Geoscience Reference
In-Depth Information
plot(x,y)
where
x
is the input signal and
y
is the output signal. An example of a
nonlinear system is
x = (-100:100)';
y = x.^2;
plot(x,y)
•
Time
invariance
- h e system output
y
(
t
) does not change as a result of a
delay in the input
x
(
t
+
i
): the system characteristics are constant with time.
Unfortunately, natural systems ot en change their characteristics with
time. For instance, benthic mixing or bioturbation depends on various
environmental parameters such as nutrient supply, and the system's
properties consequently vary signii cantly with time. In such a case it is
dii cult to determine the actual input of the system from the output, e.g.,
to extract the actual climate signal from a bioturbated sedimentary record.
•
Invertibility
- An invertible system is a system in which the original input
signal
x
(
t
) can be reproduced from the system's output
y
(
t
). h is is an
important property if unwanted signal distortions are to be corrected, in
which case the known system is inverted and the output then used to
reconstruct the undisturbed input. For example, a core logger measuring
magnetic susceptibility with a loop sensor integrates the signal over a
specii c core interval, with the sensitivity highest at the position of the
loop and decreasing down-core and up-core. h is system is invertible,
i.e., we can compute the input signal
x
(
t
) from the output signal
y
(
t
) by
inverting the system. h e inverse of the above linear system is
x = (1:100)';
y = 0.5*x;
plot(x,y)
where
x
is the input signal and
y
is the output signal. A nonlinear system
x = (-100:100)';
y = x.^2;
plot(x,y)
is not invertible. Since this system yields equal responses for dif erent
inputs, such as
y=4
for inputs
x=-2
and
x=+2
, the input
x
cannot be
reconstructed from the output
y
. A similar situation can also occur in
linear systems, such as
