Digital Signal Processing Reference
In-Depth Information
0.6
x[n]
y[n]
0.2
D
1.1
D
Figure 3.26: A third lter with feed-back.
input
output
0
0
1
0.6
0
0.86
0
0.946
0
1.0406
0
1.14466
0
1.259126:
The output will continue to get larger in magnitude. This demonstrates a prob-
lem with IIR lters, that the output may approach innity (positive or negative
innity). It is also possible for an IIR lter's output to oscillate toward innity;
that the output becomes larger in magnitude, even though the sign may change. A
lter is said to be stable when the output approaches zero once the input falls to
zero. If the output oscillates at a constant rate, we call it conditionally stable. If
the output approaches positive or negative innity (such as the example above), or
if it oscillates toward innity, we say that the IIR lter is unstable.
The general form of the IIR lter is shown in Figure 3.27 [11]. Other texts refer
to this as Direct Form I, due to the direct correspondence between the gure and
the equation that describes it.
3.7
Trends of a Simple IIR Filter
Suppose we have a simple IIR lter, as in Figure 3.28.
By examining the gure, we can nd the input/output relation as:
y[n] = bx[n] + ay[n1]:
