Sampling has been playing a major role in the signal theory. According to Shannon sampling theorem, however, sampling rate should not be smaller than Nyquist rate, which means that UWB signals have to be sampled at a quite high sampling rate and non-bandlimited signals can not be reconstructed exactly.The thesis analyses the reason why the wavelet sampling theorem can break Nyquist barrier and its advantages over Shannon sampling theorem. Some signals processing techniques, such as non-uniform sampling and sampling signals and their derivatives simultaneously, are superior to conventional uniform sampling. Simulation results show that the wavelet sampling theorem is effective for compactly supported signals. Since the decimation of discrete time signals is similar to the sampling of continuous signals, it is also studied in the thesis.Finally, the thesis investigates several other effective signals processing ways the signals can be reconstructed from their samples at less than Nyquist rate under some conditions. |