Kantorovich指数抽样级数对间断函数的逼近
Approximation of discontinuous functions by Kantorovich exponential sampling series
摘要：
本文分析了有界可测信号f在跳跃间断处的Kantorovich指数抽样序列。建立了该级数的一个表示引理，并利用该引理证明了某些不连续信号的逼近定理。研究了该级数用对数光滑模表示的逼近阶。此外，已经获得了基于过去样本值的信号的线性预测。进行了一些数值模拟以验证采样序列对不连续信号f的逼近。
英文摘要：
The Kantorovich exponential sampling series at jump discontinuities of the bounded measurable signal f has been analysed. A representation lemma for the series is established and using this lemma certain approximation theorems for discontinuous signals are proved. The degree of approximation in terms of logarithmic modulus of smoothness for the series is studied. Further a linear prediction of signals based on past sample values has been obtained. Some numerical simulations are performed to validate the approximation of discontinuous signals f by the sampling series.
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