Special affine wavelet packets: Theory and applications

Lone, Waseem Z.; Shah, Firdous A.

doi:10.1016/j.ijleo.2022.169570

Cited by 2 publications

(1 citation statement)

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“…Moreover, the symmetry property of wavelets is often desirable in practical applications, and as such, wavelets can reveal different patterns and singularities of highly nonstationary signals, such as Brownian motions, patterns on the water surfaces, fractal properties of the velocity field, computations of Renyi dimensions, Hurst and Hölder exponents. Some prominent examples of the symmetric wavelets include biorthogonal wavelets, quincunx wavelets, and carinal Bsplines [3]. Despite the fact that the wavelet transforms have captivated the scientific, engineering, and research communities with their wide range of applications and simple mathematical underpinning, however, they could not perform satisfactorily while analyzing signals whose energy is not well concentrated in the frequency domain.…”

Section: Introductionmentioning

confidence: 99%

Quadratic-Phase Wave-Packet Transform in L2(R)

2022

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Wavelet transform is a powerful tool for analysing the problems arising in harmonic analysis, signal and image processing, sampling, filtering, and so on. However, they seem to be inadequate for representing those signals whose energy is not well concentrated in the frequency domain. In pursuit of representations of such signals, we propose a novel time-frequency transform coined as quadratic-phase wave packet transform in L2(R). The proposed transform is aimed at rectifying the conventional wavelet transform by employing a quadratic-phase Fourier transform with extra degrees of freedom. Besides the formulation of all the fundamental results, including the orthogonality relation, reconstruction formula and the characterization of range, we also derive a direct relationship between the well-known Wigner-Ville distribution and the proposed transform. In addition, we study the quadratic-phase wave-packet transform in the framework of almost periodic functions. Finally, we extend the scope of the present work by investigating the composition of quadratic-phase wave packet transforms.

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Section: Introductionmentioning

confidence: 99%