Find the IDIF-FFT for a given sequence X(k)={26, -2+2j, -2, -2-2j}.

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written 6.5 years ago by

teamques10 ★ 69k

• modified 6.5 years ago

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Output stage – 1

$S_1 (0)=X(0)+X(2)=26-2=24$

$S_1 (1)=X(1)+X(3)=-2+2j+(-2-2j)=-4$

$S_1 (2)=[X(0)-X(2) ] W_4^0=(26+2)(1)=28$

$S_1 (3)=[X(1)-X(3) ] W_4^{-1}=(-2+2j-(-2-2j) )(+j)=-4$

Final Output

$x(0)=\frac{1}{4} [S_1 (0)+S_1 (1) ]=\frac{1}{4} [24-4]=5$

$x(2)=\frac{1}{4} [S_1 (0)-S_1 (1) ]=\frac{1}{4} [24+4]=7$

$x(1)=\frac{1}{4} [S_1 (2)+S_1 (3) ]=\frac{1}{4}[28-4]=6$

$x(3)=\frac{1}{4} [S_1 (2)-S_1 (3) ]=\frac{1}{4} [28+4]=8$

$x(n)={5,6,7,8}$

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