Joint Time-frequency Distribution Research Articles

Frame Selection Method for ISAR Imaging of 3-D Rotating Target Based on Time–Frequency Analysis and Radon Transform

When a target has 3-D rotation accompanying roll–pitch–yaw movement, it yields an additional phase component, which cannot be compensated for by any of the existing inverse synthetic aperture radar (ISAR) imaging methods. Under this condition, the resulting ISAR image will be severely distorted. Accordingly, selecting a proper imaging frame, where the target has only 2-D rotation, becomes the only solution, especially for range-Doppler (RD) algorithm. To do this, the conventional approach is to directly use the phase of the received signal, and however, this approach is vulnerable to noise and the cross-term interference of multiple scattering centers (SCs) in the range bin. To address these issues, we propose a new frame selection method using the range-instantaneous Doppler (RID) technique and Radon transform to detect the presence of 3-D rotation of the target within imaging frame. The proposed method comprises three steps: 1) obtain joint time–frequency distribution (JTFD) via the smoothed pseudo Wigner–Ville distribution (SPWVD); 2) estimate the orientation angle of the Radon image of the JTFD spectrum; and 3) select the suitable imaging frame using the estimated angle. Furthermore, to demonstrate the effectiveness of the proposed method, experimental results based on simulated and real measured data are provided.

Fusion Recognition of Space Targets With Micromotion

During the observation of micromotion targets in space, inverse synthetic aperture radar usually obtains the narrowband and wideband echoes simultaneously. In order to exploit their rich information in target electromagnetic scattering, shape, structure, and motion, this article proposes a recognition method of space micromotion targets based on decision fusion. The proposed method extracts physical features from the radar cross section and the joint time–frequency distribution from narrowband echoes, while extracts the data features from high-resolution range profiles and range-instantaneous-Doppler image by convolution neural network. Finally, particle swarm optimization is adopted to decision-level fusion so as to realize high-precision recognition. The recognition results of electromagnetic simulated data under various conditions have demonstrated the effectiveness and robustness of the proposed method.

Joint time-frequency distribution of rolling bearings with multiple faults on outer raceway based on asymptotic model

At present, the majority of the research on dynamic model of rolling bearings with multiple faults is conducted on the assumption that the displacement deviation between raceway and rolling element changes instantaneously. However, the deviation should vary gradually. As a result, an asymptotic model of rolling bearings with multiple faults on outer raceway is established, considering the interaction of multiple faults. Synchroextracting transformation method is employed to describe the joint time-frequency distribution of the faulty rolling bearings. The discrepancies between the asymptotic model and the traditional model are contrasted and analyzed via simulation modeling. Simultaneously, the effects of fault number and fault interval on the joint time-frequency distribution are investigated. Finally, experiments are performed to verify the rationality of the established model. Simulation results demonstrate that the joint time-frequency distribution derived by the asymptotic model includes not only the fault characteristic frequency but also the rotating frequency. The central frequency increases in a multiple of the fault characteristic frequency as the fault number increase, as does its energy amplitude. Only when multiple faults are uniformly distributed among the interval range of rolling elements, the energy amplitude of the central frequency can reach the maximum. The energy amplitude of the rotating frequency scarcely changes as the fault interval and fault number vary.

Adaptive Fourier Decomposition for Multi-Channel Signal Analysis

Evolved from the conventional Fourier decomposition based on a pre-defined basis, Adaptive Fourier decomposition (AFD) uses adaptive basis to achieve the fast energy convergence. This paper extends the AFD to the multi-channel case, which finds common adaptive basis across all channels. The proposed multi-channel AFD (MAFD) scheme includes the multi-channel core AFD for general signals and the multi-channel unwinding AFD for specific signals that have common inner functions. Owing to the merits of the original AFD, the MAFD can provide sparse joint time-frequency distribution by computing the transient time frequency distribution (TTFD) across channels. Simulations on synthetic and real-world signals demonstrate that the proposed scheme can find and apply the common adaptive basis with desired properties maintained by the AFD, showing high potentials in real-world applications.

