# Practice for Final

## Convolution

Convolve each of the following using. (aka don't use FT or LT or ZT)

### CT

1) \begin{align} x(t) &= u(t) - u(t-1) \\ y(t) &= u(t+2) - u(t-2) \\ z(t) &= x(t) * y(t) \end{align}

2) \begin{align} x(t) &= e^{jwt}u(t+2) \\ y(t) &= e^{jwt}u(t-2) \\ z(t) &= x(t) * y(t) \end{align}

3) \begin{align} x(t) &= sin(t)u(t + \pi) \\ y(t) &= cos(t)u(t-\pi) \\ z(t) &= x(t) * y(t) \end{align}

4) \begin{align} x(t) &= sin(t)\left(u(t) - u(t - 10)\right) \\ y(t) &= u(t+2) - u(t-2) \\ z(t) &= x(t) * y(t) \end{align}

5) \begin{align} x(t) &= \frac{e^{jwt}}{2} \\ y(t) &= u(t+2) - u(t-2) \\ z(t) &= x(t) * y(t) \end{align}

### DT

6) \begin{align} x[n] &= u[n] - u[n-1] \\ y[n] &= u[n+2] - u[n-2] \\ z[n] &= x[n] * y[n] \end{align}

7) \begin{align} x[n] &= e^{jwn}u[n] \\ y[n] &= e^{jwn}u[n-6] \\ z[n] &= x[n] * y[n] \end{align}

8) \begin{align} x[n] &= sin[n] \\ y[n] &= cos[n] \\ z[n] &= x[n] * y[n] \end{align}

9) \begin{align} x[n] &= sin[n]\left[u[n] - u[n - 10]\right] \\ y[n] &= u[n+2] - u[n-2] \\ z[n] &= x[n] * y[n] \end{align}

10) \begin{align} x[n] &= \frac{e^{jwn}}{2} \\ y[n] &= u[n+2] - u[n-2] \\ z[n] &= x[n] * y[n] \end{align}

## Alumni Liaison

Basic linear algebra uncovers and clarifies very important geometry and algebra.

Dr. Paul Garrett