Dual-Quaternions: Theory and Applications in Sound

Abstract: Sound is a fundamental and rich source of information; playing a key role in many areas from humanities and social sciences through to engineering and mathematics. Sound is more than just data 'signals'. It encapsulates physical, sensorial and emotional, as well as social, cultural and environmental factors. Sound contributes to the transformation of our experiences, environments and beliefs. Sound is all around us and everywhere. Hence, it should come as no surprise that sound is a complex multicomponent entity with a vast assortment of characteristics and applications. Of course, an important question is, what is the best way to store and represent sound digitally to capture these characteristics? What model or method is best for manipulating, extracting and filtering sounds? There are a large number of representations and models, however, one approach that has yet to be used with sound is dual-quaternions. While dual-quaternions have established themselves in many fields of science and computing as an efficient mathematical model for providing an unambiguous, un-cumbersome, computationally effective means of representing multi-component data. Sound is one area that has yet to explore and reap the benefits of dual-quaternions (using sound and audio-related dual-quaternion models). This article aims to explore the exciting potential and possibilities dual-quaternions offer when applied and combined with sound-based models (including but not limited to the applications, tools, machine-learning, statistical and computational sound-related algorithms).