Scaled Wigner distribution in the offset linear canonical domain

Bhat, M. Younus; Dar, Aamir H.

doi:10.1016/j.ijleo.2022.169286

Cited by 16 publications

(5 citation statements)

References 22 publications

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“…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. Recently, Dar and Bhat [25] introduced the scaled version of ambiguity function and scaled Wigner distribution in the linear canonical domain.…”

Section: Introductionmentioning

confidence: 99%

Quadratic-phase scaled Wigner distribution: convolution and correlation

Bhat

Dar

2023

SIViP

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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.

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Section: Introductionmentioning

confidence: 99%

Quadratic-phase scaled Wigner distribution: convolution and correlation

Bhat

Dar

2023

SIViP

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“…Later Dar and Bhat [30] introduced the scaled version of Ambiguity function and Wigner distribution in the linear canonical transform domain. They also introduced scaled version of Wigner distribution in the offset linear canonical transform [31][32][33][34][35], hence provides a novel way for the improvement of the cross-term reduction time-frequency resolution and angle resolution.…”

Section: Introductionmentioning

confidence: 99%

Scaled Ambiguity Function Associated with Quadratic-Phase Fourier Transform

Bhat¹,

Dar²,

Bhat³

et al. 2023

Time Frequency Analysis of Some Generalized Fourier Transforms

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Quadratic-phase Fourier transform (QPFT) as a general integral transform has been considered into Wigner distribution (WD) and Ambiguity function (AF) to show more powerful ability for non-stationary signal processing. In this article, a new version of ambiguity function (AF) coined as scaled ambiguity function associated with the Quadratic-phase Fourier transform (QPFT) is proposed. This new version of AF is defined based on the QPFT and the fractional instantaneous auto-correlation. Firstly, we define the scaled ambiguity function associated with the QPFT (SAFQ). Then, the main properties including the conjugate-symmetry, shifting, scaling, marginal and Moyal’s formulae of SAFQ are investigated in detail, the results show that SAFQ can be viewed as the generalization of the classical AF. Finally, the newly defined SAFQ is used for the detection of linear-frequency-modulated (LFM) signals.

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“…The linear canonical transform (LCT) with four parameters (a, b, c, d) [1][2][3] has been generalized to a six parameter transform (a, b, c, d, p, q) known as offset LCT (OLCT). [4][5][6][7] Due to the time shifting parameter p and frequency modulation parameter q, the OLCT has gained more flexibility over classical LCT and hence has found wide applications in image and signal processing (see previous studies 4,5,[8][9][10] ). On the other side, the convolution has some applications in various areas of mathematics like linear algebra, numerical analysis, and signal processing.…”

Section: Introductionmentioning

confidence: 99%

“…The linear canonical transform (LCT) with four parameters

\left(a,b,c,d\right)

1–3 has been generalized to a six parameter transform

\left(a,b,c,d,p,q\right)

known as offset LCT (OLCT) 4–7 . Due to the time shifting parameter

p

and frequency modulation parameter

q

, the OLCT has gained more flexibility over classical LCT and hence has found wide applications in image and signal processing (see previous studies 4,5,8–10 ).…”

Section: Introductionmentioning

confidence: 99%

The two‐sided short‐time quaternionic offset linear canonical transform and associated convolution and correlation

Bhat

Dar

2023

Math Methods in App Sciences

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In this paper, we introduce the two‐dimensional short‐time quaternion offset linear canonical transform (ST‐QOLCT), which is a generalization of the classical short‐time offset linear canonical transform (ST‐OLCT) in quaternion algebra setting. Several useful properties of the ST‐QOLCT are obtained from the properties of the ST‐QOLCT kernel. Based on the properties of the ST‐QOLCT and the convolution and correlation operators associated with QOLCT, we derive convolution and correlation theorems for the ST‐QOLCT. Finally, some potential applications of the ST‐QOLCT are introduced.

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Scaled Wigner distribution in the offset linear canonical domain

Cited by 16 publications

References 22 publications

Quadratic-phase scaled Wigner distribution: convolution and correlation

Quadratic-phase scaled Wigner distribution: convolution and correlation

Scaled Ambiguity Function Associated with Quadratic-Phase Fourier Transform

The two‐sided short‐time quaternionic offset linear canonical transform and associated convolution and correlation

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