Joint Time-Frequency Domain-Based CAD Disease Sensing System Using ECG Signals

In this paper, the time-frequency matrix-based modified features are proposed. The proposed features are applied to detect the presence of coronary artery disease (CAD) using electrocardiogram (ECG) signals. These features are utilized to detect the presence of CAD using ECG signals. In the proposed work, ECG beats are subjected to the improved eigenvalue decomposition of Hankel matrix and Hilbert transform (IEVDHM-HT)-based method. This approach provides the time-frequency representation (TFR) of the ECG beats of both classes. Further, the time-frequency-based parameters are computed from the TFR matrix. These parameters are mixed averages time-frequency ( ${\mathrm {Avg}}_{tw}$ ), frequency average ( ${\mathrm {Avg}}_{w}$ ), and time average ( ${\mathrm {Avg}}_{t}$ ) of joint time-frequency distribution functions. In this paper, these features are extracted from the complete TFR and also for the local regions of the same TFR. These features are fed to the random tree and J48 classifiers. The proposed method has obtained an accuracy of 99.93% in the separation of CAD and normal ECG beats. The ${\mathrm {Avg}}_{w}$ features are found to be more effective as compared to the other features.

Time-frequency characteristics of acoustic emission signal for monitoring of welding structural state using Stockwell transform.

The stockwell transform (S transform) is used to conduct analysis and processing of the Acoustic Emission (AE) signal in the welding process. The multi dimension instantaneous frequency information of AE signal in the joint time frequency distribution is obtained to analyze and recognize the welding structure state. The changing paces of window functions under different parameters are analyzed, and the parameters of S transform are determined to realize the optimal adaptive multi resolution and time frequency clustering. The S transform is performed to analyze the time frequency characteristics of the collected AE signal in weldment tensile testing experiment. According to the analysis results of the weldment tensile AE signal, the time frequency distribution and the first-order moment of the AE signal are observed to identify and detect the elastic, plastic deformation, and crack in the welding restrictable experiment. The results indicate that the feature information of the AE signal obtained by S transform can present the welding structural state, which provides an effective method for online detection of welding crack.

Identification of Radar Signals Based on Time-Frequency Agility using Short-Time Fourier Transform

With modern advances in radar technologies and increased complexity in aerial battle, there is need for knowledge acquisition on the abilities and operating characteristics of intercepted hostile systems. The required knowledge obtained through advanced signal processing is necessary for either real time-warning or in order to determine Electronic Order of Battle (EOB) of these systems. An algorithm was therefore developed in this paper based on a joint Time-Frequency Distribution (TFD) in order to identify the time-frequency agility of radar signals based on its changing pulse characteristics. The joint TFD used in this paper was the square magnitude of the Short-Time Fourier Transform (STFT), where power and frequency obtained at instants of time from its Time-Frequency Representation (TFR) was used to estimate the time and frequency parameters of the radar signals respectively. Identification was thereafter done through classification of the signals using a rule-based classifier formed from the estimated time and frequency parameters. The signals considered in this paper were the simple pulsed, pulse repetition interval modulated, frequency hopping and the agile pulsed radar signals, which represent cases of various forms of agility associated with modern radar technologies. Classification accuracy was verified using the Monte Carlo simulation performed at various ranges of Signal-to-Noise Ratios (SNRs) in the presence of noise modelled by the Additive White Gaussian Noise (AWGN). Results obtained showed identification accuracy of 99% irrespective of the signal at a minimum SNR of 0dB where signal and noise power were the same. The obtained minimum SNR at this classification accuracy showed that the developed algorithm can be deployed practically in the electronic warfare field for accurate agility classification of airborne radar signals.

