dimensional cubic spline, which tends to preserve frequency content. 

 The full algorithm Is Included In SUBROUTINE MAPCTN. 



The subsequent stage of processing requires band-pass filtering of 

 the Interpolated data at ten nearly equl-spaced frequency bands. Fil- 

 tering is done by sequential application of low-pass and high-pass 

 filters, using a non-recursive, symmetric, least-squares filter devel- 

 oped by Martin (1957). The frequency response of this bank of filters 

 Is Illustrated In Figure B-1. A review of the performance of the Martin 

 filter can be found In McClaln and Walden (1979). The filter cutoffs 

 are designed to juxtapose at the 100% energy pass level. The total fre- 

 quency bank was selected to span .02 - .25 cycles/data Interval, or 

 wavelengths of approximately 2 - .16 nautical miles for data recorded at 

 12 second Intervals, or 10 - .8 nautical miles for one minute data. The 

 filtering Is performed by SUBROUTINE FILTER. 



The next step of the algorithm requires estimating the Instanta- 

 neous amplitude of all ten band-passed signals. Davis (1974) used a 

 simple full-wave rectification, followed by a low-pass smoother to esti- 

 mate the energy envelope. For this study, a true Hllbert transform Is 

 performed and manipulated to generate the energy envelope. The reader 

 Is referred to Kanasewlch (1981) for a full development. Notice that 

 the calculation of the envelope via Hllbert transform does require oper- 

 ating In the frequency domain. However, because the complete Fourier 

 Transform Is retained throughout, the requirement of statlonarlty Is not 

 applicable. The enveloping algorithm Is contained In SUBROUTINE ENVEL. 



The envelope generated In the previous step represents a continuous 

 estimate of amplitude through space, for each selected frequency band. 

 To estimate the full amplitude spectrum at each point on the profile. 



136 



