Exercise 3.2: Write a MATLAB script that loads the ultrasound pulse in the file us_pulse.mat, then determine (by experimentation) a suitable model of the pulse in the file. Try to find a model of as low order as possible. Plot (and discuss) the following:
• The original pulse and the modeled pulse, for a few different choices of model order.
• The frequency response of the resulting model. What type of filter is this, low-pass,
bandpass or high-pass? Is it stable?
• The model error, for the different model orders. Is the Padé method suitable for this type of signals?
Hint: Use the filter command to compute the output of your filter, using an input of the same length as the original pulse, constructed as u0 = [1; zeros(length(x)-1,1)]);, where x is the original ultrasound pulse.

Exercise 3.3: Repeat Exercise 3.2 using the Prony approximation instead (Section 4.4 in the text book). How much were you able to lower the model order and still obtain a good results. Discuss possible reasons for this.

Exercise 3.4: Write a MATLAB script to do the following:
• Loop through all possible model orders for the Prony method.
• Find the minimum model order resulting in an error no larger than 2% of the energy1 of the original ultrasound pulse.
• Compute the resulting error (as percentage of the signal energy)
• Find the minimum model order of the Padé approximation achieving an error no larger
than that of the Prony method.
Compare the resulting model orders. It will be clear that the Prony method results in a lower model order for the same average error, but comment also on how the errors are distributed over the pulse. What are the main differences? Looking at the derivation of the two methods, try to explain these differences.

Exercise 3.2: Write a MATLAB script that loads the ultrasound pulse...