Extensions of the Heisenberg Group by Dilations and Frames
نویسندگان
چکیده
Two standard tools for signal analysis are the short{time Fourier transform and the continuous wavelet transform. These tools arise as matrix coeecients of square integrable representations of the Heisenberg and aane groups respectively, and discrete frame decompositions of L 2 arise from approximations of corresponding reproducing formulae. Here we study two groups, the so-called aane Weyl-Heisenberg and upper triangular groups, which contain both aane and Heisenberg subgroups. Generalized notions of square{integrable group representations allow us to fashion frames for L 2 and other function spaces. Such frames combine advantages of the short-time Fourier transform and wavelet transform and can be tailored to analyze speciic types of signals.
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