**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.

**My music player has sound visualisation - are Sunics related to this ?**

**How does Sunics relate to the Fourier Transform ?**

**What type of signals can Sunics be applied to ?**

**What is the definition of 'cycles' used by Sunics ?**

**What is the 'pitch' of a signal ?**

**What is the 'wave shape' of a signal ?**

**Can the colouring of the images be changed ?**

**Can the range and distribution of colours be changed ?**

**What is the difference between Sunics and a 'Waterfall' diagram ?**

**What is the 'normalisation' of the data ?**

**How well does Sunics perform computationally ?**

**Can Sunics be implemented on devices with limited capacity ?**

** **

**My music player has sound visualisation - are Sunics related to this ?**

No, not at all. Media players generate images which are influenced by the sound. Sunics show the sound itself.

**How does Sunics relate to the Fourier Transform ?**

Sunics does not involve spectral analysis or transformation into the frequency domain. It is as an alternative way of modelling a signal. Roughly speaking, Fourier splits a signal into its overtones - while Sunics splits it into its timbre and pitch.

**What type of signals can Sunics be applied to ?**

Any signal, time-series or data can be modelled as Sunic, if the following holds true:

- allows for the definition of 'cycles' (see next question)
- consists of a relatively large number of cycles, i.e. hundreds or thousands.

Put simply, any data that represents a vibration, oscillation, rotation, pulsating, knocking or other type of repetitive process of some duration can be modelled and visualised via Sunics.

**What is the definition of 'cycle' used by Sunics ?**

The definition of what constitutes a cycle depends on the context of the signal. Generally, a cycle represents one of a succession of recurring signal segments, such as:

- a period of a sound wave
- a cardiac cycle
- a full rotation of a shaft
- a lunar month.

For each of these examples, a cycle represents a unit of information for which comparison and trend analysis is of some importance.

**What is the 'pitch' of a signal ?**

The pitch is the number of cycles occurring within a fixed time. Depending on the context, this is defined by e.g. the note of a sound, the pulse rate of a heart or the rotation speed of a machine.

**What is the 'wave shape' of a signal ?**

The wave shape represents the geometric shape of the time-waveform considered over the duration of a cycle. To make it comparable, it is expressed as a mathematical function over the interval [0,1], thus independent of the length of the originating cycle (see normalisation).

For example, a sine wave at 50Hz and a sine wave at 100Hz both have the same wave shape, commonly referred to as 'sine'. Other examples include 'square' or 'sawtooth' wave shapes. If you say 'eeeee', you produce a sound with a wave shape that you may call the 'e' wave shape.

In most cases, the wave shape of a signal changes over time, however. If you say 'eeooo', you create a sound that changes its wave shape from 'e' to 'o' as time evolves.

Sunics images show exactly this change of wave shape. At a glance, you can tell if the sound is an 'eeeee', an 'eeooo' or something crazy like an 'eeowaahooa'.

**Can the colouring of the images be changed ?**

Yes. The colouring is a visualisation option that can be changed to suit the application and user preferences.

This choice is made in consideration of aspects such as range and distribution of signal values, accessibility, standards and personal taste.

**Can the range and distribution of colours be changed ?**

Yes. For signals where small deviations from the base line are important, such as ECG recordings, more colours are used to represent the range around the base line. This highlights even small changes in distinct graphical patterns.

For signals with a more evenly distributed range of values, such as audio signals, a equal distribution of colours is of advantage.

**What is the difference between Sunics and a 'Waterfall' diagram ?**

Waterfall diagrams are created by splitting time-waveforms into segments or 'windows' of fixed duration. In most cases, this segmentation produces overlapping or gaps causing replication or loss of data. In some instances, multiple segments are averaged to one, causing a further loss of potentially important information. A waterfall representation is given in time-time coordinates.

Sunics is based on a segmentation into the cycles or 'periods' of the time-waveform. The segmentation takes into account the varying duration of these cycles. No data is lost or replicated and no averaging is performed to ensure that all detail, in particular the occurence of short events, is preserved. Sunics are modelled in the time-phase domain.

**What is the 'normalisation' of the data ?**

During the calculation of a Sunic model, the time intervals of all cycles of the time-waveform are rescaled to the norm interval [0,1]. The original cycle lengths are stored as the Sunic's pitch.

With all cycle data normalised to equal duration, the geometric shape of the time-waveform over the length of a cycle becomes independent of the signal pitch, defining the wave shape.

**How well does Sunics perform computationally ?**

As a rule of thumb, it takes less time to calculate the Sunic of a signal than the duration of the signal is. In this sense, the calculation is 'real-time'.

**Can Sunics be implemented on devices with limited computational capacity ?**

Yes. The accuracy of the modelling algorithm and resulting data can be reduced to suit lower memory and processing capabilities. Despite this reduction, the features and benefits of Sunics are still applicable.