Advanced Z-transform

Abstract: Modern signal processing and control algorithms are invariably implemented digitally, yet most real-world systems evolve in continuous time. Hence, the interaction between sampling and the behavior of continuous-time systems is an important ingredient in all real-world signals and systems problems.

Abstract: Most conventional control algorithms cause numerical problems where data is collected at sampling rates that are substantially higher than the dynamics of the equivalent continuous-time operation that is being implemented. This is of relevant interest in applications of digital control, in which high sample rates are routinely dictated by the system stability requirements rather than the signal processing needs. Digital control systems exhibit bandwidth limitations enforced by their closed-loop frequency requirements that demand very high sample rates. Considerable recent progress in reducing sample frequency requirements has been made through the use of non-uniform sampling schemes, so called alias - free signal processing. The approach prompts the simplification of complex systems and consequently enhances the numerical conditioning of the implementation algorithms that otherwise would require very high uniform sample rates. However, the control communities have not yet investigated the use of intentional non-uniform sampling. The purpose of this article is to address some algorithmic issues when using such regimes for digital control.

Abstract: Besides the proceedings, participants were invited to prepare an extended version of their SAMPTA contribution for a special issue of STSIP. Ten papers were accepted, covering a wide range of aspects of sampling theory (classical sampling, frame theory, wavelets, multi-resolution, operator approximation) and applications (impulse radio ultra-wide band, non-uniform sampling and filtering, multichannel sampling).