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.

10 pages, 7 figures