Graphics Programs Reference
In-Depth Information
Unit Impulse
Impulse Response
2
2
1
1
0
0
ï
1
ï
1
ï
2
ï
2
0
5
10
15
20
0
5
10
15
20
t
t
a
b
Fig. 6.3
Transformation of
a
a unit impulse to compute
b
the impulse response of a system.
The impulse response is often used to describe and predict the performance of a fi lter.
transformation of
Y
(
f
). In many cases, the signals are often convolved in the
frequency domain for simplicity of the multiplication as compared to a con-
volution in the time domain. However, the FFT itself introduces a number of
artifacts and distortions and therefore convolution in the frequency domain
is not without problems. In the following examples we apply the convolu-
tion only in the time domain.
First we generate an unit impulse:
clear
t = (0:20)';
x6 = [zeros(10,1);1;zeros(10,1)];
stem(t,x6),axis([0 20 -4 4])
The function
stem
plots the data sequence
x6
as stems from the
x
-axis ter-
minated with circles for the data value. This might be a better way to plot
digital data than using the continuous lines generated by
plot
. We now feed
this to the fi lter and explore the output. For nonrecursive fi lters, the impulse
response is identical to the fi lter weights.
b6 = [1 1 1 1 1]/5;
m6 = length(b6);
y6 = filter(b6,1,x6);
We correct this for the phase shift of the function
filter
again, although
this might not be important in this example.
