Instantaneous Frequency Of Signal Research Articles

Investigating bridge vibrational modes under operational conditions using time-frequency analysis

This study aims to accurately and effectively investigate the instantaneous frequency (IF) of the monitored acceleration of the bridge, as well as the individual components of the monitored signal, using advanced time-frequency techniques. To achieve this, first, synthetic signals resembling the monitored acceleration are constructed and processed using four time-frequency techniques. The accuracy of IF tracking, signal reconstruction, and representation resolution are obtained and compared between these different time-frequency techniques. Subsequently, the monitored vertical and torsional accelerations from the Humber Bridge are analysed using the Fourier synchrosqueezed transform and the improved multisynchrosqueezing transform. This allows for the reconstruction of individual acceleration components along with the corresponding variation of the natural frequency. The magnitude of each component of the monitored acceleration is then obtained. The relative importance of modes in the monitored acceleration is evaluated based on the acceleration root mean square. This study presents a novel approach that involves reconstructing the monitored acceleration and assessing the magnitude of individual components of the monitored data of the bridge under operational conditions using the advanced time-frequency method. The method is particularly suitable for addressing multicomponent monitored data and is expected to benefit future practical research in the bridge health monitoring field.

Estimation and interpreting instantaneous frequency of signals in non-stationary measurement sensor systems: An overview

The basic concepts and methods of joint time-frequency distributions are discussed. The primary purpose is to demonstrate how a signal's spectral composition alters over time as well as to modify the underlying physical and mathematical concepts of a time-varying spectrum. Main intent is to generate energy or intensity of signal distribution which was represented in both time and frequency. Over last 40 years, fundamental ideas have been developed steadily so that significant advances have occurred. The variety of ideas and motivations that have led to the development of the concepts are highlighted in this review, which is written with non-specialists in mind. An overview of several attempts to determine instantaneous frequency (IF) was given. Numerous characteristics, including the product of bandwidth time (BT), analytic signal as well as the link between time frequency distribution and IFs are explored. Finally, discussions of mono-component, multi-component, and instantaneous bandwidth signals are presented. It is shown that the context of the put forth theory adequately describes each of these ideas. These estimation and interpreting schemes find immediate applications like biomedical signal analysis, speech processing, health care sensor systems.

Nonlinear vibration feature extraction based on power spectrum envelope adaptive empirical Fourier decomposition

Analyzing the vibration features of a shipboard stabilized platform (SSP) is significant to the design or vibration compensation of a marine gravimetric survey vibration isolation system. Empirical Fourier decomposition (EFD) is a recently developed method for nonlinear and non-stationary signal decomposition. However, the spectral segmentation boundary needs to be set in advance according to sophisticated experience, and it is easy to be disturbed by noise, and the decomposition result is inaccurate. In order to accurately extract the nonlinear vibration characteristics of SSP, this paper proposes a new method called power spectrum envelope adaptive empirical Fourier decomposition (PSEEFD). Firstly, the number of selected modal decomposition is determined based on the mutual information to realize adaptive segmentation. Then, the improved power spectrum envelope segmentation method is adopted to effectively diminish the interference of noise since the segmentation boundary is formed by the minimum of the adjacent extreme points enveloped by the maximum value of the power spectrum. The spectrum segments obtained from segmentation contain less interference. Finally, the component signal in each frequency band is reconstructed by inverse fast Fourier transform, and the instantaneous frequency signal component with physical significance is obtained. Through the analysis of vibration simulation signals and measured data of SSP, the proposed method is compared with EMD, AFVMD, EWT and EFD. The results show that PSEEFD has a well suppression of noise interference and can effectively extract the characteristics of nonlinear vibration signals.

