Digital Signal Processing Reference
In-Depth Information
1
1
0
0
−1
−1
−10
−5
0
5
10
−10
−5
0
5
10
(a) n (Seq1)
(b) n (Seq2)
1
1
0
0
−1
−1
−10
−5
0
5
10
−10
−5
0
5
10
(c) n
(d) n
1
1
0
0
−1
−1
−10
−5
0
5
10
−10
−5
0
5
10
(e) n
(f) n
Figure 2.22:
(a) First Sequence; (b) Second Sequence; (c) Second sequence time reversed (TR) and
oriented to compute the first value of the convolution sequence (arrow shows direction the second sequence
will slide, sample-by-sample, to perform convolution); (d) TR second sequence oriented to compute the
second value of the convolution sequence; (e) TR second sequence oriented to compute the third value of
the convolution sequence; (f ) TR second sequence oriented to compute the fourth value of the convolution
sequence.
y
[
n
]=
h
[
n
]
x
[
n
]=
x
[
n
]
h
[
n
]
which we showed by example above.
2.5.5 STABILITY AND CAUSALITY
An LTI system is said to be stable if every bounded (finite magnitude) input results in a bounded output
(sometimes abbreviated as BIBO). An LTI system is stable if and only if the the impulse response is
absolutely summable, which is to say, the sum of the magnitudes of
h
[
n
]
for all
n
is finite, i.e., if
∞
|
h
[
n
]|
<
∞
n
=−∞
A certain IIR's impulse response is 0
.
9
n
u
Example 2.9.
[
n
]
. Determine if the IIR is a stable system.
