Question

Given a sequence x (n)
x [n] = {1,2,1,2}
x [0] = 1
x [1] = 2
x [2] = 1
a.Determine the sequence w [n] whose 6-point DFT is:
W (k) = Re {X (k)}
Where X (k) is the 6-point DFT of x [n].
b. Given the sequence x [n], determine the sequence v [n] whose 3-point DFT is V (k) = X (2k + 1)
Where X (k) is the 6-point DFT of x [n]

Solve step by step

Answer 1

Question (a)

The N point DFT of a sequence x[n] is given by

So the 6 point DFT X[k] is given by

So the sequence x[n] will be appended with 2 zeros as the sequence x[n] has only 4 elements and it is a 6 point DFT

Taking Inverse DFT, we get

Where is the circular folded sequence of x[n]

So