and 
S(@) = a“ = ay v(@ + 27tn). (2.61) 
n=—© 
As is shown in Fig. 2.7, at frequency wo, the spectra not only of v(wo) but also of 
W(@o + 271), V(Wo + 47), V(Wo £ 62)... .. are folded as the spectrum s(wo), as 
S(W0) = V(W0) + (Mo + 27) + V(Wo + 42) + VM + O2)+.... 
= V(Wo) + V2 + Wo) + V(40 + Wo) +V(6% + W)+..... (2.61’) 
w(wo) + W227 Wo) + v(27 + Wo) t---- 
Fig. 2.7. Aliasing of the spectrum. 
This is also illustrated in Fig. 2.8, where the harmonic functions of not only frequency 
1/5, but also of 4/5, 6/5; 9/5, 11/5; 14/5, 16/5;.... can pass through the same 
sampling point O, as marked in the figure, at Ar = 1 sec intervals (see Table 2.1). 
21 
