general form 



B(t, T) =/ x(t^ T)A(t-t')dt' 

 •'-co 



where the linear filter x(t, t) represents the distor- 

 tion of the pulse due to the backscattering surface. The 

 second moment of the signal is therefore given by 



R(ti, t2, T) =jj^ <x(t% T^+T)x*(f, T^)>A(ti-t')A*(t2-t")dt'dt" 



For most scattering models (including the ones discussed 

 here) the autocorrelation of the filter function is signifi- 

 cantly non-zero only for time differences t^ - t" of the 

 order of the carrier period. Hence in integrating over the 

 much longer pulse duration the second moment of x may be 

 approximated by a o -function, 



<x(t^ T'+T)x*(t", T^)> = P(t', T)6(t'-t") 



which yields 



R(ti, t2, 1) = J A(ti-t')A*(t2-tOP(t^T)dt^ 



—00 



or, in terms of the doppler spectra^ 



T(ti, t2, ^) " J A(ti-t')A*{t2-t")S(t", CO)dt" 



25-31 



