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} $

One Solution

$ 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} $

One Solution

$ 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} $

One Solution

$ 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} $

One Solution

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

One Solution

$ 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} $

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