Untangling Phase and Time in Monophonic Sounds
Henning Thielemann
DOI: 10.4236/jsip.2010.11001   PDF   HTML     4,396 Downloads   8,166 Views   Citations


We are looking for a mathematical model of monophonic sounds with independent time and phase dimensions. With such a model we can resynthesise a sound with arbitrarily modulated frequency and progress of the timbre. We propose such a model and show that it exactly fulfils some natural properties, like a kind of timeinvariance, robustness against non-harmonic frequencies, envelope preservation, and inclusion of plain resampling as a special case. The resulting algorithm is efficient and allows to process data in a streaming manner with phase and shape modulation at sample rate, what we demonstrate with an implementation in the functional language Haskell. It allows a wide range of applications, namely pitch shifting and time scaling, creative FM synthesis effects, compression of monophonic sounds, generating loops for sampled sounds, synthesise sounds similar to wavetable synthesis, or making ultrasound audible.

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H. Thielemann, "Untangling Phase and Time in Monophonic Sounds," Journal of Signal and Information Processing, Vol. 1 No. 1, 2010, pp. 1-17. doi: 10.4236/jsip.2010.11001.

Conflicts of Interest

The authors declare no conflicts of interest.


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