Continuous-Time Systems HW

Continuous Time Convolution:

1. Solve the following for y(t)=x(t)*h(t)

x(t) = u(t)-u(t-4); h(t) = r(t)

2. Convolve the following:

3. Find the response of a system to an input of x(t)=2u(t-10) if h(t)=sin(2t)u(t).

4. A linear time invariant system has the following impulse response:

Use convolution to find the response y(t) to the following input:

Sketch y(t) for the case when a = 1.

h t e u tat( ) ( )= −2

x t u t u t( ) ( ) ( )= − − 4

5. Determine y(t) = x(t)*h(t) where x(t0 = u(t) and

6. Compute x(t)*v(t) 1

2

2 t

h(t)