(much slower) variation of pulse shape with t arising 

 then through the time dependence of the backscatterlng 

 surface. Assuming that the scattering process is statis- 

 tically stationary with respect to t and that the phase 

 distribution of B is statistically uniform, the first 

 moment of B vanishes and the second moments are given 

 by 



<B(ti, t'+t) B* (t2,T")> = R(tl,t2,T) 

 <B(ti, T^+T) B (t2,T')> = 



The ensemble averages < • • • > may be Interpreted here 

 also as time means with respect to t' 



The doppler spectrum of the general second moment is 

 defined as the Fourier transform 



T(ti, t2, CO) = -i / R(ti, ti, T)e dT. 



2TT J 



T depends on both the shape of the emitted pulse and the 

 statistical properties of the scattering surface. The two 

 effects may be separated by introducing the scattering 

 function, which describes the (input Independent) second- 

 moment statistics of the time-varying "channel" representing 

 the backscatterlng sea surface, cf [17]- 



In terms of the complex envelope A(t) of the trans- 

 mitted pulse, the received pulse can be expressed in the 



25-30 



