35

   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)