Abstract. Let h be a generalized frame in a separable Hilbert space H indexed by a measure space (M, S, µ), and assume its analysing operator is surjective. It is shown that h is essentially discrete; that is, the corresponding index measure space (M, S, µ) can be decomposed into atoms E 1 , E 2 , · · · such that L 2 (µ) is isometrically isomorphic to the weighted space 2 w of all sequences {c i } of complex numbers with ||{c i }|| 2 = |c i | 2 w i < ∞, whereThis provides a new proof for the redundancy of the windowed Fourier transform as well as any wavelet family in L 2 (R).
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