Digital Signal Processing Reference
In-Depth Information
3
2
1
0
−1
−2
−3
0
200
400
600
800
1000
Sample
Figure 2.17:
The result from convolving a linear chirp sampled at 1000 Hz of one second duration,
having frequencies from 0 to 500 hz, with the LTI system defined by the coefficients [0.1,-1,1,-0.1].
both over
N
samples. An arbitrary delay of
Del
samples can be inserted at the leading side of
x
1
[
n
]
and
x
2
[
]
n
.
Figure 2.18 was generated by making the call
LVxLinearab(2,-3,13,5,128,0,[2,-1,1,2])
which demonstrates the superposition property for the LTI system defined as
y
[
n
]=
2
x
[
n
]−
x
[
n
−
1
]+
x
[
n
−
2
]+
2
x
[
n
−
3
]
(2.5)
Note that subplots (f ) and (h) show, respectively,
ay
1
[
n
]
+
by
2
[
n
]
and
LT I (ax
1
[
n
]+
bx
2
[
n
]
)
where the
LT I
operator in this case represents the system Eq. (2.5). Subplots (f ) and (h) show that
LT I (ax
1
[
n
]+
bx
2
[
n
]
)
=
ay
1
[
n
]+
by
2
[
n
]
For contrast, let's consider the second order (i.e., nonlinear) system
