How to determine the sine Fourier coefficients of discrete data?
In accordance with the case of a continuous function $f(x)$ where
$$b_n=\frac{2}{L}\int_{0}^Lf(x)\sin\left(\frac{mπx}{L}\right)dx$$
I came with the following expression:
$$A_m=\frac{1}{N-1}\sum_{n=1}^{N}w_n\sin\left(\frac{mπx_n}{L}\right)$$
Can anyone confirm or not that solution?