QuasiRandom Sequences for Signal Sampling and Recovery

Miroslaw Pawlak (1) , Ewaryst Rafajlowicz (2)

1 Department of Electrical & Computer Engineering [Manitoba]
2 Institute of Computer Eng., Control and Robotics

The problem of reconstruction of band-limited signals from sampled and noisy observations is studied. It is proposed to sample a signal at quasi-random points, that form a deterministic sequence with properties resembling a random variable being uniformly distributed. Such quasi-random points can be easily and efficiently generated yielding signal reconstruction algorithms with the improved accuracy. In fact, in this paper we propose a reconstruction method based on the modified orthogonal sampling formula where the sampling rate and the reconstruction rate are treated separately. This distinction is necessary to ensure consistency of the reconstruction algorithm in the presence of noise. Asymptotical properties of the algorithm are evaluated including its convergence to the true signal and the corresponding rate. It is shown that the rate of convergence is better than that for reconstructions algorithms that utilize the traditional uniform sampling. Similar results are also obtained for the case of multivariate signals.

Domaines: Théorie de l'information et codage [math.IT]; Théorie de l'information [cs.IT]; Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Miroslaw Pawlak, Ewaryst Rafajlowicz. QuasiRandom Sequences for Signal Sampling and Recovery. SAMPTA'09, May 2009, Marseille, France. pp.General session. ⟨hal-00453276⟩