Reproduce “PolarBM: Complex-valued Boltzmann Machine for Modeling Audio Signals in Polar and Log-polar Coordinates” on OpenResearch

About this paper

Toru Nakashika, Kohei Yatabe

Researchers from The University of Electro-Communications and Tokyo University of Agriculture and Technology developed PolarBM and LogPolarBM, novel Boltzmann machine frameworks that directly model complex-valued data, particularly audio signals, in polar and log-polar coordinates. LogPolarBM achieves superior speech reconstruction quality (e.g., PESQ of 4.00, MOS of 4.65) compared to state-of-the-art deep learning and signal processing methods by explicitly capturing the interdependence between amplitude and phase and incorporating logarithmic amplitude modeling.

Key insights

• Explicitly modeling complex-valued data in polar coordinates and capturing the inherent interdependence between amplitude and phase is more effective for signal representation than using Cartesian or decoupled complex representations.
• Incorporating logarithmic amplitude modeling into the Boltzmann Machine framework enhances the ability to represent audio signals, aligning with human auditory perception mechanisms.
• The derived Power-Weighted Noncentral Complex Gaussian (PW-NCCG) distribution offers a flexible probabilistic framework that can model diverse signal characteristics and generalizes several established statistical distributions.

Summary by alphaXiv.