G,(@1,@2 .. . Wn) = | et | entera, 306 Gy) 
[ee 
n 
exp LS enfin dr (2126) 
j=l 
The function G,(w},@2 .. . @,) is the nth degree frequency response function and 
is also symmetric in its arguments G,(@1,@2 .. . Mn) =Gp(W2,@), ...@,)=... for 
any rearrangement of w; because the impulse response functions are real. 
G,(—@1,-@2, Oy 0 —OW,) = G7(@1,@2, oe Wn) (12.127) 
here the * denotes the complex conjugate. 
In Dalzell’s paper,>° the spectrum S,(w) was defined a little differently from those 
used by this author in Parts I, II, and II. He used 27 times our s(w) , 
S,A(@) = 27s(w), (12.128) 
and also took the one-sided spectrum 
U;,[|@|] = 2s(@) = = 5.(w), forw@ > 0. (12.128’) 
The initially assumed functional polynomial process was reformulated as the 
response to a white noise excitation, and a new set of frequency response functions was 
defined which contains both characteristics of the original frequency response to the 
exCitation and that of the excitation spectrum. 
The two-sided spectrum of white noise is 
Sea ile (12.129) 
and the autocorrelation of white noise is a delta function 
Ry, AT) = = | exp[iwt]dw = 6(t). (12.130) 
We think of the spectrum filter L(w) that expresses the spectrum of input S,.(w) 
with the white noise as 
Six(w) = 0? Lo)? (12.131) 
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