I'm trying to figure out, how coefficients of Discrete Fourier Transform in complex form are converted into coefficients of Trigonometric Polynomials Interpolation:
Say, I have a function vector with 7 coordinates:
I can try to decompose it into Trigonometric Polynomials like this: $$f(x) = \frac{a_0}{2}+\sum_{l=1}^3 a_l \cos(l x) + b_l \sin(lx)$$
At the same time I can decompose it into DFT like this:
What bothers me is that 6-dimensional DFT vectors correspond to 7-dimensional Trigonometric Polynomials harmonics. I don't get, how I can establish a correspondence between trigonometric coefficients $$a_l, b_l$$ and DFT coefficients as there are 7 of first kind and 6 of the second, cause I can't use full f(x) 7-vector for DFT - I'll have to drop one coordinate. Or there's no correspondence in discrete case and it works only for seria?