Characteristic measurement for femtosecond laser pulses using a GaAs PIN photodiode as a two-photon photovoltaic receiver

Photodiodes that exhibit a two-photon absorption effect within the spectral communication band region can be useful for building an ultra-compact autocorrelator for the characteristic inspection of optical pulses. In this work, we develop an autocorrelator for measuring the temporal profile of pulses at 1550 nm from an erbium-doped fiber laser based on the two-photon photovoltaic (TPP) effect in a GaAs PIN photodiode. The temporal envelope of the autocorrelation function contains two symmetrical temporal side lobes due to the third order dispersion of the laser pulses. Moreover, the joint time-frequency distribution of the dispersive pulses and the dissimilar two-photon response spectrum of GaAs and Si result in different delays for the appearance of the temporal side lobes. Compared with Si, GaAs displays a greater sensitivity for pulse shape reconstruction at 1550 nm, benefiting from the higher signal-to-noise ratio of the side lobes and the more centralized waveform of the autocorrelation trace. We also measure the pulse width using the GaAs PIN photodiode, and the resolution of the measured full width at half maximum of the TPP autocorrelation trace is 0.89 fs, which is consistent with a conventional second-harmonic generation crystal autocorrelator. The GaAs PIN photodiode is shown to be highly suitable for real-time second-order autocorrelation measurements of femtosecond optical pulses. It is used both for the generation and detection of the autocorrelation signal, allowing the construction of a compact and inexpensive intensity autocorrelator.

The acoustical features analysis of Indo-Pacific humpback dolphins’ whistle and modeling research

Depending on species-specific characteristics of echolocation and recognition,dolphin could travel in groups without collision, and they could also prey and defend mutually. As a multi-harmonics, frequency-modulated signal, the variety of whistles revealed the rich group identification and location information of free-ranging Indo-Pacific humpback dolphins (Sousa chinensis). This paper introduces the features of whistle on the basis of Joint time-frequency distribution, dealing with recording data collected in the area of Guangxi and Zhanjiang seacoast, in China. Then the ability of individual identification is discussed from the correlation of whistles, we will get the knowledge of dolphins how to cognize the communication information in the complex environment. The transmission loss function will be depicted using the BELLHOP at last. By extracting the acoustical features, the modeling of whistle signal is implemented based on the Sinusoids Model (Buck, 2000). Specifically, the validity of mathematical model is proved according to comparison with the recording data.

Low frequency acoustic signals associated with rock falls, thunderstorms, and wind turbulences in field environment

This paper characterized the observed low frequency acoustic signals generated by rock falls, thunderstorm, and wind turbulence in large rocky landslide. A digital infrasonic recording system was deployed on site to capture real-time low frequency acoustic signals associated with rock falls. An advanced non-stationary signal analysis method, i.e. Empirical Mode Decomposition (EMD), was applied to get insight to the characteristics of the low frequency acoustic signals induced by the hazards. Joint time–frequency distribution spectra technique was used to detect distinctive features of the events. The study shows that the low frequency acoustic signals can be excited by rock falls, thunderstorm and wind turbulence in the field environment, but the signal varies in both time domain and frequency domain with different patterns depending on the physical processes. The results demonstrated that the EMD-based signal processing technique is capable of extracting distinctive features to differentiate acoustic signals in real environment.

Micro-Doppler Features Analysis and Extraction of Vibrating Target in FMCW SAR Based on Slow Time Envelope Signatures

The combination of frequency-modulated continuous wave (FMCW) technology and synthetic aperture radar (SAR) leads to lightweight, cost-effective, and low-power dissipation imaging sensors of high resolution. For extracting the features of vibrating targets on ground in FMCW SAR, the displaced phase center antenna technique is introduced into the FMCW SAR system to suppress the ground clutter, and then, the signal characteristic is analyzed. It indicates that the energy of the joint time–frequency distribution is presented as an uneven distribution that is induced by a slow time envelope (STE). In this letter, a novel extracting method of vibrating features based on STE signatures is proposed. With this method, the vibrating frequency and amplitude can be calculated from some extracted positions in the STE. Some simulations are given for validating the feasibility and effectiveness of the method.

