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Quaternions are still largely misunderstood and often considered an “exotic” signal representation without much practical utility despite the fact that they have been around the signal and image processing community for more than 30 years now. The main aim of this article is to counter this misconception and to demystify the use of quaternion algebra for solving problems in signal and image processing.
Sound can be described with thermodynamic variables, the most common being pressure p, or kinematic flow variables such as particle acceleration a and velocity v. All of these continuous field variables represent, in the linear acoustic regime, small perturbations from their background values. For example, in a static fluid (a common approximation for sea water), p and v are related through the linearized Euler equation, with ρ the ocean density and t the time.
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