Signal analysis and quantum formalism: Quantizations with no Planck constant

Signal analysis is built upon various resolutions of the identity in signal vector spaces, e.g. Fourier, Gabor, wavelets, etc. Similar resolutions are used as quantizers of functions or distributions, paving the way to a time-frequency or time-scale quantum formalism and revealing interesting or unexpected features. Extensions to classical electromagnetism viewed as a quantum theory for waves and not for photons are mentioned.