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DECOMPOSITION OF HARDY FUNCTIONS INTO SQUARE INTEGRABLE WAVELETS OF CONSTANT SHAPE
An arbitrary square integrable real-valued function (or, equivalently, the associated Hardy function) can be conveniently analyzed into a suitable family of square integrable wavelets of constantExpand
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Wave propagation and sampling theory—Part I: Complex signal and scattering in multilayered media
From experimental studies in digital processing of seismic reflection data, geophysicists know that a seismic signal does vary in amplitude, shape, frequency and phase, versus propagation time ToExpand
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Wave propagation and sampling theory—Part II: Sampling theory and complex waves
Morlet et al (1982, this issue) showed the advantages of using complex values for both waves and characteristics of the media. We simulated the theoretical tools we present here, using theExpand
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Sampling Theory and Wave Propagation
In the seismic reflection method, the seismic signal does vary in amplitude, shape, frequency and phase versus the propagation time.
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Transforms associated to square integrable group representations. I. General results
Let G be a locally compact group, which need not be unimodular. Let x→U(x) (x∈G) be an irreducible unitary representation of G in a Hilbert space H(U). Assume that U is square integrable, i.e., thatExpand
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TRANSFORMS ASSOCIATED TO SQUARE INTEGRABLE GROUP REPRESENTATION. 2. EXAMPLES
We give examples of integral transforme defined through square integrable group representations, described in the first paper of this series. We focus on the Weyl and «ax+b» groups and study theirExpand
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Wave propagation and sampling theory; discussion and reply
Investigating waves for sedimentary series, Morlet et al. start from basic formulas for elastic waves. I have compared formulas used by Morlet et al. for: (a) compressional velocity of elastic waves,Expand
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Reply by J. Morlet to J. D. Laski
Point (a): I agree with this remark. Here for 3‐D propagation medium, one must use the bulk modulus K rather than Young’s modulus E, which must be strictly restricted to the case of a 1‐D propagationExpand