Hybrid linear/quadratic time-frequency attributes

We present an efficient method for robustly calculating time–frequency attributes of a signal, including instantaneous mean frequency, bandwidth, kurtosis, and other moments. Most current attribute estimation techniques involve a costly intermediate step of computing a (highly oversampled) two-dimensonal (2-D) quadratic time–frequency representation (TFR), which is then collapsed to the one-dimensonal (1-D) attribute. Using the principles of hybrid linear/quadratic time–frequency analysis (time–frequency distribution series), we propose computing attributes as nonlinear combinations of the (slightly oversampled) linear Gabor coefficients of the signal. The method is both computationally efficient and accurate; it performs as well as the best techniques based on adaptive TFRs. To illustrate, we calculate an attribute of a seismic cross section.