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Find the DFT of the sequence x[n] = {1, 2, 3, 4, 4, 3, 2, 1} using radix-2 decimation in time FFT algorithm.
1 Answer
written 2.3 years ago by |
Solution:
Given ={1,2,3,4,4,3,2,1}
We knowthat WkN=e−j(2πN)k
Given N=8
Hence, W18=e−j(2π8)0=1
=W18=e−j(2π8)1=cosπ4−jsinπ4=0.707−j0.707
=W28=e−j(2π8)2=cosπ2−jsinπ2=−j
=W38=e−j(2π8)3=cos3π4−jsin3π4=−0.707−j0.707
$ \begin{gathered} 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\} \\\\ \mathbf{X}(\mathbf{k})=\{\mathbf{2}, \mathbf{0 . 5}-\mathbf{j} \mathbf{1} \mathbf{2 0 7}, \mathbf{0}, \mathbf{0 …