Question

5 Question (4 marks) Given the 90-point signal x(n) = 30 \delta (n - 5) + \cos \left(\frac{\pi}{15} n\right) 0 \le n \le 89 having the 90-point DFT X(k). It is required to find X(k=2) and X(k=3). Show the final step in calculation leading the numerical final answer of X(k=2) and X(k=3).

          5
Question
(4 marks) Given the 90-point
signal
x(n) = 30 \delta (n - 5) + \cos \left(\frac{\pi}{15} n\right)
0 \le n \le 89
having the 90-point DFT X(k). It
is required to find X(k=2) and
X(k=3). Show the final step in
calculation leading the
numerical final answer of
X(k=2) and X(k=3).

5
Question
(4 marks) Given the 90-point
signal
x(n) = 30 δ(n - 5) + cos((π)/(15) n)
0 ≤n ≤89
having the 90-point DFT X(k). It
is required to find X(k=2) and
X(k=3). Show the final step in
calculation leading the
numerical final answer of
X(k=2) and X(k=3).

Added by Hannah A.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Sam Stansfield

Step 1

X(k) = Σ[n=0 to N-1] xn * e^(-j2πkn/N) Show more…

Show all steps

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Given the 90-point signal xn = 30n^5 + cos(2Ï€n/89), it is required to find Xk-2 and Xk-3 for the 90-point DFT X(k). Show the final step in the calculation leading to the numerical final answer of Xk=2 and Xk=3.