In this paper we present a generalized quantitative version of a result due to M.Revers concerning the exact convergence rate at zero of Lagrange interpolation polynomial to f (x) = |x| α with on equally spaced nodes in [−1, 1].
There is a lot of interference in underwater environment, which can affect underwater signal transmission. For this reason, an abnormal perception model of underwater signals based on multi-sensor data fusion is proposed. The underwater frequency hopping communication method is used to select the channel and construct the mathematical model of underwater communication signal. A signal modulation and recognition system for multi-sensor reception is established, and the multi-sensor data fusion model is obtained by calculating the support margin. The energy spectrum distribution is obtained by decomposition of abnormal features with wavelet detector in time domain. The deep learning algorithm is used to reorganize the signal with the minimum detection error, and the mathematical model of underwater signal anomaly perception is obtained. The experimental results show that the average accuracy of the method for locating abnormal underwater communication signals is 95.5%, the misrecognition rate of abnormal underwater signals is less than 2%, and the time-consuming for sensing abnormal signals of 420 MB underwater communication is less than 3 s.
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