Tikhonov regularization of instantaneous frequency attribute computations

Matt Yedlin, Gary F. Margrave, Daryl Van Vorst and Yochai Ben Horin

ABSTRACT

We present a brief review of the concept of instantaneous frequency, obtained by differentiating the instantaneous phase, computed using the Hilbert Transform. This computation is recast as a Tikhonov regularized linear inverse problem and is compared with the alternative Fomel smoothing regularization . Both smoothing methods, and an equivalent frequency measure obtained via the normalized first moment of the spectrum of the Gabor Transform are applied to synthetic data, an earthquake and a quarry blast. From analysis, a new measure, the local frequency, emerges. The local frequency concept arises directly from the smoothing apparent in all the three algorithms utilized.

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