Translations:Wavelet processing/33/en

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A spiking filter converts the input wavelet into an approximation of a perfect spike signal. Wavelet spiking generally is implemented in the time domain; other options can be obtained conveniently in either domain. In the frequency domain, the minimum-phase wavelet spectrum can be found with the Hilbert transform. In particular, this minimum-phase spectrum can be computed as the Hilbert transform of the wavelet’s log-amplitude spectrum. In other words, the minimum-phase spectrum and the log-amplitude spectrum are a Hilbert transform pair, as shown in Silvia and Robinson (1979)[1].

  1. Silvia, M. T., and E. A. Robinson, 1979, Deconvolution of geophysical time series in the exploration for oil and natural gas: Elsevier.