SpharaPy: A Python toolbox for spatial harmonic analysis of non-uniformly sampled data

Abstract

SpharaPy is a Python implementation of a new approach for spatial harmonic analysis (SPHARA). SPHARA extends the classical spatial Fourier analysis to non-uniformly positioned samples on arbitrary surfaces in R3. The basis functions (BF) used by SPHARA are determined by the eigenanalysis of the discrete Laplace–Beltrami operator, which is defined on a triangular mesh specified by the spatial sampling points. The SpharaPy Python toolbox provides classes and functions to compute the SPHARA BF for data analysis and synthesis as well as classes to design and apply spatial filters. An illustrative example of applying the SpharaPy package in the field of biosignal processing using electroencephalography data is presented. Keywords: Spatial harmonic analysis, Eigenanalysis of the discrete Laplace–Beltrami operator, Generalized spatial Fourier analysis, Spatial filtering, Online filtering, EEG Data Processing