Wigner-Ville Time-frequency Distribution Research Articles

Modeling the acoustic repertoire of Cuvier's beaked whale clicks.

This paper investigates the evolution of spectral properties observed in Cuvier's beaked whale (Ziphius cavirostris) click trains recorded by fixed hydrophones in the Gulf of Mexico. In the context of deep water and high-frequency sounds and observed inter-click intervals, the authors assumed that the main effect responsible for the modification of the spectral content between adjacent clicks in the same click train is the source beam pattern. The spectral structure is studied by using the Wigner-Ville time-frequency distribution and is compared with the conventional Fourier spectrogram. The results show that the observed Cuvier's beaked whale clicks are a superposition of upsweep and downsweep chirps, unlike the currently accepted upsweep only structure of beaked whale clicks in bioacoustics literature. The spectral structure variations simulated by using a flat circular piston model as a beam pattern transmission model are consistent with the evolution of spectral click properties observed in experimental data. A better understanding of the properties of observed echolocation clicks of Cuvier's beaked whales will provide useful information for click annotations and, therefore, will contribute to improving accuracy of detecting, classifying, tracking, and estimating the density of Cuvier's beaked whales.

Characterization of Nonstationary Phase Noise Using the Wigner–Ville Distribution

Oscillators and atomic clocks, as well as lasers and masers, are affected by physical mechanisms causing amplitude fluctuations, phase noise, and frequency instabilities. The physical properties of the elements composing the oscillator as well as external environmental conditions play a role in the coherence of the oscillatory signal produced by the device. Such instabilities demonstrate frequency drifts, modulation, and spectrum broadening and are observed to be nonstationary processes in nature. Most of the tools which are being used to measure and characterize oscillator stability are based on signal processing techniques, assuming time invariance within a temporal window, during which the signal is assumed to be stationary. This letter proposes a new time-frequency approach for the characterization of frequency sources. Our technique is based on the Wigner–Ville time-frequency distribution, which extends the spectral measures to include the temporal nonstationary behavior of the processes affecting the coherence of the oscillator and the accuracy of the clock. We demonstrate the use of the technique in the characterization of nonstationary phase noise in oscillators.

Mechanical behaviour of jute fibre-reinforced polyester composite: Characterization of damage mechanisms using acoustic emission and microstructural observations

The present work deals with the mechanical characterization of a woven jute fabrics reinforced polyester resin composite. Two stacking sequences were considered: [0]8 and [+45/−45]2S. In-situ acoustic emission technique, X-ray computed tomography (X-ray CT) and post-mortem microscopic observations were used to characterise the damage mechanisms and to follow their evolutions during uniaxial tension. The microstructural analysis and X-ray CT revealed the following damage modes for the two lay-ups: fibre-matrix debondings which constitute the dominant mechanism, matrix crackings and fibre breakages and pull-outs. The acoustic emission data were processed using an unsupervised pattern recognition technique which combines principal components analysis and k-means optimized by a genetic algorithm. Both temporal and frequential features of acoustic emission signals were considered. The Laplacian score and dendrogram were used to determine the relevant and uncorrelated descriptors for clustering. Three clusters of events were obtained and the waveforms of each one were examined. Furthermore, the frequency contents of signals of each cluster were accurately investigated using power density spectrum and smoothed pseudo Wigner-Ville time-frequency distribution and the discrepancies between clusters are highlighted. Cluster 1 (Cl 1) characterized by signals of low frequency and intermediate amplitude, cluster 2 (Cl 2) characterized by signals of higher frequency and an amplitude similar to that of Cl 1 and cluster 3 (Cl 3) characterized by signals of higher amplitude. A correlation between the clusters and the damage mechanisms was established by means of interrupted tensile tests: Cl 1 is assigned to the matrix cracking, Cl 2 to the fibre-matrix debonding and Cl 3 to the fibre breakage and pull-out. The kinetic of evolution of each damage mode was monitored for the two stacking sequences.

Detection of Nonlinear Frequency Modulated Signal Based on Fractional Fourier Transform

Based on fractional Fourier transformation (FRFT), the feature of the signals which vary smoothly from time domain to frequency domain is given. The FRFT method is applied to the estimation and detection of nonlinear frequency modulated signals to which piecewise linearly approach. Wigner-Ville time frequency distribution of the signals is used after approaching and the masking results of the original signal accumulate energy as detecting statistic. A signal detector based on energy accumulation from time frequency domain in the angle of analysis of both time and frequency is proposed. Finally, a comparison with traditional non-coherent energy accumulation methods is made, which shows the proposed method has superior performance.

Modulation effect and inverse synthetic aperture radar imaging of rotationally symmetric ballistic targets with precession

The modulation effect of rotationally symmetric ballistic targets (BTs) with precession is concerned. To further approach the actual case, the modulation in amplitude and Doppler is considered in the radar backscattering and revealed by short-time Fourier transform (STFT). The results indicate that the micro-Doppler (m-D) effect induced by periodical precession is not represented as a sinusoidal modulation on the edge of BTs as usual, and the amplitude modulation may lead to discontinuity of time-frequency curve. The phenomenon in STFT is confirmed by both simulated and real data from a BT model with precession measured in the microwave anechoic chamber. Based upon the measured data, inverse synthetic aperture radar imaging results have been obtained by smoothed pseudo Wigner-Ville time-frequency distribution.

