency transformations. The implementation of the algorithm for analyzing vibration measurement data is proposed. An example of vibration measurement data and the results of their processing based on frequency wavelet analysis are given

Some Results for the Windowed Fourier Transform Related to the Spherical Mean Operator

We define and study the windowed Fourier transform associated with the spherical mean operator. We prove the boundedness and compactness of localization operators of this windowed. Next, we establish new uncertainty principles for the Fourier and the windowed Fourier transforms associated with the spherical mean operator. More precisely, we give a Shapiro-type uncertainty inequality for the Fourier transform that is, for s > 0 and {αk}k be an orthonormal sequence in L2(dνn+ 1) $$ \sum\limits_{k=1}^{M}\left( \||(r,x)|^{s}\alpha_{k}\|^{2}_{2,\nu_{n+1}}+\||(\mu,\lambda)|^{s}\mathcal{\tilde{F}}(\alpha_{k})\|^{2}_{2,\nu_{n+1}}\right) \geqslant R_{n,s}M^{1+\frac{s}{2n+1}}. $$ Finally, we prove an analogous inequality for the windowed Fourier transform.

Multifrequency beam-based migration in inhomogeneous media using windowed Fourier transform frames

SUMMARY We consider the problem of inhomogeneous subsurface imaging using beam waves. The formulation is based on the ultra-wide-band phase-space beam summation (UWB-PS-BS) method, which is structured upon windowed Fourier transform (WFT) expansions of surface fields and sources. In this approach, the radiated field is given as a superposition of beam propagators. Here, we use the beams first for expanding the surface sources and the scattered data, and then for imaging where we use the backpropagation and cross-correlation of beams. This formulation enables a target oriented imaging approach, where we take into account only pairs of source and receiver beams that pass near a region of interest, and thus extract only the relevant data arriving from this region. It also leads to a priori sparse representation of both the beam domain data and the beam propagators. A physical cogent for the beam domain data is obtained under the Born approximation. The beam domain data can be approximated as the local interaction between the beam propagators and the medium reflectivity. Thus, one may interpret the beam domain data as a local Snell’s law reflection in the direction defined by the vector summation of the incident beam and backpropagated beam ray parameters. We demonstrate a physical model for the beam domain data and the salient features of the proposed imaging algorithm using numerical examples.

Wavelength-dependent orientation of the principal axes of photonic crystal fibers measured by windowed Fourier-transform spectral interferometry.

We present a novel polarization alignment technique based on windowed Fourier-transform (WFT) spectral interferometry to determine the wavelength-dependent orientation of the principal polarization axes of photonic crystal fibers (PCFs). To test the technique, a commercially available, 82.5-cm-long HC-800-02 type hollow-core PCF was measured. The angles belonging to the fast and the slow principal axes of the fiber were determined from the peak intensity values of the ridges in the WFT map at different wavelengths. We demonstrate that the orientation of the principal polarization axes of the tested PCF is wavelength-dependent. The precision of the angle measurement was better than 0.3°.

Dynamics of a toroidal pure electron plasma using 3D PIC simulations

Nonlinear dynamics of toroidally confined, initially cold, collisionless pure electron plasma has been numerically simulated in a tight aspect ratio, axisymmetric device, confined using a toroidal magnetic field, using a 3D3V particle-in-cell code PEC3PIC. A set of three numerical experiments are conducted by loading the toroidal electron cloud at varying radial distances from the central axis at the vertical midplane, and a comparative analysis of the progression of cloud dynamics and particle transport in the three experiments is carried out. In each experiment, the cloud is seen to initiate toroidal Diocotron oscillations with the following interesting features: (i) initial nonlinear reshaping and density peaking, (ii) elliptical orbital path in the poloidal cross section along with chirp or rotational frequency dynamics and the increase and decrease in the peak density of the filled electron cloud, (iii) cross-field transport and particle loss, and (iv) the measured wall probe signals showing close similarity to experimental signals. It is demonstrated that relatively better confinement of electrons in the toroidal configuration is achieved by loading the initial plasma at the vertical midplane, close to the inner wall of the chamber, supporting the mean-field theoretical predictions. For all cases, the density distribution profiles in the (r−θ) and (r − z) planes of the cylindrical coordinate system (r,θ,z) have consistent peaked density central profiles. The time dependency of the dominant frequencies of the dynamics, obtained from wall probe data using Hilbert–Huang transformation and windowed Fourier transformation, suggests toroidicity induced low poloidal number m (∼1−12) coupling and dynamical chirping.

Detection and segmentation of underwater CW-like signals in spectrum image under strong noise background

Aiming at the detection and segmentation of underwater Continuous wave-like (CW-like) signals of under strong noise sea background, this paper introduces a Gaussian mixture model clustering method by analyzing the signal spectrum features. First, the time domain original signal is converted to its frequency domain correspondence by Windowed Fast Fourier Transform. Second, by studying on the feature of target signal, we introduce a spectrum filtering to alleviate the background noise of ocean environment, which is analyzed and calculated with both time and frequency information. Then, the target echo location signals is constructed using a Gaussian mixture mode based binary clustering algorithm. Finally, we use the EM algorithm and adaptive binarization for solving and optimizing the clustering results. Experimental results have shown the accuracy and efficiency of our detection, which can be also simply modified and applied for detecting similar and specific signal from complex background noise.