On approximated sampling theorem and wavelet denoising for arbitrary waveform restoration

In this work, an approximated sampling theorem for any arbitrary continuous time waveform is established. The approximation error bounds for some typical classes of signals are computed. This theorem is essential for performing wavelet analysis if the signal concerned is time limited rather than band limited. An efficient reconstruction method making use of wavelet denoising is proposed to restore a source signal that is contaminated by white Gaussian noise. Under certain conditions, it is proved theoretically that the method is able to bound the estimation mean square error in the order of log²(n)/n, where n is the number of discrete samples in the reconstruction