Signal Modeling in the Time-Phase Domain

Signals are traditionally modelled in the time domain or in the time-frequency domain. We've developed a fundamentally new approach that 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 the combination of their pitch and cyclogram:

  • pitch: the 'fundamental frequency', 'key' or 'note' as a function of time
  • wave shape or "cyclogram": the pitch-removed time-waveform, transformed into the time-phase domain.

 

The transformation between a signal and its sunic (i.e. the signal's pitch & cyclogram combination) is lossless and reversible.

Cyclograms - an Intuitive Visualisation

The cyclogram can be either visualised as a three dimensional graph or by rendering colour-coded signal values in the time-phase plane. This delivers a visual fingerprint unique to the signal, featuring graphical patterns that reveal signal characteristics, trends and events at a glance. In analogy to spectrograms, these visualisations are referred to as cyclograms.

 

The compact yet detailed appearance of cyclograms accelerates identification, assessment and navigation within long time series.

 

Image-Based Signal Processing

The nature of typical waveshape data allows to apply standard image processing algorithms such as 'blur', 'sharpen', 'contrast', even 'liquify' or 'twist'. If the results are transformed back into the time domain, the results are strikingly intuitive and effective.

 

Existing image recognition technologies can be leveraged to implement automated assessment processes that prove to be more accurate and stable than e.g. spectral approaches.

 

A New Discipline in DSP

The development of new processes as part of an evolving scientific discipline dealing with time-phase domain represenations is in its infant days. But it is already showing results that can not be achieved with traditional algorithms. See examples in our audio section.