SEAWAY 



71 



20 r- 



1.0 _ 



07. 



0.4 



0.6 



0.8 



Fig. 8 1 Wave-amplitude spectrum measured hy Cartwright and Rydill (1957) on a ship at sea 



been reported variously hj": Chang (1!)54, 19.35fl, b); 

 Pierson and Chang (1954); Smith (1955); MarlvS and 

 Strausser (1959); Chadwick and Chang (1957). 



The first successful analog ocean-wave analyzer was 

 developed at the National Institute of Oceanography 

 (Barber, 1949). Narrow filters were used to approxi- 

 mate a Fourier-series analysis of the record (rather than 

 an energy-spectrum analysis). The amplitudes of sev- 

 eral adjacent harmonics in a band are averaged in the ana- 

 log computer and the display, Fig. 81, is one of average 

 amplitude (for 0.05 rad/.sec band) against circular fre- 

 quency. Strictly speaking, this type of analysis will ob- 

 tain spectral estimates, with two degrees of freedom, 

 which are additive with the number of such estimates. 

 The same process obtains from modern wa\-e analyzers 

 only the weighting and averaging is done continuousl.y 

 over the frecjuency band and is conseciucntly not so ol)- 

 vious. 



There are numerous ways of performing the random- 

 signal filtering process. The mo.st efficient method is a 

 bank of filters, each filter centered at a different fre- 

 quency and with a prescribed width (not necessarily the 

 same for all filters). The bank covers the entire fre- 

 quency range of the signal being analyzed and the analy- 

 sis is completed with one passage of the record. Single- 

 filter techniques rec[uire many passages of the input sig- 

 nal (spliced into a loop) as the filter continuously looks at 

 different bands in the frequency content of the signal. 

 Such an analysis may be performed by holding the center 

 frequency of the filter constant and then \'ar>'ing the fre- 

 quencies it looks at by \'arying the speed of passage of 

 the input signal. In this way, the filter always sees a 

 different range of apparent frequencies. Still another 

 method, the one employed in the SEADAC (Marks ami 

 Strausser, 1959) involves the modulation (mixing) of a 

 local oscillator wa\'e with the random signal being ana- 

 lyzed. The oscillator emits a continually varying signal 

 which is the carrier frequency (.say 97,000 cps), plus the 

 frequency that is being e.xamined (.say 100 cps). The 



20.0 



15.0 



MO.O 



3^ 



5.0 







0.245 



Q49I 



0.736 

 We = 2 T^/Te 



0.981 

 [sec-'] 



1.230 



1.470 



Fig. 82 Energy spectrum of a seakeeping record calculated by 

 digital computer and SEADAC (from Marks and Strausser, 



1959) 



modulati(jn jjrocess results in a new signal which has as 

 its components the two signals being mixed (97,100 cps 

 and 100 cps from the random signal), as well as their 

 sum (97,200 cps) and difference (97,000 cps). One of 

 these frequencies must be the standard carrier (97,000 

 c])s) and this is the only component the narrow-band 

 filter permits to pass. This staiulard carrier has an am- 

 plitude proportional to the amplitude of the frequency 

 that is being examined and it is this quantity which is 

 squared and reproduced in graphical form. 



Since digital jjrocedures are well established, the bur- 

 den of proof of eciuality or superiority is on the analog 

 computer. An early experiment in the SEADAC in- 

 volved the comparison of spectra made by analog and 

 digital computations. One result is shown in Fig. 82 

 where the analog spectrum (oscillatory curve) is superim- 



