Sampling from a system-theoretic viewpoint part II: noncausal solutions

This paper puts to use concepts and tools introduced in Part I to address a wide spectrum of noncausal sampling and reconstruction problems. Particularly, we follow the systemtheoretic paradigm by using systems as signal generators to account for available information and system norms (L2 and L1) as performance measures. The proposed optimization-based approach recovers many known solutions, derived hitherto by different methods, as special cases under different assumptions about acquisition or reconstructing devices (e.g., polynomial and exponential cardinal splines for fixed samplers and the Sampling Theorem and its modifications in the case when both sampler and interpolator are design parameters). We also derive new results, such as versions of the Sampling Theorem for downsampling and reconstruction from noisy measurements, the continuous-time invariance of a wide class of optimal sampling-and-reconstruction circuits, etcetera.

• Type: Journal
• Year: 2010
• Where: TSP
• Authors: Gjerrit Meinsma, Leonid Mirkin
• Keywords: Artificial Intelligence, Exponential Cardinal Splines, Optimal Sampling-and-reconstruction Circuits, Sampling Theorem, TSP 2010