46 



2 ,2 n n 

 TTk X y 



(A. 23) 



^ = 



- 4 



itrk" 



/ V 3,2 



S (c5 + -r k S 



nn 4 

 _ yy Y_ 



^n^^^ 



(A.2A) 



The truncated Fourier series directional spectrum is now 

 easily developed from Equation A. 14. 



If two measurements each are accurately made of r\^ and r\ , it 

 would be possible to generate all of the first and third coefficients 

 four different ways and the second coefficients two different ways 

 using various combinations of the differential gauges in auto- and 

 cross-spectra. The instrument software, (re-printed in Appendix F) , 

 generates each of the possible coefficients. There are two 

 advantages here. The program will use the mean value of each 

 calculated angular Fourier coefficient in generating the directional 

 spectrum if it is decided that each transducer is working correctly. 

 If it is concluded that a transducer is malfunctioning during a 

 sampling interval, the program will disallow that transducer's signal 

 during the final coefficient calculation. The redundancy of the 

 transducers' measurements, then, would offer a potentially more 

 accurate estimate of the directional Fourier coefficients as well as 

 a first-stage failsafe mechanism if one of the differential 



