the model parameters. Also, the Fourier transform method has the addi- 

 tional advantage of estimating the amplitude at many more frequencies 

 than the ten bands arbitrarily selected for the spatial domain 

 algorithm. 



Since the proper generation of spectra Is the basis for the entire 

 model, great care has been taken to ensure that the best estimate of the 

 true amplitude spectrum are obtained. The techniques used are described 

 In detail by Davis (1974) and will only be reviewed here. The computer 

 software used In this study was modified from programs provided by T.M. 

 Davis and Is presented as Appendix D. 



In using a finite length sample to represent an Infinite series, 

 the observer has In effect multiplied the Infinite series by another 

 Infinite series consisting of zeros beyond the sample and ones at all 

 sample locations. The multiplication of this so-called "boxcar" func- 

 tion In the spatial domain, causes the true transform of the signal to 

 be convolved with the boxcar's transform, a sine function, In the fre- 

 quency domain (see Bracewell, 1965). The presence In the frequency 

 domain of side lobes on the sine function, causes energy to be "leaked" 

 Into adjacent frequencies during convolution. Because of the red-noise 

 character of spectra of sea-floor topography, this "leakage" tends to 

 transfer energy artificially from lower to higher frequency. 



Although the use of tapered windows rather than boxcar sampling 

 tends to reduce leakage, the preferred technique uses the method of pre- 

 whltenlng. Tapered windows have a sine function transform with reduced 

 sldelobes and a broadened malnlobe, which reduce spectral leakage at the 

 expense of spectral resolution. In prewhltenlng, a specially designed 

 high-pass filter Is convolved with the signal, modifying It such that 



49 



