Therefore, the Fourier spectrum
of vibration signal for a faulty planet bearing is very complex even if the vibration data are collected from the planetary gearbox under the stationary condition.
To make the signal separable in its Fourier spectrum
, a mapping function [g.sub.m] (t) = exp(-i x [v.sub.m] (t)) with phase function [v.sub.m] (t) = 5 [pi]t + 45 sin (0.1 [pi]t) is adopted, which corresponds to the mapping frequency [f.sub.m] = 2.5 + 2.25 cos (0.1 [pi]t) Hz.
Figure 15 shows the Fourier spectrum
of the structural horizontal acceleration due to the mainshock and the aftershocks.
We have shown in Table 3 (p = 1.1) that for simulation interval of the nondimensional time [0, 125] the Fourier spectrum
exhibits only two frequencies [[omega].sub.p] and [[omega].sub.1].
EWT usually consists of two steps: segment the Fourier spectrum
of hybrid signal into multiple sub band first and then reconstruct the sources.
P represents the pinhole plane and the Fourier spectrum
plane of the input field.
The Panzhihua earthquake, Kobe earthquake, and three artificial earthquakes differ greatly in acceleration-time history and Fourier spectrum
ST can be written in the form of Fourier spectrum
Function F is also called the Fourier spectrum
of function f.
follows, which is a complex representation of s(t) containing a one-sided Fourier spectrum
Function F([xi]; [eta]) is also called the Fourier spectrum
of function /.
The time history and Fourier spectrum
curves for above three types of seismic wave are illustrated in Figure 7, and their amplitudes are scaled to be 0.15 g, 0.5 g, and 1 g, respectively.