TM No. 377 



The Coastal Engineering Research Center (CERC) has developed an analog 

 spectrum analyzer (see Caldwell and Williams,, 1963) that abstracts the wave 

 data from magnetic tape having a recording speed of 1.27 cm min = l, Samples 

 of 10 minutes are generally made. The tape is scanned by a tape-reading 

 device (at a speed of l60 cm sec"" 1 ) which contains a set of band-pass filters 

 and detectors for continuous automatic sweeping of the record at chosen fre- 

 quencieSc These filters range from 2 cycles sec~l to 200 cycles sec"l. Since 

 the data tape is played back into the detector at a much higher speed., the 

 original signal frequency increases by a factor of 7^500* Thus, a 0.5 cps 

 (2 second period) signal on the tape appears as a 3>750 cps signal to the 

 scanner. From an electronic point of view,, it is much easier and less ex- 

 pensive to fabricate narrow bandwidth filters to work in high frequency 

 ranges (i.e., a few kilocycles sec~l) than in the relatively low frequencies 

 peculiar to ocean waves (i.e., below 3 cps). By artificially increasing the 

 frequency of the wave gauge signal, a signal is produced which is quite amen- 

 able to narrow and accurate bandpass filtering . The analog spectrum analyzer 

 breaks the signal, and the signal squared, into their Fourier component fre- 

 quencies by electronic filtering in a range of bandwidths. The system then 

 produces an automatic plot of the voltage analog of the average wave height, 

 and of the average squared wave height,, against the real frequency. 



No effort has been made in the preceding brief summary to discuss in 

 detail the complexities of the CERC analog spec-crum analyzer. According to 

 workers at CERC (Williams., 1964), it is difficult to predict how auto-spectra 

 obtained by the Tukey digital method (discussed in chapter III) will compare 

 with the analog spectra A rough comparison of spectra obtained by the CERC 

 spectrum analyzer with spectra from digital methods is given by Mobarek (1965). 

 From actual comparison,, together wixh some empirical reasoning, Mobarek arrives 

 at factors for converting the "squared average" analog spectrum of the CERC 

 analyzer to the digital Tukey spectrum. Mobarek 3 s reasoning is worth examining. 



The analog spectrum analyzer provides the spectra of the wave height 

 distribution, whereas the digital analysis provides the spectra contribution 

 to the variance of the wave amplitude. Hence, the analog spectra are large 

 by a factor of four. 



Because of the manner of integrating and averaging the spectral energy 

 over frequency,, the energy per unit bandwidth of the digital method is not 

 automatically equivalent to the energy per unit bandwidth over which the 

 averaging is done in the spectrum analyzer. In the digital method, the energy 

 in the harmonics about a certain frequency band is integrated, and this sum 

 is depicted as existing at the center of the band. On the other hand, the 

 spectrum analyzer sums up energy over a 0.027 cycle sec" 1 interval. Thus, the 

 spectral energy must be made equivalent for a unit frequency sampling interval. 

 For the wave motion spectra a frequency resolution of A-f =(2'>nAT)"' was used. 

 When ynz.so and 4Tr 0'1 second, Af =o»05O cps. The energy spectrum of the analog 

 computer can therefore be made commensurate with the digitally computed spec- 

 trum by multiplying the analog spectrum function by the ratio of (0.050)(0.027r 

 or 1.9. 



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