Structural Instantaneous Frequency Identification Based on the Fractional Fourier Transform

In order to identify the instantaneous frequency of time-varying signals, this paper derives the theoretical relationship between the frequency in a signal and rotational angle α in a fractional Fourier transform. It is demonstrated that the fractional Fourier transform is actually an algorithm of ordinary Fourier transform combined with telescopic translation window. A general expression of signal instantaneous frequency in the fractional Fourier domain is thereafter formulated so that structural instantaneous frequency can be extracted accordingly. The feasibility and reliability of proposed method is verified by a simulated nonlinear frequency modulation signal and a numerical example of a three-degree-of-freedom damped time-varying structure system. The results show that the proposed method is in good agreement with the theoretical values and the method has a certain degree of anti-noise capability. Subsequently, the proposed method is capable of identifying the instantaneous frequency of time-varying structures.

Time-scale-chirp_rate operator for recovery of non-stationary signal components with crossover instantaneous frequency curves

The objective of this paper is to introduce an innovative approach for the recovery of non-stationary signal components with possibly crossover instantaneous frequency (IF) curves from a multi-component blind-source signal. The main idea is to incorporate a chirp rate parameter with the time-scale continuous wavelet-like transformation, by considering the quadratic phase representation of the signal components. Hence-forth, even if two IF curves cross, the two corresponding signal components can still be separated and recovered, provided that their chirp rates are different. In other words, signal components with the same IF value at any time instant could still be recovered. To facilitate our presentation, we introduce the notion of time-scale-chirp_rate (TSC_R) recovery transform or TSC_R recovery operator to develop a TSC_R theory for the 3-dimensional space of time, scale, chirp rate. Our theoretical development is based on the approximation of the non-stationary signal components with linear chirps and applying the proposed adaptive TSC_R transform to the multi-component blind-source signal to obtain fairly accurate error bounds of IF estimations and signal components recovery. Several numerical experimental results are presented to demonstrate the out-performance of the proposed method over all existing time-frequency and time-scale approaches in the published literature, particularly for non-stationary source signals with crossover IFs.

Longitudinal synchroextracting transform: A useful tool for characterizing signals with strong frequency modulation and application to machine fault diagnosis

In this paper, we propose a new time–frequency analysis (TFA) method termed longitudinal synchrosqueezing transform (LSST). As a post-processing time–frequency analysis method, the theory of this method is based on the Reassignment method (RM) and Fourier-based synchrosqueezing transform (FSST). LSST combines the advantages of RM and FSST in signal processing and avoids their drawbacks. Compared with RM and FSST, this method can achieve compact time–frequency representation (TFR) while retaining the ability of modes extraction and reconstruction. However, when addressing strong frequency modulation (FM) signals, there will still be energy smear in the TFR generated by LSST. Therefore, longitudinal synchroextracting transform (LSET) is further proposed to cope with signals with strong FM components and generate TFR with high energy concentration. On the basis of LSST, we only keep the energy most relevant to the instantaneous frequency (IF) of the signal through the Dirichlet function to obtain LSET. LSET estimates the signal's instantaneous frequency using a second-order approximation, which enables an accurate characterization of fast time-varying features of the signal at large window size range and it is more robust against noise. In addition, the proposed method is applied to the early fault diagnosis of rotor rub-impact and the fault feature extraction of rolling bearings under variable speed. Compared with other advanced TFA technologies, the simulated and measured signals can verify the effectiveness and competitiveness of the proposed method.

An Efficient Direction of Arrival Estimation Algorithm for Sources with Intersecting Signature in the Time–Frequency Domain

An efficient direction of arrival estimation method is proposed. The proposed algorithm accurately estimates the instantaneous frequency of signals received by multiple sensors (array of sensors/antennas). The estimated instantaneous frequency is then used to separate sources and estimate their direction of arrivals. Experimental results indicate that the proposed method achieves better performance than the existing methods both in terms of computational requirements and localization accuracy. It is also shown that the proposed method can work in under-determined situations.

