This is about the effects of sampling in time and using a DFT with a scaling to calculate Fourier Series Coefficients. See class notes on estimation of the Fourier Series Coefficients through a scaled Discrete Fourier Transform, and how the results are related to the spectrum of the continuous signal.
You might want to revisit Lecture 5 notes for this problem.
Two things I think are off about this problem (my results make more sense when I make these changes):
1) In the formula for Ck, I believe the exponential term should be [-j*2*pi*n*k*delta] or alternatively [-j*2*pi*n*k*T/N] rather than [-j*2*pi*n*k/N] .
2) I think the range of k should be […, -2, 0, 2, …] rather than […, -1, 0, 1, ….].
The formula is correct. It is (1/N). DFT(xn, N), where N is the number of samples in the Period. Refer to Lecture 5 where we did a very similar example and we derived the relationship between the estimated Ck and the actual Ck.
Sorry you should be showing results from k=-18, -17, -16, ….0, 1, … to k=+18, corresponding to fk=-36 Hz to +36 Hz.
This is about the effects of sampling in time and using a DFT with a scaling to calculate Fourier Series Coefficients. See class notes on estimation of the Fourier Series Coefficients through a scaled Discrete Fourier Transform, and how the results are related to the spectrum of the continuous signal.
You might want to revisit Lecture 5 notes for this problem.
Two things I think are off about this problem (my results make more sense when I make these changes):
1) In the formula for Ck, I believe the exponential term should be [-j*2*pi*n*k*delta] or alternatively [-j*2*pi*n*k*T/N] rather than [-j*2*pi*n*k/N] .
2) I think the range of k should be […, -2, 0, 2, …] rather than […, -1, 0, 1, ….].
The formula is correct. It is (1/N). DFT(xn, N), where N is the number of samples in the Period. Refer to Lecture 5 where we did a very similar example and we derived the relationship between the estimated Ck and the actual Ck.
Sorry you should be showing results from k=-18, -17, -16, ….0, 1, … to k=+18, corresponding to fk=-36 Hz to +36 Hz.