CEPSTRUM ALIASING AND THE CALCULATION OF THE HILBERT TRANSFORM
1974; Society of Exploration Geophysicists; Volume: 39; Issue: 4 Linguagem: Inglês
10.1190/1.1440446
ISSN1942-2156
AutoresPaul L. Stoffa, Peter Buhl, George M. Bryan,
Tópico(s)Geophysical and Geoelectrical Methods
ResumoSchafer (1969) has pointed out that the Hilbert transform approach used in computing the minimum‐phase spectrum of a given amplitude spectrum corresponds to a special case of complex‐cepstrum analysis in which the phase information of the original function is ignored. The resulting complex cepstrum is an even function. Since a minimum‐phase function has no complex‐cepstrum contributions for T<0, its even part must exactly cancel the odd part for T<0. Thus, by setting all complex‐cepstrum contributions for T<0 equal to zero and doubling all contributions for T>0, we obtain the complex cepstrum of the minimum‐phase function corresponding to the original function. However, the DFT-calculated complex cepstrum is an aliased function (Stoffa et al., 1974). Thus some negative periods will appear at positive locations and vice versa. Appending the original function with zeros will reduce the aliasing. Shuey (1972), in computing the Hilbert transform for magnetic data, indicates that the computation breaks down near the end of the profile, or at long cepstrum periods. This is precisely the point in the even cepstrum where aliasing will have its greatest effect.
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