Determine the sequence xn x0 x1 x2 x3 x4 x5 x6 x7 by comput

Determine the sequence x[n] = {x[0), x[1], x[2], x[3], x[4], x[5], x[6], x[7]} by computing the 8-point IDFT of the following 8-point DFT sequences. You can check your answer with Matlab, but show how the answers can be obtained without brute force or a calculator. X[k] = {8, 0, 0, 0, 0, 0, 0, 0} X[k] = {0, 0, 0, 0, 8, 0, 0, 0} X[k] = {8, 8, 8, 8, 8, 8, 8, 8} X[k] = {-8, 8,-8, 8, -8, 8, -8, 8}

Solution

a)

x(n)=IDFT[x(K)]=[1 1 1 1 1 1 1 1];

the first value of FFt sequence will give the addition of all input samples, also here all other values are zero, then all values must be equal. so the answer is x(n)=[1 1 1 1 1 1 1 1];

b)x(n)=IDFT[x(K)]=[ 1 -1 1 -1 1 -1 1 -1]

here the fisrt value of IIFt sequenc is 0 and, thex[4]=8; where x[4] represet the differnce between even and odd sampled, so the answer must be x(n)= [ 1 -1 1 -1 1 -1 1 -1]

c)x(n)=IDFT[x(K)]=[ 8 0 0 0 0 0 0 0 ];

here the 1st value is 8,and x[4]=8 and all other values also equal.. so tthe x[n]=[ 8 0 0 0 0 0 0 0]

d)x(n)=IDFT[x(K)]=[   0 0 0 0 -8 0 0 0 ];