The Bivariate Mixture Space: A Compact Spectral Representation of Bivariate Signals

Presti G. The Bivariate Mixture Space: A Compact Spectral Representation of Bivariate Signals. J Audio Eng Soc. 2023;71(7/8):481-491. doi:10.17743/jaes.2022.0090

@article{Presti2023_22153,
  author = {Presti, Giorgio},
  title = {{The Bivariate Mixture Space: A Compact Spectral Representation of Bivariate Signals}},
  journal = {Journal of the Audio Engineering Society},
  volume = {71},
  number = {7/8},
  pages = {481--491},
  year = {2023},
  month = jul,
  publisher = {Audio Engineering Society},
  doi = {10.17743/jaes.2022.0090},
  url = {https://doi.org/10.17743/jaes.2022.0090}
}

TY  - JOUR
TI  - The Bivariate Mixture Space: A Compact Spectral Representation of Bivariate Signals
AU  - Presti, Giorgio
T2  - Journal of the Audio Engineering Society
J2  - J. Audio Eng. Soc.
VL  - 71
IS  - 7/8
SP  - 481
EP  - 491
PY  - 2023
DA  - 2023/07/06
DO  - 10.17743/jaes.2022.0090
UR  - https://doi.org/10.17743/jaes.2022.0090
PB  - Audio Engineering Society
LA  - en
AB  - The Fourier Transform (FT) is a widely used analysis tool. However, FT alone is not suited for the analysis of bivariate signals, e.g., stereophonic recordings, because it is not sensitive to the relationship between channels. Different works addressing this problem can be found in the literature; the BivariateMixture Space (BMS) is introduced here as an alternative representation to the existing techniques. BMS is still based on the FT and can be thought of as an extension of it, such that the relationship between two signals is considered as additional information in the frequency domain. Despite being simpler than other techniques aimed at representing bivariate signals, this representation is shown to have some desirable characteristics that are absent in traditional representations, which lead to novel ways to perform linear and non-linear decomposition, feature extraction, and data visualization. As a demonstrative application, an Independent Component Analysis algorithm is derived from the BMS, which shows promising results with respect to existing implementations in terms of performance and robustness.
ER  -