The instantaneous frequency rate spectrogram

An accelerogram of the instantaneous phase of signal components referred to as an instantaneous frequency rate spectrogram (IFRS) is presented as a joint time-frequency distribution. The distribution is directly obtained by processing the short-time Fourier transform (STFT) locally. A novel approach to amplitude demodulation based upon the reassignment method is introduced as a useful by-product. Additionally, an estimator of energy density versus the instantaneous frequency rate (IFR) is proposed and referred to as the IFR profile. The energy density is estimated based upon both the classical energy spectrogram and the IFRS smoothened by the median filter. Moreover, the impact of an analyzing window width, additive white Gaussian noise and observation time is tested. Finally, the introduced method is used for the analysis of the acoustic emission of an automotive engine. The recording of the engine of a Lamborghini Gallardo is analyzed as an example.

Radar Signature Analysis Using a Joint Time-Frequency Distribution Based on Compressed Sensing

A previously proposed time-frequency distribution based on compressed sensing (CS) is applied to radar backscattered signals for signature analysis. The CS joint time-frequency (CSJTF) distribution is based on the Wigner-Ville distribution, but employs CS to remove undesirable cross terms. To adapt the algorithm for radar signals, we develop a search procedure to find the optimal region in the ambiguity plane for achieving the best CSJTF distribution. The algorithm is then applied to backscattering data from several structures of interest, including a pipe, rotating turbine blades, and a moving human. The performance of the CSJTF is compared to that of the short-time Fourier transform and the reassigned spectrogram, and its limitations in time-frequency localization and resolution are discussed.

Non-Stationary Signal Segmentation and Separation from Joint Time-Frequency Plane

Multi-components sinusoidal engineering signals who are non-stationary signals were considered in this study since their separation and segmentations are of great interests in many engineering fields. In most cases, the segmentation of non-stationary or multi-component signals is conducted in time domain. In this paper, we explore the advantages of applying joint time-frequency (TF) distribution of the multi-component signals to identify their segments. The Spectrogram that is known as Short-Time Fourier Transform (STFT) will be used for obtaining the time-frequency kernel. Time marginal of the computed kernel is optimally used for the signal segmentation. In order to obtain the desirable segmentation, it requires first to improve time marginal of the kernel by using two-dimensional Wiener mask filter applied to the TF kernel to mitigate and suppress non-stationary noise or interference. Additionally, a proper choice of the sliding window and its overlaying has enhanced our scheme to capture the discontinuities corresponding to the boundaries of the candidate segments.

Application of joint time-frequency distribution for estimation of time-varying modal damping ratio

The logarithmic decrement method has been long used to estimate damping ratios in systems with only one modal component such as linear single degree of freedom (SDOF) mechanical systems. This paper presents an application of a methodology that uses joint time-frequency distribution (JTFD) as input, instead of the raw signal, to systems with several vibration modes. A most important feature of the present approach is that it can be applied to a system with time-varying damping ratio. Initially the precision and robustness of the method is determined using a synthetic model with multiple harmonic components, one of them displaying a time-varying damping ratio, subsequently the results obtained from experiments with a reduced model are presented. A comparison is made between the results obtained with this methodology and those using the classical technique of Least Squares Complex Exponential Method (LSCE) in order to highlight the advantages of the former, such as, good precision, robustness and excellent performance in extreme cases, e.g., when very low frequency components and time varying damping ratio are present.

