The paper describes an approach to semiconductor noise analysis that is entirely within the framework of the semiclassical transport theory. The key aspect that differentiates this approach from other noise models is that this approach directly connects noise characteristics with the physics of scattering in the semiclassical transport model and makes no additional assumptions regarding the nature of noise. Employing the machinery of stochastic differential equation theory, a method is developed to compute the autocovariance function and spectral density of current fluctuations from the solutions of the Boltzmann transport equation (BTE). As a result, current fluctuations due to scattering are directly accounted for without the usual ad hoc addition of the "Langevin source term" to the transport equation. Simulation results are presented for the noise spectral density and autocovariance functions in silicon due to elastic-acoustic and optical-phonon scattering. The autocovariance and spectral density are computed in bulk silicon for different electric fields and temperatures based on the space-independent solutions of the BTE. In the practical case of Ohmic contacts, an explicit expression for the current noise spectral density is derived in terms of the scattering transition rate, the steady-state distribution function, and the average current density.