Solving for the Real and Imaginary Number

  • Thread starter Tan Thom
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  • #1
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Homework Statement



Find the 4th Coefficient in a sample of 4 discrete time Fourier Series coefficients in a real time valued periodic sequence. k = 0,1,2,3

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

Homework Equations



upload_2019-2-19_13-20-48.png


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The Attempt at a Solution



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

Step 2: [(1-2j)(cos (pi/2)n + j sin (pi/2)n) + a_3 (cos (pi/2)n)-j sin (pi/2)n]

Solving for a_3 in the final step is where I am confused.
 

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Answers and Replies

  • #2
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I had a lot of experience with such things and the question doesnt seem to be fully formed to me. Perhaps there is some extra info somewhere? Perhaps the solution revolves around making sure that the resulting function will be real valued as stated in question. That sets constraints between coefficients.
However only summing over positive k values Will make it imposible to get a purely real signal. Normally that would happen when a(-k) is the complex conjugate of a(k). Or should it be using a discrete Fourier sin series, summing over real basis functions rather tan over exp(ikx) complex functions? Though you wouldnt need complex coeffs in that case. Need to see the full question I think.
 

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