(1) a matrix vector product and (2) theconvcommand. Describe the form of the convolution matrix and whyit works.
(6)
g
(
n
) =
u
(
n
+ 4)

u
(
n

3)
(7)
First, plot the signals
f
,
g
, and
f
⇤
g
by hand, without using MATLAB. Note the start and end points.
Next, use MATLAB to make plots of
f
,
g
, and
f
⇤
g
. Be aware that the
conv
function increases the length of
vectors.
To turn in: The plots of
f
(
n
),
g
(
n
),
x
(
n
), and your Matlab commands to create the plots.
1.3.13 Smoothing data by
N
point convolution.
Save the data file
DataEOG.txt
from the course website. Load the data into Matlab using the command
load
DataEOG.txt
Type
whos
to see your variables. One of the variables will be
DataEOG
. For convenience, rename
it to
x
by typing:
x = DataEOG;
This signal comes from measuring electrical signals from the brain of a human
subject.
Make a stem plot of the signal
x
(
n
). You will see it doesn’t look good because there are so many points. Make
a plot of
x
(
n
) using the
plot
command. As you can see, for long signals we get a better plot using the
plot
command. Although discretetime signals are most appropriately displayed with the
stem
command, for
long
discretetime signals (like this one) we use the plot command for better appearance.
14
Create a simple impulse response for an LTI system:
h = ones(1,11)/11;
Compute the convolution of
h
and
x
:
y = conv(x, h);
Make a MATLAB plot of the output
y
.
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 Spring '14
 Digital Signal Processing, Signal Processing, LTI system theory, Impulse response, Inverse Systems