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Bing-Zhao Li

Publications and source records attributed to Bing-Zhao Li.

30 records · Page 2Linked to original sources
arXiv2023

Unlimited Sampling Theorem Based on Fractional Fourier Transform

The recovery of bandlimited signals with high dynamic range is a hot issue in sampling research. The unlimited sampling theory expands the recordable range of traditional analog-to-digital converters (ADCs) arbitrarily, and the signal is folded back into a low dynamic range measurement, avoiding the saturation problem. We study the unlimited sampling problem of high dynamic non-bandlimited signals in the Fourier domain (FD) based on the fractional Fourier transform (FRFT). First, a mathematical signal model for unlimited sampling is proposed. Then, based on this mathematical model, the annihilation filtering method is used to estimate the arbitrary folding time. Finally, a novel unlimited sampling theorem in the FRFD is obtained. The results show that the non-bandlimited signal can be reconstructed in the FD based on the FRFT, and it is not affected by the ADC threshold.

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arXiv2022

Spectral graph fractional Fourier transform for directed graphs and its application

In graph signal processing, many studies assume that the underlying network is undirected. Although the digraph model is rarely adopted, it is more appropriate for many applications, especially for real world networks. In this paper, we present a general framework for extending the graph signal processing to directed graphs in graph fractional domain. For this purpose, we consider a new definition for fractional Hermitian Laplacian matrix on directed graph and generalize the spectral graph fractional Fourier transform to directed graph (DGFRFT). Based on our new transform, we then define filtering, which is used in reducing unnecessary noise superimposed on temperature data. Finally, the performance of the proposed DGFRFT approach is also evaluated through numerical experiments using real-world directed graphs.

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arXiv2022

Discrete Linear Canonical Transform on Graphs

With the wide application of spectral and algebraic theory in discrete signal processing techniques in the field of graph signal processing, an increasing number of signal processing methods have been proposed, such as the graph Fourier transform, graph wavelet transform and windowed graph Fourier transform. In this paper, we propose and design the definition of the discrete linear canonical transform on graphs (GLCT), which is an extension of the discrete linear canonical transform (DLCT), just as the graph Fourier transform (GFT) is an extension of the discrete Fourier transform (DFT). First, based on the centrality and scalability of the DLCT eigendecomposition approach, the definition of GLCT is proposed by combining graph chirp-Fourier transform, graph scale transform and graph fractional Fourier transform. Second, we derive and discuss the properties and special cases of GLCT. Finally, some GLCT examples of the graph signals are given to illustrate the improvement of the transformation.

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arXiv2022

Convolution theorems for the free metaplectic transformation and its application

The free metaplectic transformation (FMT) is widely used in many fields such as filter design, pattern recognition, image processing and optics. In order to obtain a more concise and intuitive convolution form, this paper studies two kinds of new convolution theorems in the FMT domain. First, based on the expression of the generalized translation, we derive the convolution theorem of the first kind in the FMT domain, which has elegance and simplicity comparable to the classical results of Fourier transform (FT). Second, we again give the convolution theorem of the second kind in the FMT domain to further study the diversity of convolution theory. It has the advantage that it can be represented by a simple integral and is easy to implement in multiplying filter designs. Finally, based on the simple form of the above convolution theorems, we discuss multiplicative filters in the MFT domain.

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arXiv2021

The two-dimensional OLCT of angularly periodic functions in polar coordinates

The two-dimensional (2D) offset linear canonical transform (OLCT) in polar coordinates plays an important role in many fields of optics and signal processing. This paper studies the 2D OLCT in polar coordinates. Firstly, we extend the 2D OLCT to the polar coordinate system, and obtain the offset linear canonical Hankel transform (OLCHT) formula. Secondly, through the angular periodic function with a period of 2π, the relationship between the 2D OLCT and the OLCHT is revealed. Finally, the spatial shift and convolution theorems for the 2D OLCT are proposed by using this relationship.

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arXiv2021

Multi-dimensional graph fractional Fourier transform and its application

Many multi-dimensional signals appear in the real world, such as digital images and data that has spatial and temporal dimensions. How to show the spectrum of these multi-dimensional signals correctly is a key challenge in the field of graph signal processing. This paper investigates the novel transform for multi-dimensional signals defined on Cartesian product graph and studies several related properties. Our work includes: (i) defining the multi-dimensional graph fractional Fourier transform (MGFRFT) based on Laplacian matrix and adjacency matrix; (ii) exploring the advantages of MGFRFT in processing multi-dimensional signals in terms of spectrum and computational time; (iii) applying the proposed transform to data compression to highlight the utility and effectiveness of it.

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arXiv2021

Uncertainty principle for the two-sided quaternion windowed linear canonical transform

In this paper, we investigate the (two-sided) quaternion windowed linear canonical transform (QWLCT) and study the uncertainty principles associated with the QWLCT. Firstly, several important properties of the QWLCT such as bounded, shift, modulation, orthogonality relation, are presented based on the spectral representation of the quaternionic linear canonical transform (QLCT). Secondly, Pitt's inequality and Lieb inequality for the QWLCT are explored. Moreover, we study different kinds of uncertainty principles for the QWLCT, such as Logarithmic uncertainty principle, Entropic uncertainty principle, Lieb uncertainty principle and Donoho-Stark's uncertainty principle. Finally, we give a numerical example and a potential application in signal recovery by using Donoho-Stark's uncertainty principle associated with the QWLCT.

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arXiv2019

Uncertainty principles for the windowed offset linear canonical transform

The windowed offset linear canonical transform (WOLCT) can be identified as a generalization of the windowed linear canonical transform (WLCT). In this paper, we generalize several different uncertainty principles for the WOLCT, including Heisenberg uncertainty principle, Hardy's uncertainty principle, Beurling's uncertainty principle, Lieb's uncertainty principle, Donoho-Stark's uncertainty principle, Amrein-Berthier-Benedicks's uncertainty principle, Nazarov's uncertainty principle and Logarithmic uncertainty principle.

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arXiv2019

Uncertainty principles for the short-time linear canonical transform of complex signals

The short-time linear canonical transform (STLCT) can be identified as a generalization of the short-time Fourier transform (STFT). It is a novel time-frequency analysis tool. In this paper, we generalize some different uncertainty principles for the STLCT of complex signals. Firstly, one uncertainty principle for the STLCT of complex signals in time and frequency domains is derived. Secondly, the uncertainty principle for the STLCT of complex signals in two STLCT domains is obtained. Finally, the uncertainty principle for the two conditional standard deviations of the spectrogram associated with the STLCT is discussed.

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arXiv2019

Uncertainty principles for the windowed Hankel transform

The aim of this paper is to prove some new uncertainty principles for the windowed Hankel transform. They include uncertainty principle for orthonormal sequence, local uncertainty principle, logarithmic uncertainty principle and Heisenberg-type uncertainty principle. As a side result, we obtain the Shapiro's dispersion theorem for the windowed Hankel transform.

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arXiv2019

Quaternion Windowed Linear Canonical Transform of Two-Dimensional Quaternionic Signals

We investigate the 2D quaternion windowed linear canonical transform(QWLCT) in this paper. Firstly, we propose the new definition of the QWLCT, and then several important properties of newly defined QWLCT, such as bounded, shift, modulation, orthogonality relation, are derived based on the spectral representation of the quaternionic linear canonical transform(QLCT). Finally, by the Heisenberg uncertainty principle for the QLCT and the orthogonality relation property for the QWLCT, the Heisenberg uncertainty principle for the QWLCT is established.

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