Consider the same impulse response of the filter. Now, suppose that such filter will have as input a rectangular pulse represented by a discrete-time sequence that was obtained by sampling at 1 microsecond and is of length 4, i.e., the input row vector is

x = [1 1 1 1]

Find out how to use the MATLAB command conv which is used to calculate the convolution of functions. Use this command to obtain the output of the filter when the input is the given signal x.

Obtain the following:

Plot the result obtained from using the convolution command as a function of time. Specify this plot as a convolution in the time domain by writing a title for the plot.

Provide the length of the vector obtained from the convolution.

What relationship has the length of the convolution and that of the impulse response and the signal x?