Heisenberg uncertainty inequality for Gabor transform on nilpotent Lie groups

Smaoui, Kais; Abid, Khouloud

doi:10.1007/s10476-021-0112-8

Cited by 5 publications

(2 citation statements)

References 14 publications

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“…The Heisenberg inequality applied to a Gabor transform [20] constitutes a determining property when we want to treat the resolution in time and frequency jointly:…”

Section: Detection With the Gabor Transformmentioning

confidence: 99%

“…In order to choose the best parameters (Nh and α) for the proposed detector, we show the analysis window h and its corresponding synthesis window 𝛾 with different values of Nh and α in the following figures (see Figures 7-9): The Heisenberg inequality applied to a Gabor transform [20] constitutes a determining property when we want to treat the resolution in time and frequency jointly:…”

Section: Detection With the Gabor Transformmentioning

confidence: 99%

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Clutter Map Constant False Alarm Rate Mixed with the Gabor Transform for Target Detection via Monte Carlo Simulation

Mbouombouo Mboungam,

Zhi,

Fonzeu Monguen

2024

Applied Sciences

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Radar detection is a technology frequently used to detect objects and measure the range, angle, or velocity of those objects. Several studies have been performed to improve the accuracy and performance of detection methods, but they encountered a strong challenge, which was the minimization of false alarms and the distinguishing of real targets from false alarms, especially in nonhomogeneous environments. We propose a new detection method that uses time-frequency analysis tools to improve detection performance and maintain a low constant false alarm rate. Different from existing works, this paper combines the clutter map constant false alarm rate technique with the Gabor transform for accurate target detection in cluttered environments. We suggest the combination of a CFAR detector with a time-frequency method that enables us to tackle challenging scenarios involving near targets. The proposed method allows for locating the exact position of the target by reducing the impact of clutter and maintaining a low rate of false alarms, while the Gabor transform facilitates the extraction of pertinent target characteristics and improves differentiation from clutter. Through experiments and simulations in different scenarios and clutter models, we demonstrate that the method is efficient in measurements and performs well in cluttered environments. This research has a major impact on signal processing and significantly improves target detection in cluttered environments, allowing this method to be deeply developed and implemented.

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“…The Heisenberg inequality applied to a Gabor transform [20] constitutes a determining property when we want to treat the resolution in time and frequency jointly:…”

Section: Detection With the Gabor Transformmentioning

confidence: 99%

Section: Detection With the Gabor Transformmentioning

confidence: 99%

Clutter Map Constant False Alarm Rate Mixed with the Gabor Transform for Target Detection via Monte Carlo Simulation

Mbouombouo Mboungam,

Zhi,

Fonzeu Monguen

2024

Applied Sciences

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Heisenberg uncertainty principle for Gabor transform on compact extensions of $$\mathbb {R}^n$$

Smaoui,

Abid

2024

J. Pseudo-Differ. Oper. Appl.

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The uncertainty principle generalization for a connected semi-simple Lie group

Yaremenko

2023

Asian-European J. Math.

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In this paper, we are establishing the generalized variant of the Hardy theorem, which states that for [Formula: see text] a separable Hilbert space, [Formula: see text] a connected semi-simple Lie group with a Haar measure [Formula: see text] a unitary representation of [Formula: see text] in [Formula: see text], and [Formula: see text] a dual measure on [Formula: see text], if inequalities [Formula: see text] and [Formula: see text] hold for [Formula: see text], then the function [Formula: see text] must equal zero almost for all [Formula: see text].

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Heisenberg uncertainty inequality for Gabor transform on nilpotent Lie groups

Cited by 5 publications

References 14 publications

Clutter Map Constant False Alarm Rate Mixed with the Gabor Transform for Target Detection via Monte Carlo Simulation

Clutter Map Constant False Alarm Rate Mixed with the Gabor Transform for Target Detection via Monte Carlo Simulation

Heisenberg uncertainty principle for Gabor transform on compact extensions of $$\mathbb {R}^n$$

The uncertainty principle generalization for a connected semi-simple Lie group

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