信号的量子算符分析方法及测不准定理研究  

Signal's Quantum Operator Analysis and Uncertainty Principle

作　　者：王鹏[1] 谢千河[1] 

机构地区：[1]成都信息工程大学并行计算实验室

出　　处：《成都信息工程学院学报》2015年第5期409-414,共6页Journal of Chengdu University of Information Technology

基　　金：国家自然科学基金资助项目(60702075);中国博士后科学基金资助项目(20090451420);广东省科技厅高新技术产业化科技攻关资助项目(2011B010200007);四川省青年科学基金资助项目(09ZQ026-068)

摘　　要：借鉴量子力学中不同表象的算符定义方法,分别定义了信号在频率表象和时间表象中的频率算符和时间算符,证明了频率算符和时间算符均为线性厄米算符并且在同方向上是不对易的,利用频率算符和时间算符的对易性关系分析证明了一维和二维信号的测不准定理,发现二维信号在不同方向上的频率和时间是可以同时准确测定的。最后利用信号的测不准定理分别证明了时域和频域上的采样定理,时域和频域上可恢复的采样频率分别与信号的最高频率和最长持续时间的两倍有关,证明过程表明信号的采样定理本质上是信号测不准定理的另一种表述方法。With reference to the definition of different representation＇s operator in quantum mechanics,frequency operator in frequency representation and time operator in time representation are defined. It＇s proved that frequency operator and time operator are linear hermitian and noncommuting operator in the same direction. One-dimensional and two-dimensional signal＇s uncertainty principle is proved from the commuting relation between frequency operator and time operator. Two-dimensional signal＇s frequency and time in different directions can be measured accurately. Finally,this paper proves the sampling principle in time domain and frequency domain using signal＇s uncertainty principle,recoverable sampling frequency in time domain and frequency domain have relationship with twice of signal＇s highest frequency and longest lasting time. It＇s proved that sampling theory is another representation of signal＇s uncertainty principle.

关 键 词：信号 厄米算符 测不准定理 采样定理 对易 

分 类 号：TN911.6[电子电信—通信与信息系统]