Practice for Final
This page is intended as a way to practice, please solve the problems on a new page and link your solutions here!
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} $
