The frequency stability is studied by using the stochastic signal processing theory and a new variance definition in the time domain

the Generilized Allan Variance σp2

q（T） is given. It is proved that the variances including the Allan Variance and the Modified Allan Variance are all the special cases of σp2

q（T）. For the power law spectral noises

the signal processing models for calculating σp2

q（T） from Sy（f） and its calculation formulas are obtained

the conversion formulas between σ32

2 （T） and Sy（f） are derives

the calculation formulas of the other variances in the time domain from σ32

2（T） are given and the conversion between Sy（f） and σp2

q（T） can be made easily

the formulas of σ32

2（T） by computer simulation are verified.