PROPERTIES OF SINE WA VE PLUS NOISE 



145 



of this section, may be checked by inserting (7.28) in the expression (7.16) 

 for fi(r) in terms of yi and y2. 



Values of yi and yo tabulated as functions of k for various values of p are 

 given in Table 3. Negative values of k have not been considered since they 



Table 3 



Values of yi and y z Used in Comp utation of Correlation Function of dd/dt 



n(r) = d'{t)d'it + r) = [g'^(y, - y,) - gi''y,]/(2g^) 



g = gir) 



-i 



w(f) cos Irrif - f,)r df, k = g(r)/g(0) 



are not required for the case in which In has a normal law power spectrum, 

 the case discussed in the next section. 



8. Power Spectrum of — When I^ has Normal Law Power Spectrum 

 dt 



The problem of computing the power spectrum W(f) of d'{t) appears to 

 be a difficult one.* In order to obtain an answer without an excessive amount 

 of work we have had to do two things which are rather restrictive. First, 

 we confine our attention to the case in which the power spectrum w{f) of 



*Since the above was written the general f . m. problem has been studied by D. Middle- 

 ton. He generalizes our (7.11) and (7.12), introduces polar coordinates, expands the 

 integrand in powers of g, and integrates termwise. W(f) then follows somewhat as in 

 a.m. theory. 



