  In this paper, we present an exact formalism for transient current-current
correlations and transient noise spectra. The exact solution of transient
current correlations in both the time domain and the frequency domain are
obtained. Without taking the wide band limit, we investigate transient
current-current correlations with different bias voltages and different finite
temperatures. Transient noise spectra over the whole frequency range are
calculated and that in the steady-state limit are also reproduced. From
transient current-current correlations and noise spectra, we analyze the
frequency-dependence of electron transport for the system evolving far away
from equilibrium to the steady state. Various time scales associated with the
energy structure of the nanosystem are also obtained from the transient
current-current correlations and transient noise spectra.
