Time series, both simulated and measured, are analyzed by auto-Wigner distridution (AWD). In this paper, two main analyses are carried out : ( 1 ) Frequency-responses are derived from discrete -Wigner distribution (DWD), then compared with both those calculated from pseudo-Wigner distribution (PWD), and fast Fourier transform (FFT). ( 2 ) An algorithm on the automatic determination of optimum Lag-window length in RID (reduced interference distribution) is developed. As the result, ( 1 ) the frequency responses calculated from DWD are proved to be the most accurate among all of the methods tested, ( 2 ) it is made clear that for several kinds of signal, the algorithm developed in this study can generate an optimum Lag-window length in RID.