The natural way of mode identification from line-profile variations is the method of line-profile fitting. By comparing the observed line-profile variations with theoretically calculated ones for many wavenumbers (, m) and for a large grid of other parameters, one chooses the modes which best fit the observations. Unfortunately, this technique suffers of a major drawback: the unrealistic computation time for multiple modes.
The idea of the moment method is to replace each line profile by its first three moments, which describe respectively the centroid velocity of the line, the line width and the line skewness. The modes and other parameters are then determined in such a way that the theoretically computed moment variations best fit the observed ones.
The moment method was first introduced by Balona (Balona 1986ab, 1987) and further developed by Aerts et al. (1992) and Aerts (1996). They derived analytical expressions of the first three moment variations, which are valid for stars with a slow rotational period compared to pulsation periods.
In this paper, we present a new numerical version of the moment method, which is more efficient than the previous one. First, the technique is no more restricted to slow rotators since we extend its application to rotating pulsating stars as described by Lee & Saio (1987). Then, we use a new discriminant by considering the moments calculated at each time of observation. Finally, the identification of multiple modes, which was still difficult with the 1996 version of the moment method, becomes more feasible and accurate.
We apply the new method to four stars showing multiperiodicity: two Cephei stars and two Slowly Pulsating B stars.

 
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