Comparison of the muscle activation pattern for the vastus lateralis before and after an 8-week resistance training program

The purpose of this investigation was to use wavelet analyses and pattern classification techniques to examine potential changes in the joint time–frequency distribution of surface electromyographic (EMG) signals due to an 8-week resistance training program. Thirteen untrained men (mean ± S.D. age = 22.2 ± 4.0 yrs) performed eight separate submaximal isometric muscle actions of the dominant leg extensors in 10% increments from 10 to 80% of the maximum voluntary contraction (MVC). During each muscle action, a monopolar surface EMG signal was detected from the vastus lateralis. All signals were then analyzed with a wavelet analysis designed specifically for EMG signals, and the resulting intensity patterns were classified using pattern classification techniques into their respective pre-training versus post-training categories. The results showed accuracy rates (% of correctly classified patterns) that ranged from approximately 62 to 92%, but these rates did not change consistently with increases in force. In addition, for five of the eight submaximal force levels, the classification was considered to be significantly different from random. Thus, although the differences between the pre- and post-training EMG intensity patterns were not always consistent, our findings did suggest that there is the potential for wavelet analyses and pattern classification techniques to be used to examine neuromuscular adaptations during resistance training.

Experimental implementation of ultrashort laser pulses in the von Neumann picture

The characterization and interpretation of ultrashort laser pulses is most intuitive in the joint time–frequency domain, where structures like multiple pulses become immediately apparent. For practical reasons, ultrafast femtosecond laser pulse shaping, however, is commonly carried out in the frequency domain. Here we implement pulse shaping of optical fields defined in the von Neumann representation, which is a joint time–frequency distribution with complex-valued Gaussian basis functions. We discuss the feasibility as well as the principal limitations of this technique, show illustrative examples, and propose possible applications in coherent control.

Instantaneous frequency estimation based on directionally smoothed pseudo-Wigner-Ville distribution bank

In the cases of low signal-to-noise ratios (SNRs), estimating the instantaneous frequency (IF) curves of signals of interest is an interesting topic with many practical applications. Most of the existing methods are based on quadratic time-frequency (TF) distributions, which, however, yield a number of outliers in the cases of low SNRs. In this paper, we construct a new family of TF distributions, namely, the joint distributions, to estimate the IF curves in order to reduce outliers in the cases of low SNRs. The construction of the joint distributions is based on the definition of the directionally smoothed pseudo-Wigner-Ville distributions (DSPWVD) and pointwise adaptive weight averaging of a bank of DSPWVDs with different directions. The segments of the IF curve whose directions are close to that of the DSPWVD can be highlighted by each DSPWVD and the entire IF curve will be enhanced by the joint TF distribution. Simulation results show that the IF estimator based on the joint distributions outperforms that using quadratic TF distributions and the adaptive optimal adaptive kernel distribution in the cases of low SNRs.

Instantaneous frequency estimation based on directionally smoothed pseudo-Wigner-Ville distribution bank

In the cases of low signal-to-noise ratios (SNRs), estimating the instantaneous frequency (IF) curves of signals of interest is an interesting topic with many practical applications. Most of the existing methods are based on quadratic time-frequency (TF) distributions, which, however, yield a number of outliers in the cases of low SNRs. In this paper, we construct a new family of TF distributions, namely, the joint distributions, to estimate the IF curves in order to reduce outliers in the cases of low SNRs. The construction of the joint distributions is based on the definition of the directionally smoothed pseudo-Wigner-Ville distributions (DSPWVD) and pointwise adaptive weight averaging of a bank of DSPWVDs with different directions. The segments of the IF curve whose directions are close to that of the DSPWVD can be highlighted by each DSPWVD and the entire IF curve will be enhanced by the joint TF distribution. Simulation results show that the IF estimator based on the joint distributions outperforms that using quadratic TF distributions and the adaptive optimal adaptive kernel distribution in the cases of low SNRs.

Application of the Reassigned Joint Time-Frequency Transform to Wideband Scattering From Waveguide Cavities

The wideband return from a circular waveguide cavity is investigated in the joint time-frequency space using the reassigned joint time-frequency (RJTF) transform. Equations for generating the reassigned joint time-frequency distribution from a frequency domain signal are presented. The performance of the reassigned transform is compared with that of the short-time Fourier transform (STFT) based on data obtained from both simulation and measurement.