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Vassilakis, P.N. (2003).  Three-dimensional sound signals and their relevance to wave energy quantities and sound interference products.  J. Acoust. Soc. Am., 114(4/2): 2350 (invited presentation at the 146th meeting of the Acoustical Society of America, Austin, TX).


Signals are graphic representations of vibrations / waves and, like every representation, capture only selected attributes of the phenomenon they are meant to represent. The often assumed equivalence between signals and sound waves obscures the fact that two-dimensional sound signals are not fit to (a) represent wave-energy quantities consistently across frequencies, (b) account for the alternating positive / negative amplitude values of modulated waves with AM-depth > 100%, and (c) represent the energy content of interference.
An alternative sound signal representation is proposed that is based on the complex equation of motion describing a wave. It results in spiral sine signals and twisted-spiral complex signals, similar to complex analytic signals. Spiral sine signals offer a consistent measure of sine-wave energy across frequencies, while twisted spiral complex signals account for the negative amplitude values observed in modulated signals and map the modulation parameters onto the twisting parameters. In terms of interference, 3D-signals illustrate that amplitude fluctuations and the signal envelopes that describe them are not just boundary curves but waves that trace changes in the total instantaneous energy of a signal over time, representing the oscillation between potential and kinetic energies within a wave. Examples of 3D animations illustrating the proposed signals are presented. [see also "those twisted beats"]