Consider the finite-duration signal x(n) = {1, 2, 3, 1}(a) Compute its four-point DFT by solving...

Question

Consider the finite-duration signal
x(n) = {1, 2, 3, 1}
(a) Compute its four-point DFT by solving explicitly the 4-by-4 system of linear equations defined by the inverse DFT formula.
(b) Check the answer in part (a) by computing the four-point DFT, using its definition.

Robert · Accepted Answer

Question Id: 404468: Finding Out Four-point DFT for
a Finite Duration Signal:
03.01.2017
1
Question Id: 404468: Finding Out Four-point DFT for a Finite Duration Signal ( ):
Mathematical Formulation
(a) Computation of four-point DFT by solving explicitly the 4-by-4 system of linear equations
defined by the inverse DFT formula
We know the formula of inverse DFT:
x(n) =
1
N
N−1∑
K=0
X(K)ej
2π
N nK
⇒ x(n) =1
4
3∑
K=0
X(K)ej
π
2 nK [Here N = 4]
(1)
For the data points: x(0) = 1, x(1) = 2, x(2) = 3, and x(3) = 1, we can write from Eq.

Consider the finite-duration signal x(n) = {1, 2, 3, 1} (a) Compute its four-point DFT by solving explicitly the 4-by-4 system of linear equations defined by the inverse DFT formula. (b) Check the...

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