Geoscience Reference
In-Depth Information
yields the output
ans =
0.5491
0.0181
-0.5868
-0.8124
-0.8498
-0.8333
ans =
0.5491
0.0181
0
0
0
0
h e vectors are identical up to element
y(end-m3+1)
, but then the second
vector
y4
contains zeros instead of true data values. Plotting the results with
subplot(2,1,1), plot(t,x3,'b-',t,y3,'r-')
subplot(2,1,2), plot(t,x3,'b-',t,y4,'r-')
or in one single plot,
plot(t,x3,'b-',t,y3,'g-',t,y4,'r-')
shows that the results from using
conv
are identical with those from using
filter
, except at the upper end of the data vector. h ese observations are
important for our next steps in signal processing, particularly if we are
interested in leads and lags between various components of signals.
6.6 Recursive and Nonrecursive Filters
We now expand the nonrecursive i lters by a recursive component, such that
the output
y
(
t
n
) depends not only on the i lter input
x
(
t
), but also on previous
output values
y
(
t
n-
1
),
y
(
t
n-
2
),
y
(
t
n-
3
), and so on. h is i lter requires not only
the nonrecursive i lter weights
b
i
, but also the recursive i lters weights
a
i
(Fig.
6.2), and can be described by the
dif erence equation
:
Although this is a non-causal version of the dif erence equation, MATLAB
again uses the causal indexing,
