Suppose I have a discrete function $f( x_i ) = y_i$.
I can use these pairs $(x_i, y_i)$ as complex number $z_i = x_i + j \, y_i$.
Now, having this set $z_i$, I can apply discrete Fourier transform, as show in Wikipedia.
Now, suppose the calculated Fourier coefficients are ${X_i}$, where each ${X_i}$ is, of course, a complex number.
So, what is the interpretation of these numbers? For example:
- what does the real part of these number means (if anything at all)?
- what does the imaginary part of these number means (if anything at all)?
- what does the module $|{X_i}|$ means? Does these values give the spectrum of the function? If so, what it's used for?