Sine Wove Porameters 



H 



m 



8 



4> 



1 

 1 

 1 



98 

 120 

 161 



02 

 04 

 -0.4 



-1.20 

 -1 48 

 -1.97 



D Acfuol Phase of Sine Wove 

 ° Phase Estimated by Eg, (24) 



80 



Figure 10. 



100 



120 

 Frequency (Hz x 1024) 



140 



160 



Phase versus frequency from FFT analysis of artificial 

 signal composed of three sinusoidal waves, with N = 4,096 

 and At = 0.25 second. 



The phase variations which can be induced by FFT analysis are thus con- 

 siderable. Spectral phases calculated when the cosine bell data window is 

 used are equally if not more variable. Harris' (1974) analysis for a single 

 sinusoidal wave indicates three successive phase shifts of it radians at 

 three adjacent analysis frequencies surrounding the true peak when the cosine 

 bell window is used. If phases are constrained to an interval of ir radians, 

 phases very near the peak are given by equation (24) . 



These difficulties in producing a reasonably accurate estimate of spectral 

 phase and in getting high resolution in frequency for relatively short records 

 may have been a major factor in leading previous investigators to conclude 

 that spectral components are independent and their phases are random. An 

 essential step in this study was to devise a method for estimating prominent 

 frequencies, amplitudes, and phases, a method free of the above limitations. 



c. Multiple Regression Screening Analysis . A technique which appears to 

 give consistent phase information and avoids the direct resolution versus 

 record length trade-off inherent in the FFT is the MRS. Although the MRS has 

 apparently never been applied to ocean wave record analysis, it appears to 

 have real advantages over the FFT analysis for the purposes of this study. 



The MRS analysis fits, in the least squares sense, a sum of sinusoids with 

 preassigned frequencies to a given data record. The analysis identifies and 



32 



