In the investigation of rotor vibration, we must know the direction of a whirling motion as well as its angular velocity. In FFT (or DFT), elements of data sequence 
obtained by sampling are considered as real numbers and those of data sequence
obtained by discrete Fourier transform are considered as complex numbers. In the following, we introduce a method that can distinguish between whirling directions utilizing the revised FFT. In this FFT, rotor whirling motion is represented by a complex number by overlapping the whirling plane on the complex plane and applying FFT to these complex sampled data. Let us assume that a disc mounted on a elastic shaft is whirling in the y-z -plane. We get sampled data 
and 
by measuring the deflections 
and
in the y and z directions respectively. Taking the y -axis as real axis and the z -axis as imaginary axis, we overlap the whirling plane on the complex plane. Using sampled data 
and 
,
we define the complex numbers as follows:
(11.38)
and apply FFT (DFT) to them. We call such a method the complex-FFT method.