The mathematical foundation of distributed interleaved systems

The distribution and interleaving (D&I) of signals is a common method for ripple attenuation in various engineering applications in such areas as control, communication, and power electronics. Similarities to this technique may also been found in nonengineering fields such as biology and medicine. This paper presents a mathematical exploration of distributed interleaved systems along with a simple frequency-domain model of interleaving. We are hoping that the insights provided by this mathematical framework and the newly proposed model for interleaved systems will lead to enhanced techniques for evaluating D&I processes, and facilitate the design of better systems. In particular, we hope this work results in new approaches to low-pass filtering that will exhibit fast dynamics and very efficient ripple attenuation (in theory, this can produce complete ripple removal in some cases).