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https://www.alwayslearn.com/DFT%20and%20FFT%20Tutorial/DFTandFFT_FFT_Butterfly_8_Input.html

I was reading above link and then i came across a confusing sentence, i highlighted it in attached snapshot. It says there are 12 , 2 input butterflies ,while i am only able to see only 4, 2 input butterflies at left most of snap in stage1 but unable to see any 2 input butterfly in stage 2 or stage 3 enter image description here

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Please see below diagram to see the Stage 2 and Stage 3 butterflies.

enter image description here

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  • $\begingroup$ Two butterflies at top and 2 at bottom in stage 2, total 4 butterflies in stage 2. But apparently they are not 2 input, they appear to have 4 inputs. Aren't they? $\endgroup$ – engr Jun 15 at 10:47
  • $\begingroup$ @engr no; that's not the case. Look closely. You might be optically confused by the fact that the butterfly is not across adjacent horizontal lines. $\endgroup$ – Marcus Müller Jun 15 at 13:30
  • $\begingroup$ @MarcusMüller Butterflies at stage 1 are single pass?aren't they? If yes, what about 2nd and 3rd stage butterflies?How many passes,each of them have? $\endgroup$ – engr Jun 16 at 5:53
  • $\begingroup$ @engr they are all the same, just different input/outputs are connected so they cross over each other in the diagram but each one is simply the sum and difference of the two inputs with a phase rotator term. Each stage identically has 4 butterflies done in a single pass. $\endgroup$ – Dan Boschen Jun 17 at 3:51

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