How to use sampling and summation instead of integration to calculate FS coefficients?

Question

How to use sampling and summation instead of integration to calculate FS coefficients?
I have to calculate the fourier series coefficients of the sawtooth function but instead of integrating i have to sample the function and the carrier then summate. when i do that the results arent correct. i dont know what i'm doing wrong, any ideas?

Answer 1

The best you can hope for with a numerical integration is a close approximation.

Instead of using t or ωt as your independent variable, convert to x = cos(nωt), y = sin(nωt), and run a linear regression of z = ax + by. You end up doing 5 sums for each frequency, but your reward is a nearly exact approximation. Don't forget to bias your function with its average value.

| Σx Σxy | | a | | ΣxF |
| Σxy Σy | | b | | ΣyF |

Your spreadsheet is ideal for running these regressions.

Answer 2

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Answer 3

its the same