# Periodogram: an inconsistent estimator

What is the reason that a periodogram is not a consistent method for obtaining information about frequency response of a system?

To be more precise, why even after increasing number of samples doesn't the variance of the estimator decrease?

The Periodogram implicitly uses a window to get an idea of the spectrum. Implicitly this is either a rectangular window, with frequency response which is like $\dfrac{\sin(\omega n)}{N\sin(\omega)}$, or a triangular window $(N-k)/N$.