A sign-preserving filter for signal decomposition

Abstract

There are optimization problems in which an improvement in performance or a reduction in cost can be attained if the input signal of the system is split into multiple components. Splitting the signal allows customizing the design of the system’s hardware for a narrower range of frequencies, which in turn allows making a better use of its physical properties. There exist applications that have very specific signal-splitting requirements, such as ‘counter-flow avoidance’, that conventional signal processing tools cannot meet. Accordingly, a novel ‘Sign-Preserving’ filter has been developed and is presented in this article. The underlying algorithm of the filter is comprehensively explained with the aim of facilitating its reproduction, and the aspects of its operation are thoroughly discussed. The filter has two key features: (1) it separates a discrete signal a into two components – a mostly low-frequency signal b and a predominantly high-frequency signal c such that the sum of b and c replicates exactly the original signal a and, more importantly, (2) the signs of the two output signals are equal to the sign of a at all times. The article presents two case studies which demonstrate the use of the Sign-Preserving filter for the optimization of real-life applications, in which counter-flow must be avoided: the hybridization of the battery pack of an electric vehicle and the parallelization of a packed bed thermal energy store.