  We calculate the non-symmetrized finite-frequency NS-FF noise for a
single-level quantum dot connected to reservoirs in the spinless
non-interacting case. The calculations are performed within the framework of
the Keldysh Green's function formalism in the wide band approximation limit. We
establish the general formula for NS-FF noise for any values of temperature,
frequency and bias voltage. The electron transfer processes from one to the
other reservoir act via the transmission amplitude and transmission coefficient
depending on the energy. By taking the symmetrized version of this expression,
we show that our result coincides with the expression of the finite frequency
noise obtained by B\"uttiker using the scattering theory. We also give the
explicit analytical expression for the NS-FF noise in the zero temperature
limit. By performing numerical calculations, we finally discuss the evolution
of the NS-FF noise spectrum when varying temperature, dot energy level, and
coupling strength to the reservoirs, revealing a large variety of behaviors
with different symmetry properties.
