Scaled Wigner distribution using fractional instantaneous autocorrelation

Zhang, Zhichao; Xia, Jiang; Qiang, Sheng-Zhou; Sun, Ao; Liang, Zi-Yue; Shi, Xi-Ya; Wu, An-Yang

doi:10.1016/j.ijleo.2021.166691

Cited by 19 publications

(5 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Similar to the LCT parameter embedding method, Zhang proposed the scaled WD (SWD), 10 k-WD, 11 and kernel functionτ -WD (KF-τ -WD). 12 The KF-τ -WD is defined as…”

Section: W DLmentioning

confidence: 99%

The short-time Wigner-Ville distribution associated with linear canonical transform

Chen,

2024

Fifteenth International Conference on Signal Processing Systems (ICSPS 2023)

View full text Add to dashboard Cite

This article proposes the unified short-time Wigner-Ville distribution (USWD) and explores its various properties, which is a generalized integral transform suitable for time-varying signals with varying features. Recognizing the complexity involved in this transformation and aiming for practical applications, we focused our research on a specific case, denoted as SWDL. In this study, we derived the Heisenberg's uncertainty principle for SWDL and presented its discrete form. Furthermore, we investigated the potential applications of SWDL in the analysis of stepped-frequency linear frequency modulation (SF-LFM) signals.

show abstract

“…Similar to the LCT parameter embedding method, Zhang proposed the scaled WD (SWD), 10 k-WD, 11 and kernel functionτ -WD (KF-τ -WD). 12 The KF-τ -WD is defined as…”

Section: W DLmentioning

confidence: 99%

The short-time Wigner-Ville distribution associated with linear canonical transform

Chen,

2024

Fifteenth International Conference on Signal Processing Systems (ICSPS 2023)

View full text Add to dashboard Cite

show abstract

“…Zhang et al [23] in 2021 introduced the novel Scaled Wigner distribution (SWD) by replacing the classical instantaneous auto-correlation f t + ρ 2 f * t − ρ 2 found in (1) with the fractional instantaneous autocorrelation f t + k ρ 2 f * t − k ρ 2 in the definition of classical wigner distribution. For a finite energy signal the SWD is defined as…”

Section: Scaled Wigner Distributionmentioning

confidence: 99%

“…In [23], authors presented a novel way for the improvement of the of the cross-term reduction timefrequency resolution and angle resolution when dealing with the multi-component LFM signals by introducing the scaled Wigner distribution (SWD) which is parameterized by a constant k ∈ Q. Later authors in [24] extended the WD associated with offset linear canonical transform to the novel one.…”

Section: Introductionmentioning

confidence: 99%

Quadratic-phase scaled Wigner distribution: convolution and correlation

Bhat

Dar

2023

SIViP

View full text Add to dashboard Cite

In this paper, we propose the novel integral transform coined as the Quadratic-phase Scaled Wigner Distribution (QSWD) by extending the Wigner distribution associated with quadratic-phase Fourier transform(QWD) to the novel one inspired by the definition of fractional bispectrum. A natural magnification effect characterized by the extra degrees of freedom of the quadratic-phase Fourier transform (QPFT) and by a factor k on the frequency axis enables the QSWD to have flexibility to be used in cross-term reduction. By using the machinery of QSWD and operator theory, we first establish the general properties of the proposed transform, including the conjugate-symmetry, non-linearity, shifting, scaling and marginal. Then, we study the main properties of the proposed transform, including the inverse, Moyal's, convolution and correlation. Finally, the applications of the newly defined QSWD for the detection of single-component and bi-component linearfrequency-modulated (LFM) signal are also performed to show the advantage of the theory.

show abstract

“…which is a function of parameters a 1 , b 1 , b. With an equality constraint (11), the optimization model ( 8) can be converted to the following conditional extremum problem:…”

Section: Solution Of the Optimization Model Substituting (mentioning

confidence: 99%

“…Wigner distribution (WD) [9][10][11] is the generating distribution for Cohen's class time-frequency representations [12]. It can be suitable in the process of linear frequency-modulated (LFM) signals, which are frequently encountered in many engineering applications such as satellite communications [13] and synthetic aperture radar (SAR) [14].…”

Section: Introductionmentioning

confidence: 99%

A Computationally Efficient Optimal Wigner Distribution in LCT Domains for Detecting Noisy LFM Signals

Shi

Sun

et al. 2022

Mathematical Problems in Engineering

View full text Add to dashboard Cite

Recently, Wigner distribution (WD) associated with linear canonical transforms (LCTs) is quickly becoming a promising technique for detecting linear frequency-modulated (LFM) signals corrupted with noises by establishing output signal-to-noise ratio (SNR) inequality model or optimization model. Particularly, the closed-form instantaneous cross-correlation function type of WD (CICFWD), a unified linear canonical Wigner distribution, has shown to be competitive in detecting noisy LFM signals under an extremely low SNR. However, the CICFWD has up to nine LCT free parameters so that it requires a heavy computational load. To improve the efficiency of real-time processing, this paper focuses on the instantaneous cross-correlation function type of WD (ICFWD), which has only six LCT free parameters but is not a special case of the CICFWD. The main advantage of ICFWD is that it could be expected to reduce the computational complexity while maintaining detection performance. This paper first proposes an optimization model to the ICFWD’s output SNR with respect to deterministic signals embedded in additive zero-mean noises. It then deduces the model’s solution to a single component LFM signal added with white noise, leading to the optimal selection strategy on LCT free parameters. Simulation results demonstrate that the ICFWD improves almost a doubling of computing speed in comparison with the CICFWD while sharing the same level of detection performance. To be specific, the computing time of ICFWD in sampling frequencies 5 Hz, 10 Hz, 15 Hz, and 20 Hz is about 0.048 s, 0.111 s, 0.226 s, and 0.392 s, respectively, while 0.075 s, 0.233 s, 0.478 s, and 0.821 s for the computing time of CICFWD; the ICFWD and CICFWD have nearly the same output SNR higher than that of the WD.

show abstract

Scaled Wigner distribution using fractional instantaneous autocorrelation

Cited by 19 publications

References 29 publications

The short-time Wigner-Ville distribution associated with linear canonical transform

The short-time Wigner-Ville distribution associated with linear canonical transform

Quadratic-phase scaled Wigner distribution: convolution and correlation

A Computationally Efficient Optimal Wigner Distribution in LCT Domains for Detecting Noisy LFM Signals

Contact Info

Product

Resources

About