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DmytriE
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Homework Statement
The entries of the time-domain vector:
x(1) = [2 1 -1 -2 -1 1 2 1 -1 -2 -1 1] ; N = 12
are given by 2cos(ωn) where n = 0:11. what is the value of ω? express x(1) as the sum of two Fourier sinusoids. By considering the appropriate columns of the Fourier matrix V, determine the DFT X(1).
Homework Equations
ω = (2π/N)
The Attempt at a Solution
I know that ω = π/6
But when determining the Fourier sinusoid I can only express it as the sum of 7 different parts.
1/6 + 1/6cos(pi*n/6) - 1/6cos(pi/3*n)...1/6(-1)^n.
But I says to express it as 2 Fourier sinusoids. I don't know how to simplify it or how to decide which columns would lead me to a solution.
When I fft the above equation (partial shown) It get x(1) back. So the equation is right but does not fully answer the question. Any help would be greatly appreciated!
DmytriE