A parametric model for the quadratic sampling of a bandlimited signal

The paper treats the problem of ambiguity resolution using non-uniform sampling. This problem occurs for Doppler estimation in coherent pulsed Doppler radar. In the paper, the authors study the case where the duration between two samples is a linear function of time: quadratic sampling. Assuming that the continuous signal is stationary, the sampled signal will be non-stationary. The autocorrelation of this signal is derived and the Wigner distribution of the sampled signal related to the spectrum of the continuous signal. As a consequence, a time frequency relief of the signal will verify symmetries. These constraints, assuming an AR evolutive model for the sampled signal and band limitation for the continuous signal, allow the derivation of a particular time varying model for the samples. An associated estimation algorithm, leading to the unfolded spectrum is then proposed.