Environmental Engineering Reference
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stationary inputs is cyclo-stationary. Its average power spectral density
is time-independent and is computed from
where is the power spectral density of the noise at the
frequency is the aliasing transfer function from
the noise source at the frequency to the output at the
frequency
M
is the number of noise sources, and
N
is the maximum
number of sidebands considered. Both the transfer and aliasing transfer
functions from the noise sources to the output are needed in computing
the output noise power.
It was shown in Chapter 10 that the transfer functions and aliasing
transfer functions of periodically switched linear circuits can be com-
puted efficiently by using the adjoint network. For a given periodically
switched linear circuit
N
,
Replace all noisy elements in the circuit with their corresponding
equivalent circuits.
i)
ii)
Define a set of constant vectors
to specify the
nodes to which these noise sources are connected.
iii)
Further, the output of
N
is specified by a constant vector
d
, i.e.
where
is the response of
N.
iv)
The adjoint network
of
N
is constructed and the system matrices
of
are obtained as per details given in Appendix 11.A.
v)
Using transfer function theorem of this chapter, the transfer function
from the
noise source to the output of
N
at
denoted by
is obtained from
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