Sampling of signals with finite rate of innovation in parameter space

We consider the sampling of signals with finite rate of innovation (FRI) in parameter space to reach the minimal sampling rate. Although the sampling of signals with unknown time locations has been treated in previous works, it is difficult to sample the signals with unknown parameters in other parameter space. In this paper, we redefine the signal with FRI and propose a general framework of the FRI sampling. In addition, we design several different sampling schemes, including the single channel sampling, the multichannel direct sampling and the multichannel mixing sampling, to improve the sampling robustness and decrease the analog-to-digital (AD) conversion rate. By the discussions in the numerical experiment, we also show the signal with unknown parameters in time-frequency space can be sampled and reconstructed from the minimal-rate samples.