Optimization of multicomponent signals entered to the system using estimation of instantaneous frequency

The frequency signal displays are not efficient for analyzing nonstationary signals because of their inability to represent frequency changes over time. In fact, because most of the signals are real, nonstationary, and time varying, analyzing the signals in the time–frequency domain to estimate the instantaneous frequency of a signal is inevitable. The methods of estimating the instantaneous frequency of the multicomponent signals are divided into three groups, which include the methods using signal phase derivatives that are sensitive to noise, methods that calculate the number of zero points of the signal and consider the signal frequency equal to half the frequency of the zero points and are suitable for signals that can be imagined as stationary, and methods based on time–frequency distributions and distributions such as Wigner for instantaneous frequency calculations and more for instantaneous frequency calculations on nonstationary noise signals that exhibit varied time–frequency distributions. In this article, a new hybrid algorithm is used to evaluate different distribution criteria and comparing their performance in investigating one or more features of time–frequency distributions, such as resolution and energy concentration.

Instantaneous frequency enhanced peak detection for sugarcane seed cutting

Peak detection methods are widely used in various areas. This study introduces a peak detection method used for seed cutting. The envelope of signal in discrete time domain was calculated by Hilbert transform. In order to increase the reliability in noise condition, the envelope was enhanced by utilising instantaneous frequency of signal, and then a multi-rule joint search algorithm marks the peaks, which stands for the location of a node. The proposed method worked in worse SNR condition in the simulation, and was verified in the experiment of detecting sugarcane nodes. Local maximums of accelerometer data are marked, showing the position of node rings on the sugarcane surface. The position data will be used for an action signal in cutting machines, or be used for the analysis of crop growth.

Beam damage detection using synchronisation of peaks in instantaneous frequency and amplitude of vibration data

This paper explores the advantages of Variational Mode Decomposition (VMD) in detecting local damage on beam type structures (bridge) subjected to a sprung mass (vehicle). VMD is used to decompose the acceleration time history of the bridge at its midspan into its constitutive intrinsic mode functions (IMFs). The instantaneous frequency (IF) and instantaneous amplitude (IA) of the first IMF show irregularities at the damage position. We demonstrate through computer simulation that VMD is superior for detecting damage when compared to the well-known Empirical Mode Decomposition (EMD) method. A new damage sensitive feature (DSF) is also introduced that considers synchronisation of peaks between the IA and IF signals. The results show that the new DSF can enhance the peak at the damage positions while suppressing peaks at other locations.

Blood Pressure Prediction by a Smartphone Sensor using Fully Convolutional Networks.

Heart disease and stroke are the leading causes of death worldwide. High blood pressure greatly increases the risk of heart disease and stroke. Therefore, it is important to control blood pressure (BP) through regular BP monitoring; as such, it is necessary to develop a method to accurately and conveniently predict BP in a variety of settings. In this paper, we propose a method for predicting BP without feature extraction using fully convolutional neural networks (CNNs). We measured single multi-wave photoplethysmography (PPG) signals using a smartphone. To find an effective wavelength of PPG signals for the generation of accurate BP measurements, we investigated the BP prediction performance by changing the combinations of the input PPG signals. Our CNN-based BP predictor yielded the best performance metrics when a green PPG time signal was used in combination with an instantaneous frequency signal. This combination had an overall mean absolute error (MAE) of 5.28 and 4.92 mmHg for systolic and diastolic BP, respectively. Thus, our CNN-based approach achieved comparable results to other approaches that use a single PPG signal.

Fissure prediction based on wavelet transform and complex signal analysis technology

The fissure is one of the most important and active master control factors inducing geohazards such as water outburst and mud gushing. The precise and immediate forecasting fissure is a key problem to be studied and resolved currently in tunnel design and construction. Complex signal analysis is introduced to the prediction of water with the ground penetrating radar (GPR) to analyze the water response in the radar data from instantaneous amplitude, instantaneous phase and instantaneous frequency, therefore the accuracy of fissure prediction is improved. However, a large number of effective information in the instantaneous frequency will be covered by noise, thus affecting the accuracy of the prediction. To solve the problem, this paper proposes a method to improve the accuracy of fissure prediction by combining wavelet transform and complex signal analysis. In this method, wavelet transform can effectively suppress the noise, when there is no large loss of signal instantaneous frequency. At last, the engineering example demonstrates the validity of the proposed approach.

