In the field of signal analyies for time frequency, the DFT is a familiar term. Especially,when its efficient algorithm FFT given, the other operations in signal analyses are also usually translated to DFT as soon as possible so as to enhance the calculating speed. But in our exploning the virtual instrument for time frequency analyzing, two sorts of formulas to calculate DFT and its inverse transform (IDFT) are found. These results are in different value of operation from different signal analysts or from different instruments for time frequency analyzing, their physical meaning are also not clear enough.The period extent theory some previous document based on when defined DFT is firstly expatiated. Then, separately with future defining coefficient method and analogy evolvement method, the authors argue that, based on the period extent theory, it is more rational to calculate DFT with the formula given. A shortage is pointed out and corrected is appeared in some previous documents when having given the formula of DFT. The improper view is also clarified that the reason why there are two sorts of formulas is make by custom.The rationality of the authors view with three examples is visually verified in the end.