Structural Acoustics

174 Structural Acoustics: Deterministic and Random Phenomena

© 2011 by Taylor and Francis Group, LLC

By virtue of the fact that G

ij

(ω) = G

ji

*

(ω), the preceding matrix is a square

Hermitian matrix. The input matrix G

i

is

G

G G G G

G

i

i i i i

i

( )

( ) ( ) ( ) ( )

( )

ω

ω ω ω ω

ω

=

11 12 13 15

21

…



GG G

r rr1

i i

( ) ( )ω ω…

(9.17)

G

i

is also Hermitian of order r × r = s × s = r × s. The transfer function

matrix is a k × r complex matrix (not Hermitian):

H

H H H

H

H H

r

k kr

( )

( ) ( ) ( )

( )

( ) (

ω

ω ω ω

ω

ω ω

=

11 12 1

21

1

…



…

))

(9.18)

9.4 Important Quantities Derivable from the Cross Spectrum

The cross spectrum can be used as a starting point to derive several impor-

ta