Fast communication: The logarithmic, Heisenberg's and short-time uncertainty principles associated with fractional Fourier transform

Authors:
Xu Guanlei;Wang Xiaotong;Xu Xiaogang
Affiliations:
Department of Navigation, Dalian Naval Academy, Dalian 116018, China and Institute of Photoelectric technology, Dalian Naval Academy, Dalian 116018, China;Department of Navigation, Dalian Naval Academy, Dalian 116018, China and Institute of Photoelectric technology, Dalian Naval Academy, Dalian 116018, China;Department of Automatization, Dalian Naval Academy, Dalian 116018, China and Institute of Photoelectric technology, Dalian Naval Academy, Dalian 116018, China
Venue:
Signal Processing
Year:
2009

Citing 6
Cited 6

Fractional Fourier domains

Signal Processing
Time-frequency signal analysis based on the windowed fractional Fourier transform

Signal Processing - Special issue: Fractional signal processing and applications
The uncertainty principle: global, local, or both?

IEEE Transactions on Signal Processing
Two-dimensional affine generalized fractional Fourier transform

IEEE Transactions on Signal Processing
An uncertainty principle for real signals in the fractional Fouriertransform domain

IEEE Transactions on Signal Processing
Relations between fractional operations and time-frequencydistributions, and their applications

IEEE Transactions on Signal Processing

Fast communication: Generalized entropic uncertainty principle on fractional Fourier transform

Signal Processing
New inequalities for signal spreads in linear canonical transform domains

Signal Processing
New inequalities and uncertainty relations on linear canonical transform revisit

EURASIP Journal on Advances in Signal Processing
On uncertainty principle for the linear canonical transform of complex signals

IEEE Transactions on Signal Processing
Fractional Fourier transform as a signal processing tool: An overview of recent developments

Signal Processing
Heisenberg's uncertainty principles for the 2-D nonseparable linear canonical transforms

Signal Processing

Quantified Score

Hi-index	0.08

Visualization

Abstract

Firstly, based on the relation between the original function and definition of the fractional Fourier transform (FRFT), one novel logarithmic uncertainty principle and one Heisenberg's uncertainty principle in the FRFT domains are derived, which are associated with the FRFT parameter. Secondly, the uncertainty principle for the short-time fractional Fourier transform (STFRFT) is obtained. The novel logarithmic, Heisenberg's and the short-time uncertainty principles connect their bounds with the FRFT parameter, which can help us understand the physical interpretations of the uncertainty principle in nature. This discloses that for these new transforms involving the FRFT parameter the uncertainty principles continue to hold.