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(iii) (3)/(4)N=2pi k=> There is no N such that (3)/(4)N=2pi k , so x[n] is not periodic. (b) For discrete-time signals, if Omega _(x)=Omega _(y)+2pi
(iii)
(3)/(4)N=2\\\\pi k=>
There is no
N
such that
(3)/(4)N=2\\\\pi k
, so
x[n]
is not periodic.\ (b) For discrete-time signals, if
\\\\Omega _(x)=\\\\Omega _(y)+2\\\\pi k
and
\\\\Omega _(x)\\\\tau _(x)+\\\\theta _(x)=\\\\Omega _(y)\\\\tau _(y)+\\\\theta _(y)+2\\\\pi k
, then
x[n]=y[n]
.\ (i)
,(\\\\pi )/(3)!=(8\\\\pi )/(3)+2\\\\pi k
(the closest is
k=-1
), so
x[n]!=y[n]
\ (ii)
\\\\Omega _(x)=\\\\Omega _(y),(3\\\\pi )/(4)(2)+(\\\\pi )/(4)=(3\\\\pi )/(4)-\\\\pi +2\\\\pi k,k=1
, so
x[n]=y[n]
\ (iii)
\\\\Omega _(x)=\\\\Omega _(y),(3)/(4)(1)+(1)/(4)=(3)/(4)(0)+1+2\\\\pi k,k=0,x[n]=y[n]
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