  The objective of this study is to detect and quantify the periodic behavior
of the signals using topological methods. We propose to use delay-coordinate
embeddings as a tool to measure the periodicity of signals. Moreover, we use
persistent homology for analyzing the structure of point clouds of
delay-coordinate embeddings. A method for finding the appropriate value of
delay is proposed based on the autocorrelation function of the signals. We
apply this topological approach to wheeze signals by introducing a model based
on their harmonic characteristics. Wheeze detection is performed using the
first Betti numbers of a few number of landmarks chosen from embeddings of the
signals.
