A matrix vector product and 2 the conv command

(1) a matrix vector product and (2) the conv command. Describe the form of the convolution matrix and why
it 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 discrete-time signals are most appropriately displayed with the stem command, for long
discrete-time 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 .