Alias-free Discrete-time FIR System Realisation Using Hybrid Stratified Sampling

This paper proposes a method for system realisation, where the realised system is described by a continuous-time, finite-duration impulse response. The proposed discrete-time implementation deploys Digital Alias-free Signal Processing. It means that despite the use of digital signal processing, the produced results do not suffer from aliasing. However, owing to the use of random sampling, the approach relies on constructing a suitable estimator of the system output. This paper shows that the proposed estimator is unbiased. It is also consistent, i.e. its variance goes to zero when the density of signal samples increasing. It is proven that under moderately restrictive assumptions, the estimator goes to zero proportionally to the fifth power of the average distance between the samples.