  The origin of the Finite Grid Instability (FGI) is studied by resolving the
dynamics in the 1D electrostatic Particle-In-Cell (PIC) model in spectral
domain at the single particle level and at the collective motion level. The
spectral fidelity of the PIC model is contrasted with the underlying physical
system or the gridless model. The systematic spectral phase and amplitude
errors from the charge deposition and field interpolation are quantified for
common particle shapes used in the PIC models. It is shown through such
analysis and in simulations that the lack of spectral fidelity relative to the
physical system due to the existence of aliased spatial modes is the major
cause of the FGI in the PIC model.
