TM No* 377 



spectrum is substantially flat. The larger the value of M, the greater is 

 the resolution over the chosen frequency band given by; 



Thus, since the quantity AT is the time interval between successive obser= 

 vations (or interpolation points), the spectral estimates are centered at 

 frequencies: 



The Nyquist frequency position is that at which: 



£* = -*>i = ~i t - 4n • (ni-7) 



According to Blackman and Tukey (1958)* it is not desirable to use lags 

 longer than a moderate fraction (perhaps 5 or 10 percent) of the length of 

 the record* Thus, the magnitude of P\ should be adjusted so as to give 



where T is the length of the records Thus,, the value of AT determines the 

 highest frequency -f K to be studied, and the value of T determines the lowest , 



In making a statistical analysis of wave data, one must be aware that a 

 certain indeterminacy or variability of precision is inherently associated 

 with the estimates «. This degree of uncertainty is directly related to the 

 statistical methods of analysis i and is over and above those uncertainties 

 in the data caused by such instrumental deficiencies as limitations in 

 frequency response , or biasing of the sensor or the recording systems 



It may be helpful to consider briefly the fundamental method of estimating 

 the precision of spectral estimates, as presented by Blackman and Tukey (1958) 

 and elaborated upon by Kinsman (1965).- Given a series of random variables 



*•>**, >V" *V" xp • (III " 8) 



each of which can be represented by a standard normal or Gaussian distribution 

 with a mean equal to zero and a variance of unity (hence, having a standard 



52 



