Its spectrum appears flat, or white, rather than red. When this pre- 

 whitened signal is then passed through the Fourier transform, there is 

 no preferential transfer of energy in either frequency direction. To 

 obtain the "corrected" spectrum which approximates that of the true 

 (infinite) signal, the prewhitened spectrum is divided by the impulse 

 response of the prewhitening filter. This operation is equivalent to 

 deconvolving the filter in the spatial domain. 



The importance of proper prewhitening can not be overstated. Leak- 

 age of energy into high frequencies would cause a consistent underesti- 

 mation of the magnitude of b (spectral slope), and degrade the ability 

 of the model to estimate high frequency roughness (i.e., overestimation 

 of amplitude at high frequencies). Figure 5-1 illustrates prewhitening 

 by showing a raw spectrum, prewhitened spectrum, and corrected spectrum 

 on one plot. Further examples can be found in Davis (1974). 



Physical Interpretation of Spectral Model Parameters 



Before examining the distribution of the spectral roughness model in 

 selected study areas, it is worthwhile to discuss the physical meaning 

 of the model parameters a and b. The proportionality constant a in the 

 expression 



s^ 



where A » amplitude 



s * spatial frequency 



50 



