Digital Signal Processing Reference
In-Depth Information
10
0
1
−10
0
0
50
100
150
200
250
−1
(b) Sample Number of Real Output
0
100
200
10
(a) Sample Number of Input
0
+
−10
Input (Real)
0
50
100
150
200
250
(c) Sample Number of Imaginary Output
2.4+9.7i
7.8+5.9i
1.4+9.7i
1
0.5
0
0.71+0.71i
−0.5
−1
−1
0
1
Magnitude
Angle(Degrees)
(d) Real
Figure 4.34:
(a) Input sequence, a chirp; (b) Real part of output sequence, which is a continuous oscil-
lation at the frequency of the pole; (c) Imaginary part of output sequence; (d) The pole, plotted in the
complex plane.
according to the desired relative weights to be given to the current input sample and the past history of
input sample values.
Example 4.20.
Verify that Eq. (4.21) will result in a steady state value for
y
of 1.0 when
β
= 0.1 and
x
[
n
]
is a unit step.
We can use the
filter
function in a straightforward manner a first way
x = ones(1,100); y = filter(0.1,[1,-0.9],x); figure;stem(y)
or with an equivalent call, which prescales the unit step before filtering
x = 0.1*ones(1,100); y = filter(1,[1,-0.9],x); figure;stem(y)
Example 4.21.
Consider the leaky integrator defined by the difference equation
y
[
n
]
= 0
.
1
x
[
n
]+
0
.
9
y
[
n
−
1
]
.For
y
[
100
]
, determine what the relative weights are of
x
[
100
]
,
x
[
99
]
, and
x
[
98
]
as they
appear in an expression for
y
[
100
]
.
