I apologize if this comes as a basic question, but I am struggling to understand why the PSD can only be estimated and not directly computed. For example, this thread discusses several such PSD estimation methods.
If I have a deterministic signal with a fixed number of samples, shouldn't I be able to directly determine its spectral information? Also, it is well known that PSD can be defined as the Fourier transform of the auto-correlation function. Isn't this calculation deterministic?
Finally, in this paper the authors compute the PSI directly from the FFT coefficients as shown below. There doesn't seem to be anything stochastic about the computation, and the computation of FFT coefficients is not really an estimation, to the best of my understanding. What am I missing?