Revision as of 06:53, 6 May 2011

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!

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

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

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

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

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

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

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

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

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

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

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

@@ Line 29: / Line 29: @@
 === DT ===
-<math>6)  \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}</math>
+<math>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}</math>
-<math>7)  \begin{align} x[t] &= e^{jwt} \\ y[t] &= e^{jwt} \\ z[t] &= x[t] * y[t] \end{align}</math>
+[[ECE301S11_more_practice_DT_conv_1_ekhall | One Solution]]
-<math>8)  \begin{align} x[t] &= sin[t] \\ y[t] &= cos[t] \\ z[t] &= x[t] * y[t] \end{align}</math>
+<math>7)  \begin{align} x[n] &= e^{jwn}u[n] \\ y[n] &= e^{jwn}u[n-6] \\ z[n] &= x[n] * y[n] \end{align}</math>
-<math>9)  \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}</math>
+<math>8)  \begin{align} x[n] &= sin[n] \\ y[n] &= cos[n] \\ z[n] &= x[n] * y[n] \end{align}</math>
-<math>10)  \begin{align} x[t] &= \frac{e^{jwt}}{2} \\ y[t] &= u[t+2] - u[t-2] \\ z[t] &= x[t] * y[t] \end{align}</math>
+<math>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}</math>
+<math>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}</math>