The butterfly in Figure P9.15 was taken from a decimation-in-frequency FFT with N = 16,...

The butterfly in Figure P9.15 was taken from a decimation-in-frequency FFT with N = 16, where the input sequence was arranged in normal order. Note that a 16-point FFT will have four stages, indexed m = 1, . . . , 4. Which of the four stages have butterflies of this form? Justify your answer.