Translated by Yu. Kornienko
In this paper, we investigate specific features of compressed sensing methods when estimating the waveform of arbitrary analog signals based on zero-crossings of a signal summed with a periodic oscillation. An algorithm for estimating the waveform of an analog signal with the adaptation of the basis matrix to its spectrum is proposed. To solve the problem of off-grid frequencies, we employ an iterative method for finding the maxima of the spectral peaks between the nodes of a DFT frequency grid.