The Hilbert transform (HT) has been used in seismic data processing and interpretation for many years. A well-known application of HT is seismic complex-trace analysis using instantaneous phase, frequency, and amplitude (Taner et al. 1979). We present a new generalized Hilbert transform (GHT), which has many advantages over the traditional HT—particularly robustness to noise and variety of applications.

A simplified definition of GHT is that it can be considered a windowed traditional HT. A more accurate description of GHT, and the mathematical definition of GHT, will be given later.

Recently, the windowed Fourier transform was developed to allow more flexibility...

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