Periodogram

The periodogram is not a consistent estimator for the spectral density of a signal. The term was coined by Arthur Schuster in 1898.

Definition

Be

Wherein T is an integral multiple of

Is. By drawing a curve with a 2π / k on the abscissa, and

On the ordinate, the space between the curve and the abscissa represents the periodogram of f ( t).

Note

The periodogram is completely unsuitable as an estimator for the spectrum. This is because, if the observed time series is arbitrarily long, the variance of the estimator is always of the same magnitude as the expected value, and does not converge to zero. Although converges to the expected value of the periodogram to process the spectrum, but also the convergence of the variance to zero at infinitely long time series of a consistent estimator is expected.