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Find the DFT of a sequence x(n)={1,2,3,4,4,3,2,1}using radix-2 DIT algorithm.
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Solution:

The twiddle factors associated with the flow graph are,

$ \begin{aligned}\\ &w_8{ }^9=1, \quad w_8{ }^{\prime}=\left(e^{-j 2 \pi / 8}\right)^{\prime}=e^{-j \pi / 4}=0.707-j 0.707 \\\\ &w_8{ }^2=\left(e^{-j 2 \pi / 8}\right)^2=e^{-j \pi / 2}=-j \\\\ &w_8{ }^3=\left(e^{-j 2 \pi / 8}\right)^3=e^{-j 3 \pi / 4}=-0.707-j 0.707\\ \end{aligned}\\ $

enter image description here

$ \begin{aligned}\\ x(k)=&\{20,-5.828-j 2.414,0,-0.172-j 0.414,0,\\\\ &-0.172+j 0.414,0,-5.828+j 2.414\}\\ \end{aligned}\\ $

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