Reconstruction of sequences of arbitrary-shaped pulses from its low-pass or band-pass approximations using spectrum extrapolation

The paper discusses the problem of processing short-time pulse sequences. Since the spectrum of such signals occupies wide range, it is difficult to sample them at the Nyquist rate. Instead, the approach used for processing signals with finite rate of innovations is employed - sequence of pulses is filtered with low-pass or band-pass filter before sampling. A waveform reconstruction method is proposed, which is based on spectrum extrapolation in an iterative way. Due to spectral function of sequence of pulses is correlated, it is possible to recover sequences, which combine arbitrary-shaped pulses. In simulations three shapes of Gaussian based pulses are used as an example. Results demonstrate reconstruction of sequences of pulses from its low-pass and band-pass approximations. An application of the results can be used in ultra wideband impulse radio systems.