% Fall'06 - Spring'07 16.01-16.04 MATLAB Tutorials: Linear Systems
% Instructor: Violeta Ivanova, violeta@mit.edu
% Faculty: Mark Drela, Stephen Hall, Wes Harris, Ian Waitz

% Example 2: Linear Systems: Convolution
% This exercise is based on S. Hall's Signals and Systems lectures.

% D1. Compute the response based on the analytical solution
% Define time interval 0<t<4 at a step dt = 0.01s




% Compute the impulse response gt as g(t) = e^(-1.5t)


% Compute the input ut as u(t) = e^-t 


% Compute the response using an analytical solution y(t) = 2e^(-t)-2e^(-1.5t)


% D2. Compute the response using the built-in MATLAB function CONV
% Hint: the response must be scaled for the time interval t and step dt



% D3. Plot the input ut and impulse response gt vs. time t on the same plot 





% D4. Plot on the same plot and compare the response computed analytically, yt, 
% and the response computed numerically with function CONV, ty