Non-Contact Infrared-Depth Camera-Based Method for Respiratory Rhythm Measurement While Driving

This work proposes a new non-contact method based on Infrared and Depth cameras to measure respiratory rhythm in real-life situations. The proposed algorithm consists on using both video feeds to track the movements of the subject in real-time, compute the location of the face and calculate the most suitable ROI to extract the respiratory signal in adult population. 20 subjects were measured while driving in a car simulator with no constraints other than the simulator itself. The algorithm has been validated using a commercial thorax plethysmography system. An opportunistic approach has been used to obtain pieces from the tests for each subject, thus making a more realistic approach to the real-life situations where the signal is likely to contain errors. The breath-to-breath respiratory signal and the instantaneous frequency from both methods has been computed from each piece to characterise the error between the proposed method and the reference system. The results show a high correlation between the measured rhythm from the reference method and the proposed method, with relatively low error results and good sensitivity in cycle detection and low errors for the instantaneous frequency between methods. The error results have also been compared with the ones obtained in previous studies showing a good agreement between the obtained results and the ones presented in the previous studies. No relationship between the length of the pieces and the error has been found either for the respiratory cycle signal or the instantaneous frequency signal. The proposed algorithm can be used to measure respiratory rhythm in unconstrained conditions and with opportunistic measurements, thus making it suitable to perform in real-life situations while driving. Further studies taking into account vibrations or light changing conditions are needed to confirm that the proposed method performs with the same accuracy with these constraints.

Changes in echo-pulse instantaneous frequency when scanning the transducer

A theoretical model has been proposed that makes it possible to explain peculiarities in the frequency characteristics of echo signals at the output of a receiving transducer depending on the geometrical parameters of a reflecting spherical surface when the transducer axis is displaced with respect to the surface’s center of curvature, that is, during scanning. It has been demonstrated that both with and without displacement of the transducer’s geometrical axis with respect to the center of curvature of the reflecting surface, the type of changes in the temporal dependences of the instantaneous frequency of signals at the output of the receiving transducer essentially depends on the geometrical parameters of a wavefront reflected from the surface: the smaller the radius of wavefront curvature at the aperture of the receiving transducer, the stronger the changes of the instantaneous frequency in the echo pulse. It has also been shown that the larger the curvature of this surface, the stronger the changes in the frequency characteristics of the echo pulse as the transducer axis is displaced with respect to the center of curvature of the reflecting spherical surface.

Localization of Reflectors in Plates by Ultrasonic Testing with Lamb Waves

An algorithm is suggested for localizing flaws in thin-walled objects based on the analysis of dispersion characteristics of Lamb waves. It is shown that applying the technique of determining the instantaneous signal frequency by means of wavelet transform makes it possible to reconstruct extensive sections of frequency dependences of the group delay time for different modes of Lamb waves. An extra merit of the proposed method is its high noise immunity. It has been established that an optimum choice of the frequency range is required to minimize the experimental error, namely, in order to minimize the inaccuracy in determining distance one should choose the dispersion-characteristic section where the group delay time is long as compared with its nominal value while its frequency variation is maximum.

Sinusoidal Frequency Modulation Fourier-Bessel Series for Multicomponent SFM Signal Estimation and Separation

Multicomponent sinusoidal frequency modulated (SFM) signals are widely used in radar, acoustics, and biomedicine. The instantaneous frequency (IF) characterizes important physical parameters of the real applications. In this paper, a sinusoidal frequency modulation Fourier-Bessel (SFMFB) series is defined for IF estimation. It provides the signal decomposition on the Bessel function basis with a finer resolution, which proposes an extension of the performance and the applicability of the classic Fourier-Bessel transform (FBT). Based on the property analysis of the SFMFB series, an algorithm of IF estimation and signal separation is introduced. Unlike the existing estimation methods which apply sliding windows to make an instantaneous approximation, the proposed method uses the global data, which provides a longer period gain, therefore achieving a better estimation performance. Moreover, considering that most estimation methods are invalid in multicomponent separation, the individual signals are well separated by the proposed algorithm, which facilitates the further monocomponent analysis. A performance comparison between the proposed method, the FBT, and another recently proposed sinusoidal frequency modulation Fourier transform (SFMFT) is also provided. Simulation results indicate that the proposed method outperforms the existing methods in estimation precision and computation load, and it is free of interference which exists in SFMFT.

