The paper revisits the analytical solution for the correlation function matrix of the random response of a structure.

The derived solution is valid for a general system and general white noise input.

The solution shows that the rows of the classical correlation function matrix is a free response of the system, but the columns are not.

Using the columns of the classical correlation function matrix in operational modal analysis will introduce bias on the mode shape estimates.

The bias errors when using the columns of the classical correlation function matrix is illustrated in a simulation study with closely spaced modes.