  We present the most complete scattering theory for noise in noninteracting
case. The exact formula for spectral density of current fluctuations at finite
frequency is presented in terms of scattering matrix for a coherent quantum
conductor. We show that the shot noise at finite frequency in an ideally
conducting contact is finite and the spectral density of the noise has a
singularity at the "Josephson" frequency $\omega =eV/\hbar $, set by the
voltage. We also discuss fluctuations of charge in an ideal conductor.
