Corpus ID: 237571368

Convolution and Correlation Theorems for Wigner-Ville Distribution Associated with the Quaternion Offset Linear Canonical Transform

@article{Bhat2021ConvolutionAC,
  title={Convolution and Correlation Theorems for Wigner-Ville Distribution Associated with the Quaternion Offset Linear Canonical Transform},
  author={Mohammad Younus Bhat and Aamir Hamid Dar},
  journal={ArXiv},
  year={2021},
  volume={abs/2109.09682}
}
Abstract The quaternion offset linear canonical transform(QOLCT) has gained much popularity in recent years because of its applications in many areas, including color image and signal processing. At the same time the applications of Wigner-Ville distribution (WVD) in signal analysis and image processing can not be excluded. In this paper we investigate the Winger-Ville Distribution associated with quaternion offset linear canonical transform (WVD-QOLCT). Firstly, we propose the definition of… Expand
2 Citations
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The crux of the paper lies in the generalization of several well known uncertainty relations for the (O−OLCT) that include Pitt’s inequality, logarithmic uncertainty inequality, Hausdorff-Young inequality and local uncertainty inequalities. Expand
Quaternion Offset Linear Canonical Transform in One dimensional Setting
with AD − BC = 1. It is here worth to mention that if B = 0 then the OLCT defined by (1.1) is simply a time scaled version off multiplied by a linear chirp. Hence, without loss of generality, in thisExpand

References

SHOWING 1-10 OF 20 REFERENCES
Convolution and correlation theorems for Wigner-Ville distribution associated with the offset linear canonical transform
Abstract The Wigner-Ville distribution associated with the linear canonical transform (WVD-LCT) attracts serious attention in recent literatures. For this, currently, many time-frequencyExpand
A Convolution and Correlation Theorem for the Linear Canonical Transform and Its Application
TLDR
The convolution theorem in FT domain is shown to be a special case of the achieved results, and the correlation theorem is derived, which is also a one dimensional integral expression. Expand
The Wigner-Ville Distribution Based on the Linear Canonical Transform and Its Applications for QFM Signal Parameters Estimation
TLDR
A novel definition of the WVD based on the LCT and generalized instantaneous autocorrelation function (GWDL) is proposed and its applications in the estimation of parameters for QFM signals are also discussed. Expand
Wigner-Ville Distribution Associated with the Linear Canonical Transform
TLDR
This paper investigates the Wigner-Ville distribution in the linear canonical transform domain and proposes the applications of the newly defined Wigne-Villes transform in thelinear-frequency-modulated signal detection. Expand
New convolution theorem for the linear canonical transform and its translation invariance property
Abstract The linear canonical transform (LCT), which is a generalization of the Fourier transform (FT), has many applications in several areas, including signal processing and optics. Many propertiesExpand
Sampling theorem for the short-time linear canonical transform and its applications
TLDR
Based on the new sampling theorem, Gabor's signal expansion in the LCT domain is obtained, which can be considered as a generalization of the classical Gabor expansion and the fractional Gabor Expansion, and presents a simpler method for reconstructing the signal from its sampled STLCT. Expand
Generalized uncertainty principles associated with the quaternionic offset linear canonical transform
The quaternionic offset linear canonical transform (QOLCT) can be thought as a generalization of the quaternionic linear canonical transform (QLCT). In this paper we define the QOLCT, we derive theExpand
Uncertainty principles associated with the offset linear canonical transform
TLDR
Donoho-Stark's and Amrein-Berthier-Benedicks's uncertainty principles are presented and Lieb's uncertainty principle is presented for the short-time OLCT and a lower bound is given for its essential support. Expand
Generalized prolate spheroidal wave functions for offset linear canonical transform in Clifford analysis
Prolate spheroidal wave functions (PSWFs) possess many remarkable properties. They are orthogonal basis of both square integrable space of finite interval and the Paley–Wiener space of bandlimitedExpand
Quaternion Fourier Transform on Quaternion Fields and Generalizations
  • E. Hitzer
  • Mathematics, Computer Science
  • ArXiv
  • 2013
TLDR
The quaternionic Fourier transform applied to quaternion fields is treated and properties useful for applications are investigated and wide-ranging non-commutative multivector FT generalizations of the QFT are arrived at. Expand
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