拟平移不变信号的自适应采样与重构  

Adaptive sampling and reconstruction of quasi shift-invariant signals

作　　者：张海英 蒋英春[1] ZHANG Haiying;JIANG Yingchun(School of Mathematics and Computing Science,Guilin University of Electronic Technology,Guilin 541004,China)

机构地区：[1]桂林电子科技大学数学与计算科学学院,广西桂林541004

出　　处：《桂林电子科技大学学报》2024年第1期23-29,共7页Journal of Guilin University of Electronic Technology

基　　金：国家自然科学基金(12261025);广西自然科学基金(2019GXNSFFA245012,2020GXNSFAA159076);广西科技项目(2021AC06001)。

摘　　要：在采样问题的研究过程中,时间编码器作为易实现且高效的采样装置被提出。为达到高效重构信号的目的,基于时间编码器对拟平移不变空间中信号的自适应采样与重构展开研究,重点研究拟平移不变信号的重构算法。首先,基于“Crossing”和“Integrate-and-Fire”时间编码器,分别考虑了2种自适应采样方式,并建立了相应的精确重构算法。其次,讨论了一种可以产生有限自适应平均样本的IF采样器,并给出了基于样本的近似重构算法。结果表明,当时间编码器的稠密度满足一定衰减性时,建立的精确重构算法具有指数收敛性;当生成元满足一定衰减性时,近似重构算法的收敛速度线性依赖于IF采样器的阈值参数。In the research process of sampling problems,time encoding machines have been proposed as easy to implement and efficient sampling devices.In order to achieve the goal of efficient signal reconstruction,adaptive sampling and reconstruction of signals in quasi shift-invariant space based on time encoding machines are studied,with emphasis on the reconstruction algorithm of quasi shift-invariant signals.First,based on"Crossing"and"Integrated and Fire"time encoding machines,two adaptive sampling methods are considered,and corresponding exact reconstruction algorithms are established.Second,an IF sampler that can generate finite adaptive average samples is discussed,and an approximate reconstruction algorithm based on samples is given.The results show that the established exact reconstruction algorithm has exponential convergence when the density of the time encoding machines satisfies a certain attenuation property.When the generator satisfies a certain attenuation,the convergence speed of the approximate reconstruction algorithm linearly depends on the threshold parameter of the IF sampler.

关 键 词：时间编码器 拟平移不变子空间 自适应采样 精确重构 近似重构 

分 类 号：O177.92[理学—数学]