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.

A load-based approach for optimizing a packed-bed thermal store

“…More efficient or less expensive packed beds will lead to more costeffective large-scale energy storage systems. This paper build on work carried out by the University of Nottingham [38][39][40][41]. The study incorporates the numerical models previously developed into a novel optimization approach that focuses on the frequency of the duty-cycle of a packed bed with aims at reducing its roundtrip exergy losses.…”

“…Therefore they are not suitable for this application. Cárdenas et al [41] developed a "Sign-Preserving-filter" that allows separating a discrete time signal into two components ( and ) without generating the aforementioned counter-flow problem.…”

“…The mechanics of the operation of the filter will not be addressed in any more detail in this paper. A comprehensive explanation of the underlying algorithm can be found in [41]. The filter has previously been used in a similar "load-based" optimization work, which was aimed at designing a hybrid battery pack for an electric vehicle [42].…”

Load optimization for reducing the cost of an electric vehicle’s battery pack

“…A "Sign-Preserving Filter" capable of splitting a signal A into two components B and C in such a way that at every point in time (t) the two components have the same sign as A and their sum equals A has been proposed by Cárdenas et al [25] ( ) = ( ) + ( )…”

“…A brief explanation of the operation of the filter is provided but its particularities are not addressed in depth. A comprehensive explanation of the mechanics of the filter, together with examples of other applications, can be found in [25].…”