
Output of stage 1
S1(0)=x(0)+x(2)=2+4=6
S1(1)=x(0)−x(2)=2−4=−2
S1(2)=x(1)+x(3)=3+5=8
S1(3)=x(1)−x(3)=3−5=−2
Final Output
X(0)=S1(0)+S1(2)W04=6+8
X(1)=S1(1)+S1(3)W14=−2+2j
X(2)=S1(0)−S1(2)W04=6−8
X(3)=S1(1)−S1(3)W14=−2−2j
X(K)=14,−2+2j,−2,−2−2j
ii) y(n)=x(n-1), Find DFT of y(n)
by circular shifting property
x(n−l)(↔)DFTX(K).e−j2πklN
x(n−1)(↔)DFTX(k).WK4
Y(0)=X(0).W04=(14×1)=14
Y(1)=X(1).W14=(−2+2j)(−j)=+2+2j
Y(2)=X(2)W24=(−2)(−1)=2 …
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