MATLAB exercise: Your MATLAB code does not have to be turned in for this exercise. Simply print the required plots and attach them, along with your written response, to the other written exercises. 1. Create a Gaussian-shaped pulse using the command: gauss 1 = gausswin(512,10); (It is not important to understand everything about this command right now. It creates a Gaussian-shaped vector whose length is given by the first parameter and whose width is inversely proportional to the second parameter.) 2. Normalize this pulse so that its integral (i.e., the sum of all of its values) is one. In other words, divide each point by sum( gauss 1). 3. Graph this using the plot command. 4. Repeat steps 1-3 for two more Gaussian pulses of different widths. Call them gauss2 and gauss3. Best to make one somewhat wider and one somewhat narrower than the one above, but make sure they fit in the 512-length vector. 5. Create a graph using plot() that shows all three gaussian pulses on the same graph. 6. Take the Fourier transforms of the plots using the fft() function: fgl=fft(gaussl); 7. Plot the magnitudes of the Fourier transforms using the abs() function - plot all three on the same graph. You may need to change the x-axis scale to zoom in on details. 8. Save your variables to a .mat file using the save() command. We may use them again later. 9. Observe what happens to the Fourier transforms as the width of the pulse changes. Note how this relates to principles discussed in class. 10. Turn in your graphs from step 5 and step 7 and a brief discussion of your observations