A Novel Sub-Nyquist FRI Sampling and Reconstruction Method in Linear Canonical Transform Domain

Xin, Hong-Cai; Li, Bing‐Zhao

doi:10.1007/s00034-021-01759-w

Cited by 5 publications

(2 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As a generalization of the FT and FRFT, the LCT equips three free parameters, and can be seen as an affine transformation in time‐frequency domain. Since the LCT's fast discrete algorithms were proposed [ 43‐57 ] , a large number of achievements have emerged in its mathematical foundations (convolution theorems [ 5 , 58‐64 ] , sampling theorems [ 60 , 61 , 65‐79 ] , uncertainty principles [ 80‐91 ] , etc. ), theoretical expansions (time‐frequency analysis [ 92‐99 ] , compressed sensing [ 100 ] , phase retrieval [ 101 ] , etc.…”

Section: Preliminariesmentioning

confidence: 99%

Variance‐SNR Based Noise Suppression on Linear Canonical Choi‐Williams Distribution of LFM Signals

ZHANG

2022

Chinese J of Electronics

View full text Add to dashboard Cite

By solving the existing expectation‐signal‐to‐noise ratio (expectation‐SNR) based inequality model of the closed‐form instantaneous cross‐correlation function type of Choi‐Williams distribution (CICFCWD), the linear canonical transform (LCT) free parameters selection strategies obtained are usually unsatisfactory. Since the second‐order moment variance outperforms the first‐order moment expectation in accurately characterizing output SNRs, this paper uses the variance analysis technique to improve parameters selection strategies. The CICFCWD's average variance of deterministic signals embedded in additive zero‐mean stationary circular Gaussian noise processes is first obtained. Then the so‐called variance‐SNRs are defined and applied to model a variance‐SNR based inequality. A stronger inequalities system is also formulated by integrating expectation‐SNR and variance‐SNR based inequality models. Finally, a direct application of the system in noisy one‐component and bi‐component linear frequency‐modulated (LFM) signals detection is studied. Analytical algebraic constraints on LCT free parameters newly derived seem more accurate than the existing ones, achieving better noise suppression effects. Our methods have potential applications in optical, radar, communication and medical signal processing.

show abstract

Section: Preliminariesmentioning

confidence: 99%

Variance‐SNR Based Noise Suppression on Linear Canonical Choi‐Williams Distribution of LFM Signals

ZHANG

2022

Chinese J of Electronics

View full text Add to dashboard Cite

show abstract

“…It exhibits unique advantages, strong flexibility, and processing ability when dealing with non-stationary and non-Gaussian signals. Significant progress has been made in signal sampling and filtering [3,4], discrete algorithms [5,6], convolution theory [7][8][9], time-frequency analysis [10][11][12], parameter estimation [13,14], uncertainty principles [11,15,16], image encryption [17,18], etc. The linear canonical cosine transform (LCcT) is widely recognized for its excellent orthogonal properties that enable efficient compression of energy distribution.…”

Section: Introductionmentioning

confidence: 99%

Weighted Convolution for Quaternion Linear Canonical Cosine Transform and Its Application

Wang,

Feng

2024

Axioms

View full text Add to dashboard Cite

Convolution plays a pivotal role in the domains of signal processing and optics. This paper primarily focuses on studying the weighted convolution for quaternion linear canonical cosine transform (QLCcT) and its application in multiplicative filter analysis. Firstly, we propose QLCcT by combining quaternion algebra with linear canonical cosine transform (LCcT), which extends LCcT to Hamiltonian quaternion algebra. Secondly, we introduce weighted convolution and correlation operations for QLCcT, accompanied by their corresponding theorems. We also explore the properties of QLCcT. Thirdly, we utilize these proposed convolution structures to analyze multiplicative filter models that offer lower computational complexity compared to existing methods based on quaternion linear canonical transform (QLCT). Additionally, we discuss the rationale behind studying such transforms using quaternion functions as an illustrative example.

show abstract

Universal Discrete Finite Rate of Innovation Scheme for Sparse Signal Reconstruction

Reddy

Raghavendra²,

Narasimhadhan³

2022

Circuits Syst Signal Process

View full text Add to dashboard Cite

A Novel Sub-Nyquist FRI Sampling and Reconstruction Method in Linear Canonical Transform Domain

Cited by 5 publications

References 27 publications

Variance‐SNR Based Noise Suppression on Linear Canonical Choi‐Williams Distribution of LFM Signals

Variance‐SNR Based Noise Suppression on Linear Canonical Choi‐Williams Distribution of LFM Signals

Weighted Convolution for Quaternion Linear Canonical Cosine Transform and Its Application

Universal Discrete Finite Rate of Innovation Scheme for Sparse Signal Reconstruction

Contact Info

Product

Resources

About