Sinc Method In Reconstruction Of Compactly Supported Function

In real life, the reconstruction and the compression of the signal are veryimportant. The typical method to reconstruct signal is based on the ideal low-passfilter. In spite of the beautiful form of the typical method, it requires the sgnal to beprocessed is not compactly supported. What's more the ideal low-pass filter cannot berealized in fact. So some implements are used to improve it. It is evident that toreplace the ideal filter by a more realistic one is a good idea. And the rise of thewavelets has promoted the signal processing rapidly. But there are still some flawsexist. First a replaced filter makes no promise of the converge rate. Second waveletsmethod is not the best one when the signal is given in the form of differentialequations. So here I would like to introduce the Sinc method to solve them.Sinc mthod is a direct derivaty of Fourier analysis. By adding an exponentialtransform and a boundary process, we can cope with the delimma between thecompactly supported signal and the infinite supported one. And Sinc method has agreat advantage when it is used to solve the differential equations. Hence we mayreconstruct the signal from the differential equations easily. Here an exampleinvolved Hilbert transform is considered.In the finality, the problems requiring further studies are discussed. It seems toget more efficincy when the district method is added.