Generalized Hilbert transform and its properties in 2D LCT domain

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

Citing 4
Cited 6

Fractional quaternion Fourier transform, convolution and correlation

Signal Processing
Parameter estimation of 2-D random amplitude polynomial-phasesignals

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

IEEE Transactions on Signal Processing
Hypercomplex signals-a novel extension of the analytic signal tothe multidimensional case

IEEE Transactions on Signal Processing

On signal moments and uncertainty relations associated with linear canonical transform

Signal Processing
Fast communication: Reduced biquaternion canonical transform, convolution and correlation

Signal Processing
The complex bidimensional empirical mode decomposition

Signal Processing
On analysis of bi-dimensional component decomposition via BEMD

Pattern Recognition
Multi-channel filter banks associated with linear canonical transform

Signal Processing
An equivalence between typical spectrographic data analysis and the formulations for time series analysis

International Journal of Data Analysis Techniques and Strategies

Quantified Score

Hi-index	0.08

Visualization

Abstract

Hilbert transform plays an important role in signal processing. With the development of new transforms, one-dimensional (1D) Hilbert transform has been extended into fractional Fourier transform domain. However, the researches of two-dimensional (2D) Hilbert transform in linear canonical transform (LCT) domain become complicated for the reasons of the complexity of 2D signals and more parameters in LCT, and now they are in the infancy. In this paper, the definitions of half-planed Hilbert transform, cross-orthant Hilbert transform and single-orthant Hilbert transform are yielded in LCT domain. In addition, the relation between time domain and transformed domain is discussed. Moreover, some important properties and conclusions are obtained as well. Finally, we defined and derived 2D Bedrosian's principle in LCT domain.