Homework

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Revision as of 09:25, 10 December 2004 by Guenan (talk | contribs) (Homework #9)
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Homework #9

Problem Statement:
Show that, for a bandwidth limited signal (x(t) with fmax<12T)
k=|x(kT)|2=c|x(t)|2dt
And find c.

Equations:
ϕk(t)|ϕl(t)=ϕk(t)*ϕl(t)dt
x(t)=k=x(kT)ϕk(t)
Solution:
x(t)|x(t)=x(t)*x(t)dt=|x(t)|2dt
x(t)=k=x(kT)ϕk(t)
x(t)|x(t)=k=x(kT)ϕk(t)|l=x(lT)ϕl(t)=k=l=x(kT)x(lT)ϕk(t)|ϕl(t)