Figure P410 shows a 4point FFT using standard decimationinti

Figure P4–10 shows a 4-point FFT using standard decimation-in-time butterflies. Redraw that FFT using optimized decimation-in-time butterflies as shown in the text’s Figure 4–14(c). In your drawing provide the correct indices for the X(m) output samples.

Please find the both figures below.

Fig - P4-10 Given below

Fig 4–14(c) given below

x(0) 0 4 4 2 4 X(?) X(2) 2 4 4 4 2 3 x(3). x(?)

Solution

clearly option a satisfies the reqired condition and from top to bottom values of m are 0,2,1,3