Recovery of varying-bandwidth signal from samples of its extrema

The paper introduces a new method of reconstruction of varying bandwidth signal sampled at sub-Nyquist rate. The temporal bandwidth is estimated dynamically by sampling the signal at its local extrema. The extremum sampling, which produces samples irregularly in time, provides at once the samples of the signal and its first derivative, since the local extrema occur at zero-crossings of the first time-derivative. We show that for the bandlimited Gaussian random processes, the average rate of extremum sampling is directly proportional to the maximum frequency component in the signal spectrum. Furthermore, we demonstrate that the extremum sampling of the bandlimited Gaussian random processes with flat spectrum provides a sufficient number of samples to recover the original signal at the half of the Nyquist rate using the derivative nonuniform sampling theorem. For signal recovery, the time-warped reconstruction functions for nonuniform sampling are used. The simulation results validate the presented approach and show that the proposed algorithm achieves lower reconstruction error than the algorithm using polynomial interpolation.