ON APPROXIMATED SAMPLING THEOREM AND WAVELET DENOISING FOR ARBITRARY WAVE-FORM RESTORATION

In this brief, an approximated sampling theorem for MS arbitrary conti nuous time waveform is established. The approximation error bounds for some typical classes of signals are computed. This theorem is essenti al for performing wavelet analysis if the signal concerned is time lim ited rather than band limited. An efficient reconstruction method maki ng use of wavelet denoising is proposed to restore source signal that is contaminated by white Gaussian noise. Under certain conditions, it is proved theoretically that the method is able to bound the estimatio n mean square error in the order of log(2)(n)/n, where n is the number of discrete samples in the reconstruction.