Geoscience Reference
In-Depth Information
components that have been removed by the i lter in error, from within the
noise-free segment of the time series beyond
x
=500. Using the last output
of
canc
, we can calculate and display the i lter weights
w
of the i nal iteration
surf(w(3:999,:)), shading interp
which shows nicely the adaptation of the i lter weights before and at er the
change in the signal-to-noise ratio. We plot only the middle part of
w
, as the
edges
1:(l-1)/2
and
end-(l-1)/2:end
are all zero due to the length of the i lter
l
. We can also use this example to demonstrate the ef ect that the values of
u
and
l
have on the performance of the adaptive i lter. In theory, a smaller
u
leads to more accurate results, but the rapid adaptation to a changing signal-
to-noise ratio does not work well. Larger values of
l
also give better results
but the number of data points lost through the i ltering process increases by
(l-1)/2
.
h e graphical user interface (GUI) version
canctool
can be used as an
alternative to
canc
. We use the same example data set as before; this function
was created using the
GUI Design Environment
(GUIDE) (see Section 2.10).
We again generate two signals,
yn1
and
yn2
, containing the same sine wave
but dif erent Gaussian noise.
clear
x = 0 : 0.1 : 100; x = x';
y = sin(x);
rng(0)
yn1 = y + 0.5*randn(size(y));
yn2 = y + 0.5*randn(size(y));
We next run
canctool
canctool(yn1,yn2)
and watch the i lter iteratively adjusting its i lter weights. h e function
canctool
accepts the primary and reference signals as inputs. h e GUI
provides default values for the i lter length, the convergence rate, and the
number of iterations. h e user must adjust these values to the specii c data,
for example, using the formula for a suitable convergence rate that has been
described above. As an example, we choose a i lter length of 11, a convergence
rate of 0.00001, and 30 iterations. Once the calculation is complete,
canctool
exports the i ltered primary signal
yy
, the i ltered reference signal
zz
(using
the same set of i lter weights), the noise
ee
extracted from the primary signal,
and the mean-squared error
mer
for each iteration, to the workspace using the
function
assignin
. h e application of this algorithm has been demonstrated
Movie
6.7
