Quadratic-phase wave packet transform

Bhat, Mohammad Younus; Dar, Aamir H.; Urynbassarova, Didar; Urynbassarova, Altyn

doi:10.1016/j.ijleo.2022.169120

Cited by 20 publications

(7 citation statements)

References 21 publications

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“…The most neoteric generalization of the classical Fourier transform (FT) with five real parameters appeared via the theory of reproducing kernels is known as the quadratic-phase Fourier transform (QPFT) [17]. It treats both the stationary and nonstationary signals in a simple and insightful way that are involved in radar, signal processing, and other communication systems [18][19][20][21][22][23][24][25]. Here, we gave the notation and definition of the quadratic-phase Fourier transform and study some of its properties.…”

Section: Quadratic-phase Fourier Transformmentioning

confidence: 99%

Introductory Chapter: The Generalizations of the Fourier Transform

Younus Bhat

2023

Time Frequency Analysis of Some Generalized Fourier Transforms

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Section: Quadratic-phase Fourier Transformmentioning

confidence: 99%

Introductory Chapter: The Generalizations of the Fourier Transform

Younus Bhat

2023

Time Frequency Analysis of Some Generalized Fourier Transforms

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“…In Refs. [1][2][3], Castro et al introduced a superlative generalized version of the Fourier transform(FT) called quadratic-phase Fourier transform(QPFT), which not only treats uniquely both the transient and non-transient signals in a nice fashion but also with non-orthogonal directions. The QPFT is actually a generalization of several well known transforms like Fourier, fractional Fourier and linear canonical transforms, offset linear canonical transform whose kernel is in the exponential form.…”

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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“…Motivated by the knowledge and range of possibilities that opened up with the introduction of the quadratic-phase Fourier transform [1,2], as well other transforms and, in special, the wavelet transforms [3][4][5][6][7][8][9][10] that can be associated with it, we consider in this work a wavelet transform proposed by Prasad and Sharma [6] for which we will explore some of its properties. A special emphasis will be given to the possibility of envisioning new uncertainty principles and the deduction of the solubility of a class of integral equations.…”

Section: Introductionmentioning

confidence: 99%

Uncertainty principles and integral equations associated with a quadratic‐phase wavelet transform

Castro

Guerra

2023

Math Methods in App Sciences

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Taking into account a wavelet transform associated with the quadratic‐phase Fourier transform, we obtain several types of uncertainty principles, as well as identify conditions that guarantee the unique solution for a class of integral equations (related with the previous mentioned transforms). Namely, we obtain a Heisenberg–Pauli–Weyl‐type uncertainty principle, a logarithmic‐type uncertainty principle, a local‐type uncertainty principle, an entropy‐based uncertainty principle, a Nazarov‐type uncertainty principle, an Amrein–Berthier–Benedicks‐type uncertainty principle, a Donoho–Stark‐type uncertainty principle, a Hardy‐type uncertainty principle, and a Beurling‐type uncertainty principle for such quadratic‐phase wavelet transform. For this, it is crucial to consider a convolution and its consequences in establishing an explicit relation with the quadratic‐phase Fourier transform.

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Quadratic-phase wave packet transform

Cited by 20 publications

References 21 publications

Introductory Chapter: The Generalizations of the Fourier Transform

Introductory Chapter: The Generalizations of the Fourier Transform

Scaled Ambiguity Function Associated with Quadratic-Phase Fourier Transform

Uncertainty principles and integral equations associated with a quadratic‐phase wavelet transform

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