Research On Analog Signal Sampling And Reconstruction Based On Newton Interpolation Method

Signal is the carrier of information,and almost all fields of engineering and technology involve signal problems.Signal processing is essentially an operation that extracts,stores,enhances,and transmits useful information.The further study of signal processing is the most basic tool in mathematical fildes such as complex variable analysis,calculus,probability statistics,matrix algebra,numerical analysis,stochastic process,functional analysis,etc.This paper is a further research on the sampling and reconstruction of analog signals.First of all,the reconstruction error is studied based on the Shannon sampling theorem which can perfectly reconstruct the band-limited signal when meets the Nyquist sampling theory sampling frequency.This article explains and analyzes the reason why Shannon sampling analog signal reconstruction errors occur,and why the the error presents as Gibbs phenomenon,pointing out that the sampling problem is multifaceted,and summarizing two common sampling theorems of non-band-limited signal in which the Shannon sampling theorem only solves the convergence of basic series.The actual processing of analog signals is often based on non-bandlimited signals with limited time,and errors occur in any phase of the spectrum.This is also a limitation of Shannon's sampling theorem.On this basis,we introduce the basic principle of Newton interpolation,explaining and experimentally proving that by using Newton's interpolation the error of the reconstructed signal can be estimated in the case of a given error,which has a profound meaning in the accuracy of reconstructing the signal as well as reducing the signal reconstruction error.