radix 4 butterfly diagram

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samina

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hi
I am not understanding radix 4 butterfly diagram, can anyone help me understand it?

I am not understanding the following line-
"We observe that for each value of k, direct computation of X(k) involves N complex multiplications (4N real multiplications) and N-1 complex additions (4N-2 real additions). Consequently, to compute all N values of the DFT requires N^2 complex multiplications and N^2-N complex additions."
will u please help me understand this...
 
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