Problems:
1) Calculate the convolution y(t) = x(t)*h(t) for x(t)=u(t)-u(t-3), h(t)=e-3tu(t)
2) Calculate the convolution y(t) = x(t)*h(t) for x(t)=e-4tu(t-3), h(t)=e-3tu(t)
3) Find the impulse response, h[n], for the difference equation
y[n] + 2y[n-1] = x[n] + 2x[n-2]
4) Determine the impulse response by first finding the unit step response, ys(t), for the following system
y''+ 6y' + 5y = x(t)
5) Given the continuous time causal systems represented by the differential equation below,
y" + 6y' + 5y = x'-2x
Calculate the impulse response by first calculating the ramp response, ys(t).