Excitation of a circular-aperture transducer with an echo pulse reflected from a spherical surface

A theoretical model is suggested that allows one to explain peculiarities of the frequency response of echo signals at the output of a receiving transducer versus geometrical parameters of reflecting surfaces. It is shown that the way the instantaneous frequency of signals at the output of the receiving transducer changes depends on the curvature radius of reflected wavefront at the receivingtransducer aperture. It has been established that the frequency modulation of the pulsed echo signal is due to nonuniformity of the distribution of the phase of acoustic signal at the receiving-transducer aperture; this can be characterized by the radii of Fresnel zones that correspond to the reflected wavefront in relationship to the aperture radius of the circular transducer. Data on the frequency modulation of pulsed echo signals expressed in terms of dimensionless parameters (normalized frequency deviations) that were obtained experimentally and calculated by the suggested theoretical model demonstrate fair qualitative and quantitative agreement.

Instantaneous magnitudes and instantaneous frequencies of signals with their positivity constraints via non‐smooth non‐convex functional constrained optimisation

This study proposes an iterative method to approximate an N-dimensional optimisation problem with a weighted Lp norm and L2 norm objective function by a sequence of N independent one-dimensional optimisation problems. This iterative method is inspired by the existing weighted L1 norm and L2 norm separable surrogate functional (SSF) iterative shrinkage algorithm. However, as these independent one-dimensional optimisation problems consist of weighted Lp norm and L2 norm objective functions, these optimisation problems are non-convex and they may have more than one locally optimal solutions. In general, it is very difficult to find their globally optimal solutions. To address this difficulty, this study proposes to partition the feasible set of each approximated problem into various regions such that the sign of the convexity of the objective function in each region remains unchanged. In this case, there is no more than one stationary point in each region. By finding the stationary point in each region, the globally optimal solution of each approximated optimisation problem can be found. Besides, this study also shows that the sequence of the globally optimal solutions of the approximated problems converge to the globally optimal solution of the original optimisation problem.

Extraction of formant bandwidths using properties of group delay functions

Formant frequencies represent resonances of vocal tract system during the production of speech signals. Bandwidths associated with the formant frequencies are important parameters in analysis and synthesis of speech signals. In this paper, a method is proposed to extract the bandwidths associated with formant frequencies, by analysing short segments (2–3ms) of speech signal. The method is based on two important properties of group delay function (GDF): (a) The GDF exhibits prominent peaks at resonant frequencies and (b) the influence of one resonant frequency on other resonances is negligible in GDF. The accuracy of the method is demonstrated for synthetic signals generated using all-pole filters. The method is evaluated by extracting bandwidths of synthetic signals in closed phase and open phase regions within a pitch period. The accuracy of the proposed method is also compared with that of two other methods, one based on linear prediction analysis of speech signals, and another based on filterbank arrays for obtaining amplitude envelopes and instantaneous frequency signals. Results indicate that the method based on the properties of GDF is suitable for accurate extraction of formant bandwidths, even from short segments of speech signal within a pitch period.

Based on the Singular Value Decomposition Fast Wavelet Ridge Intra Pulse Modulation Recognition

As a good time and frequency domain localization features, the method of wavelet ridge became one of effective ways to identify the pulse modulation. Aiming at the problem of the low intra pulse recognition rate of the wavelet ridge method in the situation of low signal-to-noise ratio, this paper presented a method of fast wavelet ridge intra pulse modulation based on singular value decomposition. The basic idea of this method:The first signal for fast Morlet wavelet transform; determined the singular value decomcomposition filtering threshold; According to the iterative method to extract the wavelet ridge was to calculate the instantaneous signal teristics; then to identify signal according to the different characteristics of signal instantaneous frequency. The simulation results show that: In less than or equal 0dB SNR situation, this method can improve the recognition rate of common pulse modulation.