Time - frequency and time - scale methods
نویسندگان
چکیده
and the corresponding inversion formula analyze the frequency content of f . Underlying many finer decompositions into simpler pieces are the fundamental invariance properties of R and the corresponding operators. For harmonic analysis on R these are the translations t → t+x and the dilations t → at, where t, x ∈ R and a ∈ R. The corresponding operators are the translation operator Tx (2) Txf(t) = f(t− x) t, x ∈ R , and the dilation operator Da (3) Daf(t) = |a|−d/2f(t/a) . To achieve symmetry with respect to the Fourier transform, we add the modulation operators Mξ:
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