Fractional Spectral Analysis of Randomly Sampled Signals and Applications

Nonuniform sampling can be utilized to achieve certain desirable results. Periodic nonuniform sampling can decrease the required sampling rate for signals. Random sampling can be used as a digital alias-free signal processing method in analog-to-digital conversion. In this paper, we first present the fractional spectrum estimation of signals that are bandlimited in the fractional Fourier domain based on the general periodic random sampling approach. To show the estimation effect, the unbiasedness, the variance, and the optimal estimation condition are analyzed. The reconstruction of the fractional spectrum from the periodic random samples is also proposed. Second, the effects of sampling jitters and observation errors on the performance of the fractional spectrum estimation are analyzed, where the new defined fractional characteristic function is used to compensate the estimation bias from sampling jitters. Furthermore, we investigate the fractional spectral analysis from two widely used random sampling schemes, i.e., simple random sampling and stratified random sampling. Finally, all of the analysis results are applied and verified using a radar signal processing system.