Abstract:

A lowpass sampling and reconstruction method for aperiodic nonbandlimited impulse signals is proposed. The impulse signals are passed through a lowpass filter and sampled at the rate of innovation. The sampled discrete time signals are transformed to frequency domain, from which the spectrum coefficients of original impulses are obtained. Then the amplitudes and time shifts of the impulses are found by a least square annihilating filter (LSAF) method. In the presence of noise, the LSAF method will suffer from performance loss. The only way to improve the reconstruction results is to increase the sampling rate and use the singular value decomposition (SVD) reconstruction method. Simulation results show that the proposed sampling and reconstruction methods achieve very good reconstruction results in the presence of noise at the low sampling rate.