about a constant value. This makes intuitive sense, since one would not 

 expect any particular frequencies to dominate a random series. Again in 

 analogy to the spectrum of visible light, this random component of a 

 signal is often called "white noise", reflecting the equal contribution 

 of all frequencies. 



In the same way that Rayleigh's or Parseval's theorems can be used 

 to relate energy in one domain to energy In the other, the level of 

 noise in a spatial signal can be estimated from the amplitude of the 

 noise level of an amplitude spectrum. The noise level in the spatial 

 domain is normally expressed as a simple dispersion measure of the vari- 

 ability of the data, in this case, the oceanic depths. The following 

 formula relates the white-noise level of the power spectrum to the root 

 mean square. 



RMS 



where n =» number of data points in series; and P = the mean power level 

 of the white noise. In the case of sonar systems, knowledge of this RMS 

 level defines the resolving capability of the system for a given signal 

 level. Using these simple spectral techniques, the resolving power of 

 the various sounding systems in use today can be calculated and 

 compared. 



The red-noise structure of natural systems has been mentioned and 

 Illustrated previously (see Fig. 4-3). The interaction of natural sig- 

 nals with instrument noise takes the form of a decreasing red-noise 

 spectrum of the signal "Intersecting" the horizontal white-noise level. 

 In the spatial domain perspective, lower frequency features tend to have 



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