Jittered Sampling in Linear Canonical Domain

Abstract

Linear canonical transform (LCT) based sampling has been attracted much attention in signal processing community. A variety of sampling theorems associated with the LCT are therefore derived. However, the random jittered sampling in linear canonical domain still remains unresolved. Starting from the Shannon's result for the LCT, a biased interpolated estimate for bandlimited signals in linear canonical domain from jittered samples is proposed. The inverse filter technique is then applied to correct the bias, giving rise to an unbiased estimator whose interpolation noise variance approaches zero as the jitter becomes less and less pronounced. To be specific, for bandlimited stationary stochastic signals in linear canonical domain the interpolation noise variance is increased, and this result is also verified through some examples and simulations.