On the Local Behavior of Spaces of Spectrograms

This project adapts the framework introduced by Carlsson et al. in On the Local Behavior of Spaces of Natural Images (2008) to the domain of audio signals. Where the original work revealed that high-contrast patches from natural images concentrate on a topologically nontrivial subspace, we ask whether analogous structure emerges in local patches extracted from time-frequency representations of audio. Following the same methodology, we apply persistent homology to filtered audio patch spaces and characterize the resulting topology. We further examine how different classes of audio signals distribute across this manifold, treating topological distance as a basis for comparison across speaker populations.