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Based on Figure 3-12, the x component of accelerometer mounted near the fan is chosen as x1, the y component of accelerometer mounted near the pump is chosen as x2, and the x component of accelerometer mounted on the test section is chosen as y. The system shown in Figure 3-11 can be expressed in frequency domain as Y = H1X1 +H2X2 + N (3.2)
where X, X2, N and Y are the Fourier transforms of xI, X2, n andy respectively.
The relevant power and cross spectra are given by G12 2 E
G ,(f [EXI.X2]
2
Gly(f) *L=.Y T (3.3)
2 . .
(f) T X2Y]
2 .E[y*Y]
T
where * denotes the complex conjugate.
The ordinary coherence functions are calculated as follows:
2(f) 1 *22
2
Yy GI(3.4)
2
Y2(f)G G
Assuming 22 (f) E (0,1), the noise spectrum Gnn is computed as
S=y --'H- H*H2G12 + H2H1G21 +H22 G22
G (3.s)