A Signal-Size Estimator Based on Correlation-Dimension For Auditory Signals

This paper presents an estimator of fractal signal sizes based on correlation fractal dimension as applied to auditory signals. Correlation fractal dimension has been proposed for characterization of signals coming from chaotic sources. Practical estimations are made possible using a Takens algorithm, producing different estimates in each embedding dimension. The estimator consists of four processes: (i) signal measures creation, (ii) covering-counting, (iii) critical-exponent estimation, and (iv) size calculation. We study the resulting estimates of controlled signals to validate the estimator as well as to come up with a calibration scheme. The paper further discusses a possible application of fractal sizes to characterize coughs to identify the presense of respiratory diseases, such as in Covid-19 pre-screening.