现代信息技术中的快速收敛取样定理

Sampling Theorem of the Fast Convergence in Modern Information Technology

在现代信息技术中,取样定理是模拟信号的量化以及复原为模拟信号的基础.模拟信号一般是频谱有限函数,彭瑞仁教授虽然得到了收敛速度比Shannon取样定理快得多的取样定理,然而,本文给出了收敛速度更快的负2N+1次幂取样定理(N为任意自然数),其结果比彭教授的结果更加优越.

Sampling theorem is the foundation of measuring imitative signal and recovering imitative signal in modern information technology. In general, imitative signal is the band-limited functions. Professor Peng gave the sampling theorem about the baud-limited functions in information technology, this theorem has a faster convergence rate than the shannon's. This paper has given a new higher speed sampling theorem of negative 2N + 1 (the N is arbitrary natural number) power exponent, the result of the new sampling theorem is more efficient than professor Peng's.