Narrow Results

The coupled fractional Fourier transform is a much recent ramification of the two-dimensional fractional Fourier transform, wherein the kernel is not a tensor product of one-dimensional copies, but relies on two angles that are coupled to yield a new pair of transform parameters. In this paper, we introduce a novel two-dimensional Wigner distribution, coined as coupled fractional Wigner distribution (CFrWD). The prime advantage of such a ramification of the Wigner distribution lies in the fact that the CFrWD can efficiently tackle the higher-order-phase and chirp signals, which constitute a wider class of signals arising in modern communication systems. To begin with, we study some fundamental properties of the proposed CFrWD, including marginal, shifting, conjugate-symmetry and anti-derivative properties. In addition, we also formulate the Moyal’s principle, inversion formula and the convolution and correlation theorems associated with CFrWD. Nevertheless, we demonstrate the efficacy of CFrWD for estimating and detecting both the one-component and multi-component linear-frequency-modulated signals.

Modal identification of bridges based on the responses of moving vehicles, termed as the indirect method, has drawn much attention in recent years. This indirect method has been proven to be capable of identifying bridge frequencies and mode shapes in the feasibility research. However, in the presence of additional factors such as vehicle speed and road surface roughness, it is difficult to identify high-order frequencies and high-resolution mode shapes of the bridge. The authors previously proposed a tractor-double-trailers model and the time–domain subtraction method to obtain the relative displacement of two trailers for bridge modal identification. In this study, the authors develop a methodology to improve the identification performance by combining the EMD technique and the time–frequency analysis method. The EMD technique is applied to separate the multi-source response signals of the trailers to obtain the signal component that contains only the bridge vibration. Then, different time–frequency analysis methods such as the short-time Fourier transform (STFT), Wigner–Ville distribution (WVD), and continuous wavelet transform (CWT) are adopted to construct the high-resolution bridge mode shapes. Numerical studies with one-dimensional and three-dimensional bridge models are conducted to verify the proposed method and investigate the effects of different factors. Finally, a laboratory test is implemented on a scaled bridge to verify the performance of the proposed method. The results show that the proposed method is able to separate the vehicle frequency and bridge frequencies, which facilitates the identification of bridge frequencies from the dynamic response of moving vehicles. Meanwhile, the CWT method performs the best in the identification of modal shapes among the three time–frequency analysis methods.

The study presented in this paper is concerned with the analysis of the ultrasound Doppler signal of the carotid arteries in the time-frequency domain using the short time Fourier transform (STFT) and the Wigner–Ville distribution (WVD). This study is carried out in order to investigate the behavior of the spectral broadening index (SBI) derived from spectra obtained using these methods. The variations in the shape of the Doppler power spectra as a function of time are presented in the form of sonograms in order to determine the degree of primitive carotid artery stenosis. The obtained results show a qualitative improvement in the appearance of the sonograms generated using the WVD over the STFT. However, despite this qualitative improvement the WVD suffers from some drawbacks: the presence of the cross terms which are primarily due to its quadratic nature. The application of the Choi–Williams distribution (CWD) in this analysis shows a noticeable reduction of these cross terms, improving therefore the quality of the sonograms. From these generated sonograms, the ultrasound frequency envelopes are extracted. The maximum and the mean frequencies in these envelopes are used to determine the SBI. The magnitude of the CWD-SBI is significantly greater than that of the STFT-SBI. In addition, there is a correlation between the SBIs obtained using the STFT and the CWD and the degree of severity of stenosis measured by 2D Doppler imaging.

In continuation to the recent study “Coupled Fractional Wigner Distribution with Applications to LFM Signals” in [Fractals, World Scientific; 2022], we formulate some important uncertainty inequalities including, the Hausdorff–Young, Lieb’s and Pitts inequalities for the coupled fractional Wigner distribution. In the sequel, we also establish Heisenberg’s, logarithmic, Hardy’s and Beurling’s uncertainty principles. Towards the end, we derive some Sobolev-type inequalities for the coupled fractional Wigner distribution.

The localization of Gravitational Wave (GW) sources, that is crucial in identifying their physical nature via the joint use of GW interferometers and other messengers (electromagnetic, neutrino, etc.), is mainly based on the observed delays between pairs of interferometers. Time-Frequency (TF) representations can be effectively used for GW detection and parameter estimation. In particular, it is possible to estimate the arrival time delay between the GW signals detected by two interferometers by suitably aligning the related TF maps. In this work we compare different TF representatons and alignment techniques, by using numerical simulation based on recent public-domain GW data.

Wigner-Ville distribution has good time-frequency characteristics. Its cross terms are oscillatory at high frequency. To suppress the cross terms, multiwavelets analysis is adopted to decompose and reconstruct signals' Wigner-Ville distribution. Compared with the other time-frequency representation methods, simulation results demonstrate that multiwavelets analysis is very effective to eliminate the cross terms while keep good resolution.