Environmental Engineering Reference
In-Depth Information
we arrive at
Eq.(3.11) reveals that :
The frequency response of a linear periodically time-varying system
at frequency consists of the contribution of the input signal at
both and This characteristic differs fundamentally from
linear time-invariant circuits. If the input to a linear periodically
time-varying circuit is a broadband signal, such as thermal and shot
noise, then the response of the circuit at a given baseband frequency
contains the contribution of the input at both the baseband frequency
and that at corresponding sideband frequencies, resulting in much
higher output power.
The quantity characterizes the relation between the
input at the side band frequency and the output at the base
band frequency It is called the aliasing transfer function. Note
that aliasing transfer functions are a generalization of the transfer
functions for linear time-invariant circuits where both the input and
output are evaluated at the same frequency, i.e. the frequency of the
input.
If the system is linear time-invariant, Eq.(3.11) is simplified to
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