SIGNAL RECONSTRUCTION FROM SINE WAVE CROSSINGS

In this paper we analyze the reconstruction of bandlimited signals from their sine wave crossings by a sampling type reconstruction process. The reconstruction process is highly adapted to the signal which shall be reconstructed, because the reconstruction functions and the sampling points are implicitly generated by the signal. We show that the reconstruction process is uniformly convergent for all signals in the Paley-Wiener spaces PW pi p, 1 < p <= infinity. However, the adaptivity cannot prevent the peak value of the reconstruction process to diverge for certain signals in PW pi 1.