Graphics Programs Reference
In-Depth Information
Although the function
filter
yields an output vector with the same length
as the input vector, we have to correct the output as well. In this case, the
function
filter
assumes that the fi lter is causal. The fi lter weights are in-
dexed
n
,
n
-1,
n
-2 and so on. Hence, no future elements of the input vector,
such as
x
(
n
+1),
x
(
n
+2) and so forth are needed to compute the output
y
(
n
).
This is of great importance in the fi eld of electrical engineering, the classic
fi eld of application of MATLAB, where fi lters are often applied in real time.
In earth sciences, however, in most applications the entire signal is available
at the time of processing the data. Filtering the data series is computed by
y4 = filter(b3,1,x3);
and afterwards the phase correction is carried out using
y4 = y4(1+(m3-1)/2:end-(m3-1)/2,1);
y4(end+1:end+m3-1,1)=zeros(m3-1,1);
which only works for an odd number of fi lter weights. This command sim-
ply shifts the output by
(m-1)/3
towards the lower end of the
t
-axis, then
fi lls the end of the data series by zeros. Comparing the ends of both outputs
illustrates the effect of this correction, where
y3(1:5,1)
y4(1:5,1)
yields
ans =
0.3734
0.4437
0.3044
0.4106
0.2971
ans =
0.3734
0.4437
0.3044
0.4106
0.2971
This was the lower end of the output. We see that both vectors
y3
and
y4
contain the same elements. Now we explorer the upper end of the data vec-
tor, where
y3(end-5:end,1)
y4(end-5:end,1)
