Abstract
Group theory is one of the cornerstones of wavelet analysis. Indeed, at a very general level, one may say that the following three concepts are equivalent: (i) a square integrable representation U of a group G; (ii) coherent states over G; (iii) the wavelet transform associated to U.This analysis is familiar in the two standard cases [1], which have been thoroughly discussed during this colloquium:
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(i)
the affine (ax+b) group, which yields the usual wavelet analysis;
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(ii)
the Weyl-Heisenberg group, which leads to various phase space or time- frequency representations.
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References
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© 1990 Springer-Verlag Berlin Heidelberg
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Antoine, JP. (1990). Poincaré Coherent States and Relativistic Phase Space Analysis. In: Combes, JM., Grossmann, A., Tchamitchian, P. (eds) Wavelets. inverse problems and theoretical imaging. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-75988-8_20
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DOI: https://doi.org/10.1007/978-3-642-75988-8_20
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