# Time-frequency or time-scale representation fission and fusion rules

## TL;DR

This paper introduces rules for fission and fusion in time-frequency representations, enhancing real-time analysis of time series by handling discontinuities and invalid regions, with practical system design insights.

## Contribution

It presents novel fission and fusion rules for time-frequency representations, enabling reliable online time-series analysis with handling of data discontinuities.

## Key findings

- Developed an online analysis system for time-frequency data
- Designed fission and fusion rules for time-frequency representations
- Demonstrated system's effectiveness in real-world scenarios

## Abstract

Time-frequency representations are important for the analysis of time series. We have developed an online time-series analysis system and equipped it to reliably handle re-alignment in the time-frequency plane. The system can deal with issues like invalid regions in time-frequency representations and discontinuities in data transmissions, making it suitable for on-line processing in real-world situations. In retrospect the whole problem can be considered to be a generalization of ideas present in overlap-and-add filtering, but then for time-frequency representations and including the calculation of non-causal features. Here we present our design for time-frequency representation fission and fusion rules. We present these rules in the context of two typical use cases, which facilitate understanding of the underlying choices.