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If x(n)={2,3,4,5} i) Find DFT of x(n)using DIT-FFT ii) If y(n)=x(n-1)Find DFT of y(n) iii) m(n)=x(n)+jy(n). Find DFT of m(m)using above results only.
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Output of stage 1

S1(0)=x(0)+x(2)=2+4=6

S1(1)=x(0)x(2)=24=2

S1(2)=x(1)+x(3)=3+5=8

S1(3)=x(1)x(3)=35=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=68

X(3)=S1(1)S1(3)W14=22j

X(K)=14,2+2j,2,22j

ii) y(n)=x(n-1), Find DFT of y(n)

by circular shifting property

x(nl)()DFTX(K).ej2πklN

x(n1)()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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