广义测不准原理理论研究

Research on Generalized Uncertainty Principles

测不准原理不仅是物理学中的一个基本问题,也是数学中的一个基本问题,同时对于信息学等多种学科均有较大的影响。从信号处理的角度,本文对分数阶域以及广义分数阶域(线性完整变换域或线性正则变换域)的Heisenberg测不准原理、加窗测不准原理、对数测不准原理、熵测不准原理等理论及其扩展进行了全面分析和综述,与传统测不准原理作了深入分析比较,剖析了广义测不准原理的发展和应用现状,并给出了广义测不准原理尚需进一步研究的问题。

The uncertainty principle plays an important role in both physics and mathematics, and it also plays an important role in information science. This paper reviewed the Heisenberg’s uncertainty principles, windowed uncertainty principles, logarithmic uncertainty principles, entropic uncer-tainty principles and so on in the fractional Fourier transform domains and linear canonical transform domains in great details. The development and applications of generalized uncertainty principles were analyzed, and the trend and direction were given as well.