The complete decimation-in-frequency algorithm is depicted for N = 16; x[O]=x[2]=x[4]=x[6]=x[8]=x[10]=x[12]=x[14]=1 ( x[n] = 1 whenn is even number) ; x[1]=x[3]=x[5]=x[7]=x[9]=x[11]=x[13]=x[15]= -1 (x[n] = -1 when n is odd number . Draw the 16- element decimation in frequency for N = 16 and Calculate X[9] and X[15]. for the value of the line between each node, it should be always -1 and %D The graph is an example of an 16-element decimation-in-frequency. STAGE 1 STAGE 2 STAGE 3 + STAGE 4 00 000 10 0 08 20 04 30 O -O12 400 02 50 0 O 10 6 0 06 O 14 10 OO 0-05 110-O O 13 12 OO 03 13 O0 0 011 14 O 007 15 OO 0 O 15

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A:

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