Fourier Paradoxes

Sierra J. Fourier Paradoxes. In: Convention Paper. Audio Engineering Society; 2024. Paper 10195. Available from: https://aes.org/publications/elibrary-page/?id=22698

@inproceedings{Sierra2024_22698,
  author = {Sierra, Juan},
  title = {{Fourier Paradoxes}},
  note = {Paper 10195},
  year = {2024},
  month = sep,
  publisher = {Audio Engineering Society},
  url = {https://aes.org/publications/elibrary-page/?id=22698}
}

TY  - CPAPER
TI  - Fourier Paradoxes
AU  - Sierra, Juan
M1  - Paper 10195
PY  - 2024
DA  - 2024/09/27
UR  - https://aes.org/publications/elibrary-page/?id=22698
PB  - Audio Engineering Society
LA  - en
AB  - Fourier theory is quite ubiquitous in modern audio signal processing. However, this framework is often at odds with our intuitions behind audio signals. Strictly speaking, Fourier theory is ideal to analyze periodic behaviors but when periodicities change across time it is easy to misinterpret its results. Of course, we have developed strategies around it like the Short Time Fourier Transform (STFT) [1], yet again many times our interpretations of it fall beyond what the theory really says. This paper pushes the exact theoretical description showing examples where our interpretation of the data is incorrect. Furthermore, it shows speci?c instances where we incorrectly take decisions based on such paradoxical framework.
ER  -