p a p e r s
i n v i t e d p r e s e n t a t i o n s
Vassilakis, P.N. (2007b). Representing sound energy, phase, and interference using threedimensional signals. J. Acoust. Soc. Am.,
121(5/2): 3098 (presented at the 153nd meeting of the Acoustical Society
of America, Salt Lake City, UT)
[Invited presentation  Special session on Speech Communication:
Frontiers of Spectrum Analysis with Speech Applications.]

Abstract
As graphic representations of vibrations/waves, sound signals capture only selected attributes of the phenomenon they represent. Assuming equivalence between signals and sound waves obscures the fact that twodimensional signals are unfit to a) represent waveenergy quantities consistently across frequencies, b) account for the phase flip and alternating positive/negative amplitude values in modulated waves with AMdepth>100%, and c) represent the energy content of interference. The proposed soundsignal representation is based on the complex equation of motion describing a wave. It results in spiral sine signals and twistedspiral complex signals, similar to complex analytic signals, with the imaginary component of the complex equation of motion representing the signal envelope’s argument (phase). Spiral sine signals offer a consistent measure of sinewave energy across frequencies, while twistedspiral complex signals account for the negative amplitudes observed in modulated signals, mapping 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. 