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Good morning,

I am working on a problem where I am finding the 4th Coefficient in a sample of 4 discrete time Fourier Series coefficients. I got the sum but now I have to solve for a_3 which consists of a real and imaginary part. Any assitance on how to solve for the a_3? Thank you.

$a_k = \{3, 1-2j, -1, ?\}$

Step 1: $(1-2j)e^{j*.5\pi*n} +a_3 e ^ {-(j*.5\pi*n)} + 3 + (-1)^{n+1} $

Step 2: $[(1-2j)(\cos \frac\pi2 n + j \sin \frac\pi2n) + a_3 (\cos \frac\pi2n-j \sin \frac\pi2n)]$

I am working on a problem where I am finding the 4th Coefficient in a sample of 4 discrete time Fourier Series coefficients. I got the sum but now I have to solve for a_3 which consists of a real and imaginary part. Any assitance on how to solve for the a_3? Thank you.

$a_k = \{3, 1-2j, -1, ?\}$

Step 1: $(1-2j)e^{j*.5\pi*n} +a_3 e ^ {-(j*.5\pi*n)} + 3 + (-1)^{n+1} $

Step 2: $[(1-2j)(\cos \frac\pi2 n + j \sin \frac\pi2n) + a_3 (\cos \frac\pi2n-j \sin \frac\pi2n)]$

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