信号测不准原理的量子诠释.pdfVIP

第 37 卷 第 1 期 电 子 科 技 大 学 学 报 Vol.37 No.1 2008 年 1 月 Journal of University of Electronic Science and Technology of China Jan. 2008 信号测不准原理的量子诠释 1,2 1 王 鹏 ，李建平 (1.电子科技大学计算机科学与工程学院 成都 610054 ; 2.成都信息工程学院软件工程系 成都 610225) 【摘要】根据量子力学的测不准原理，采用力学量算符的方法得到了信号在时频分析时的测不准原理，并对该原理进行 量子诠释，认为信号在某种意义下可以看作是一个存在波粒二重性的类量子系统，正是由于信号的波粒二重性导致无法同时 准确地测定信号的时间和频率。在证明信号测不准原理的同时得到了信号的频率算符，该算符具有广阔的理论应用前景。信 号的量子诠释在揭示信号量子本质的同时，为量子力学中的理论框架应用于信号处理提供了理论支持。 关 键 词 信号频率算符 类量子系统 测不准原理 波粒二重性 ; ; ; 中图分类号 TN911.6 文献标识码 A Quantum Interpretation of Signal’s Uncertainty Principle 1, 2 1 WANG Peng ，LI Jian-ping (1. School of Computer Science and Engineering, University of Electronic Science and Technology of China Chengdu 610054; 2. Department of Software Engineering, Chengdu University of Information Technology Chengdu 610225) Abstract The uncertainty principle of signal is proved according to the uncertainty principle of quantum mechanics, and is further interpreted by quantum mechanics. The signal can be considered as a kind of the quasi quantum system with wave-particle dualism. Because of the wave-particle dualism of the signal, time and frequency can not be measured at the same time. The frequency operator (FO) of signal is defined in this study, and it can be widely used in signal theory and, especially in wavelet research. The quantum interpretation for the signal explains the essence of the signal and provides the theory support for applying the framework of quantum mechanics to the signal p