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.
翻译:已经对约束可测量信号 f 的跳跃不连续时Kantorovich指数抽样序列进行了分析,确定了该序列的表示列马,并用该列马的某些近似理论对不连续信号进行了验证。正在研究该系列的对数光滑模量近似程度。还获得了根据过去样本值对信号的线性预测。进行了一些数字模拟,以验证抽样序列对不连续信号的近似程度。