SPECIAL PROBLEMS IN THE ESTIMATION OF POWER-LAW SPECTRA AS APPLIED TO TOPOGRAPHICAL MODELING

An increasing number of topographical studies find that natural surfaces possess power-law roughness spectra. Power-law spectra introduce unique difficulties in the spectral estimation process. We describe how an improper window choice allows leakage that yields a spectral estimate that is insensitive to the spectral slope. In addition, the commonly used Fourier-based spectral estimates have higher variances than other available estimators. Higher variance is particularly problematic when data records are short, as is often the case in remote-sensing studies. We show that Capon's spectral estimator has less variance than Fourier-based estimators and measures the spectral slope more accurately. We also show how estimates of a 2-D roughness spectrum can be obtained from estimates of the I-D spectrum for the isotropic power-law case.