Random sampling analysis in the linear canonical transform domain

Random sampling represents a specific class of nonuniform sampling that serves as an effective alias-free signal acquisition technique in analog-to-digital conversion systems. In this paper, we first propose the linear canonical spectrum estimators of deterministic signals which are derived from two simple random sampling methods. The proposed spectrum estimators are proven to be unbiased. Then we derive their variances to compare the accuracy of the estimators. We further analyze how sampling jitters and observation errors affect the performance of the linear canonical spectrum estimators. The sampling jitters cause bias in the estimators, which can be effectively compensated using our newly defined linear canonical characteristic function. Furthermore, we analyze the linear canonical spectrum of two types of stratified randomly sampled signals. All analytical results are validated through numerical simulations using the chirp signals.