Signal Modeling in the Time-Phase Domain
Signals are traditionally modelled in the time domain or in the time-frequency domain. Our modeling operates in the time-phase domain. Just like existing models this introduces an entirely new class of processing methods and algorithms applicable to signal analysis, modification and synthesis.
Signals are represented as a separation into timbre, pitch, amplitude envelope and phase offset. The timbre is visualised via a 2D coloured image referred to as cyclogram. We define :
- Pitch: the 'fundamental frequency', 'key' or 'note' as a function of time
- Cyclogram: the pitch-removed time-waveform, transformed into the time-phase domain.
This representation as a split into timbre and other components is referred to as a "sunic". The transformation between a signal and its sunic is lossless and reversible. The split allows to compare and classify audio signals based on their natural characteristics (timbre) independent of their fundamental frequency, amplitude envelope or phase offset. The splitting of a sound into its sunic requires high-accuracy pitch detection with resolutions significantly below sample duration.