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Conclusion

We have presented a novel numerical method for computing time-frequency representation using least-squares inversion with shaping regularization. This time-frequency-analysis technology can be applied to nonstationary signal analysis. The method is a straightforward extension of the classic Fourier analysis. The parameter used in shaping regularization, the radius of the Gaussian smoothing operator, controls the smoothness of time-varying Fourier coefficients. The smooth time-varying average frequency attribute can also be estimated from the proposed time-frequency analysis technology. We have demonstrated applications of the proposed time-frequency analysis for detecting channels and lowfrequency anomalies in seismic images. Finally, we realize that many different algorithms are capable of computing time-frequency representations. We have provided some comparisons of our method with one of them (the S-transform) but cannot make the comparison exhaustive and do not claim that our method will necessarily perform better in all practical situations. Both approaches to time-frequency analysis have advantages and disadvantages. What we see as the main advantages of our method are its conceptual simplicity, computational efficiency, and explicit controls on time and frequency resolution.


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Next: Acknowledgments Up: Liu etc.: Time-frequency analysis Previous: 2D data example for

2013-03-02