please ans both questions. Thank you!!

Problem 3. (16 points) Let a = [4,3,2,3,3,1, 1, 2) and b = [1, 2, 2, 4, 3, 2, 3, 1] be two sequences and FFT(a)=[2,0,0, 15, 1, 10, 8, 13) and FFT(b)=[1, 16, 12,8,0,4,3,13] where FFT operations are done in commutative ring modulo 17. Note that 2 is the 8-th root of unity in this ring and 8-1 = 15 = -2 mod 17 in this ring. (a) Find the inverse FFT of the sequence given by FFT(a) * FFT(6) where * is element-wise multiplication of the two FFT sequences. Show all the computational steps in this ring using butterfly network (10 points). Hint: FFT(a) can be written as [2,0,0, -2, 1, -7,8,-4) and FFT(6) can be written as (1,-1, -5,8,0,4,3,-4). 2-1 = 9 and powers of this root are 1,9, 13(-4), 15(-2), 16(-1), 8(-9), 4, 2. (b) Positive wrapped convolution c of 2 sequences a and b is given by a = $; -o a;b;-; + ;=i+, ;bnti-;. Show that the result obtained in step (a) is the positive wrapped convolution of the two sequences given in the prob- lem.(5 points) Problem 3. (16 points) Let a = [4,3,2,3,3,1, 1, 2) and b = [1, 2, 2, 4, 3, 2, 3, 1] be two sequences and FFT(a)=[2,0,0, 15, 1, 10, 8, 13) and FFT(b)=[1, 16, 12,8,0,4,3,13] where FFT operations are done in commutative ring modulo 17. Note that 2 is the 8-th root of unity in this ring and 8-1 = 15 = -2 mod 17 in this ring. (a) Find the inverse FFT of the sequence given by FFT(a) * FFT(6) where * is element-wise multiplication of the two FFT sequences. Show all the computational steps in this ring using butterfly network (10 points). Hint: FFT(a) can be written as [2,0,0, -2, 1, -7,8,-4) and FFT(6) can be written as (1,-1, -5,8,0,4,3,-4). 2-1 = 9 and powers of this root are 1,9, 13(-4), 15(-2), 16(-1), 8(-9), 4, 2. (b) Positive wrapped convolution c of 2 sequences a and b is given by a = $; -o a;b;-; + ;=i+, ;bnti-;. Show that the result obtained in step (a) is the positive wrapped convolution of the two sequences given in the prob- lem.(5 points)