Automatic recognition of radar signals based on time-frequency image shape character

Radar signal recognition is one of the key technologies of modern electronic surveillance systems. Timefrequency image provides a new way for recognizing the radar signal. In this paper, a series of image processing methods containing image enhancement, image threshold binarization and mathematical morphology is utilized to extract the shape character of smoothed pseudo wigner-ville time-frequency distribution of radar signal. And then the identification of radar signal is realized by the character. Simulation results of eight kinds of typical radar signal demonstrate that when signal noise ratio (SNR) is greater than -3 dB, the Legendre moments shape character of the time-frequency image is very stable. Moreover, the recognition rate by the character is more than 90 per cent except for the FRANK code signal when SNR > -3 dB. Test also show that the proposed method can effectively recognize radar signal with less character dimension through compared with exitsing algorithms.

The time-singularity multifractal spectrum distribution

Although the multifractal singularity spectrum revealed the distribution of singularity exponent, it failed to consider the temporal information, therefore it is hard to describe the dynamic evolving process of non-stationary and nonlinear systems. In this paper, we aim for a multifractal analysis and propose a time-singularity multifractal spectrum distribution (TS-MFSD), which will hopefully reveal the spatial dynamic character of fractal systems. Similar to the Wigner–Ville time-frequency distribution, the time-delayed conjugation of fractal signals is selected as the windows function. Furthermore, the time-varying Holder exponent and the time-varying wavelet singularity exponent are deduced based on the instantaneous self-correlation fractal signal. The time-singularity exponent distribution i.e. TS-MFSD is proposed, which involves time-varying Hausdorff singularity spectrum distribution, time-varying large deviation multifractal spectrum and time-varying Legendre spectrum distribution, which exhibit the singularity exponent distribution of fractal signal at arbitrary time. Finally, we studied the algorithm of the TS-MFSD based on the wavelet transform module maxima method, analyzed and discussed the characteristic of TS-MFSD based on Devil Staircase signal, stochastic fractional motion and real sea clutter.

Numerical comparison of techniques for estimating Doppler velocity time series from coherent sea surface scattering measurements

A number of techniques for estimating the Doppler velocity time series from coherent sea surface scattering measurements are compared by observing their behaviour with computer simulated signals. These techniques include the finite difference instantaneous frequency estimator, the covariance moment estimation technique, tracking the peak of the short-time Fourier transform and tracking the peak of the cross Wigner–Ville time–frequency distribution. This comparison is achieved by examining the ability of each technique to track the instantaneous frequency of a unity amplitude, sinusoidal frequency law, complex exponential signal embedded in white Gaussian noise. The response of the estimators to various signal conditions, including low signal-to-noise ratios, high Doppler frequency excursions and high modulation frequencies, is investigated. Using the results, consideration is given to the suitability of each technique for estimating the magnitude, phase and power spectrum of the Doppler velocity time series. These are fundamental quantities required for studying sea surface scattering mechanisms and remotely sensing oceanographic properties.

Time-frequency signal analysis of hydrophone data

The acoustic spectrum of a transiting aircraft, when received by a hydrophone located beneath the sea surface, changes with time due to the acoustical Doppler effect. The traditional method for analysing signals whose frequency content changes with time is the short-time Fourier transform that selects only a short segment of the signal (or window of data) for spectral analysis at any one time. The short-time Fourier transform requires the frequency content of the signal to be stationary during the analysis window, otherwise the frequency information will be smeared by the transformation. Recently, joint time-frequency distributions, which highlight the temporal localisation of a signal's spectral components, have been used to analyse nonstationary signals whose spectra are time dependent. In this paper, the short-time Fourier transform and the Wigner-Ville time-frequency distribution are applied to time-series data from a hydrophone so that the instantaneous frequency of the propeller blade rate of a turbo-prop aircraft can be estimated at short time intervals during the aircraft's transit over the hydrophone. The variation with time of the estimates of the Doppler-shifted blade rate is then compared with the corresponding temporal variation predicted using a model that assumes the sound propagates from the airborne acoustic source to the subsurface receiver through two distinct isospeed media (air and water) separated by a plane boundary (the air-sea interface). The results for five transits are presented in which the altitude of the aircraft ranged from 350 to 6050 ft with the speed of the aircraft varying from 232 to 245 kn.

Pseudo Wigner–Ville Time-Frequency Distribution and Its Application to Machinery Condition Monitoring

Machinery operating in a nonstationary mode generates a signature that at each instant of time has a distinct frequency. A Time-frequency domain representation is needed to characterize such a signature. Pseudo Wigner–Ville distribution is ideally suited for portraying a nonstationary signal in the time-frequency domain and is carried out by adapting the fast Fourier transform algorithm. The important parameters affecting the pseudo Wigner–Ville distribution are discussed and sensitivity analyses are also performed. Practical examples of an actual transient signal are used to illustrate its dynamic features jointly in time and frequency.

Pseudo Wigner–Ville Time-Frequency Distribution and Its Application to Machinery Condition Monitoring

Machinery operating in a nonstationary mode generates a signature that at each instant of time has a distinct frequency. A Time-frequency domain representation is needed to characterize such a signature. Pseudo Wigner–Ville distribution is ideally suited for portraying a nonstationary signal in the time-frequency domain and is carried out by adapting the fast Fourier transform algorithm. The important parameters affecting the pseudo Wigner–Ville distribution are discussed and sensitivity analyses are also performed. Practical examples of an actual transient signal are used to illustrate its dynamic features jointly in time and frequency.

Computation of Wigner-Ville distribution for complex data

An extension of the computation of the Wigner-Ville time frequency distribution for complex sonar data is discussed. The method of computation provides insight to the cross terms of the distribution that can be used in pattern recognition.