Short time coupled fractional fourier transform and the uncertainty principle
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Ramanathan Kamalakkannan
Abstract
In this paper, we introduce a short-time coupled fractional Fourier transform (scfrft) using the kernel of the coupled fractional Fourier transform (cfrft). We then prove that it satisfies Parseval’s relation, derive its inversion and addition formulas, and characterize its range on ℒ2(ℝ2). We also study its time delay and frequency shift properties and conclude the article by a derivation of an uncertainty principle for both the coupled fractional Fourier transform and short-time coupled fractional Fourier transform.
Acknowledgements
The work of Mr R. Kamalakkannan is supported by a Junior Research Fellowship from CSIR-UGC, India.
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© 2021 Diogenes Co., Sofia
Artikel in diesem Heft
- Frontmatter
- Editorial Survey
- In memory of the honorary founding editors behind the FCAA success story
- Research Paper
- Short time coupled fractional fourier transform and the uncertainty principle
- (N + α)-Order low-pass and high-pass filter transfer functions for non-cascade implementations approximating butterworth response
- Sharp asymptotics in a fractional Sturm-Liouville problem
- Multi-term fractional integro-differential equations in power growth function spaces
- Galerkin method for time fractional semilinear equations
- Müntz sturm-liouville problems: Theory and numerical experiments
- Simultaneous inversion for the fractional exponents in the space-time fractional diffusion equation ∂tβ u = −(− Δ)α/2 u − (− Δ)γ/2 u
- Nonlinear convolution integro-differential equation with variable coefficient
- An efficient localized collocation solver for anomalous diffusion on surfaces
- Approximate calculation of the Caputo-type fractional derivative from inaccurate data. Dynamical approach
- Sliding methods for the higher order fractional laplacians
- Global stability of fractional different orders nonlinear feedback systems with positive linear parts and interval state matrices
Artikel in diesem Heft
- Frontmatter
- Editorial Survey
- In memory of the honorary founding editors behind the FCAA success story
- Research Paper
- Short time coupled fractional fourier transform and the uncertainty principle
- (N + α)-Order low-pass and high-pass filter transfer functions for non-cascade implementations approximating butterworth response
- Sharp asymptotics in a fractional Sturm-Liouville problem
- Multi-term fractional integro-differential equations in power growth function spaces
- Galerkin method for time fractional semilinear equations
- Müntz sturm-liouville problems: Theory and numerical experiments
- Simultaneous inversion for the fractional exponents in the space-time fractional diffusion equation ∂tβ u = −(− Δ)α/2 u − (− Δ)γ/2 u
- Nonlinear convolution integro-differential equation with variable coefficient
- An efficient localized collocation solver for anomalous diffusion on surfaces
- Approximate calculation of the Caputo-type fractional derivative from inaccurate data. Dynamical approach
- Sliding methods for the higher order fractional laplacians
- Global stability of fractional different orders nonlinear feedback systems with positive linear parts and interval state matrices
