Discrete Fourier Series question... Consider the following three periodic sequen

Question

Discrete Fourier Series question...

Consider the following three periodic sequences (note that the time origin is not given): x_1[n] = {...,0,-1,1,1,0, -1,1,1,0, -1,...}, x_2[n] = {...,0,0,0,1,1,0,0,0,1,1,...}, x_3[n] = {...,-1,-1,1,1,-1,-1,1,1,...}. (a) For which sequence is it possible to have all DFS values real-valued? If it is possible, explain how. (b) For which sequence is it possible to have all (except for k = lN) DFS values imaginary-valued? If it is possible explain how. (c) For which sequence are the DFS coefficients zero for k = plusminus2, plusminus4?

Explanation / Answer

b/) for x1= [ 1 -1 0 0 ]

DF is realed value function

c)

for x1= [ 1 1 0 0 1 1 ]

DF is imaginaryvalue function

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