| Line 11: | Line 11: | ||
<math>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}</math> | <math>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}</math> | ||
| + | [[ECE301S11_more_practice_CT_conv_1 | Partial Solution]] | ||
| − | <math>2) \begin{align} x(t) &= | + | <math>2) \begin{align} x(t) &= e^{jwt} \\ y(t) &= e^{jwt} \\ z(t) &= x(t) * y(t) \end{align}</math> |
| − | <math>3) \begin{align} x(t) &= | + | <math>3) \begin{align} x(t) &= sin(t) \\ y(t) &= cos(t) \\ z(t) &= x(t) * y(t) \end{align}</math> |
| − | <math>4) \begin{align} x(t) &= sin(t) \\ y(t) &= | + | <math>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}</math> |
| − | <math>5 | + | <math>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}</math> |
| − | + | ||
| − | + | ||
=== DT === | === DT === | ||
| − | <math> | + | <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> | + | <math>7) \begin{align} x[t] &= e^{jwt} \\ y[t] &= e^{jwt} \\ z[t] &= x[t] * y[t] \end{align}</math> |
| − | <math> | + | <math>8) \begin{align} x[t] &= sin[t] \\ y[t] &= cos[t] \\ z[t] &= x[t] * y[t] \end{align}</math> |
| − | <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> | + | <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> |
Revision as of 06:03, 29 April 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!
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} $ Partial Solution
$ 2) \begin{align} x(t) &= e^{jwt} \\ y(t) &= e^{jwt} \\ z(t) &= x(t) * y(t) \end{align} $
$ 3) \begin{align} x(t) &= sin(t) \\ y(t) &= cos(t) \\ 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[t] &= u[t] - u[t-1] \\ y[t] &= u[t+2] - u[t-2] \\ z[t] &= x[t] * y[t] \end{align} $
$ 7) \begin{align} x[t] &= e^{jwt} \\ y[t] &= e^{jwt} \\ z[t] &= x[t] * y[t] \end{align} $
$ 8) \begin{align} x[t] &= sin[t] \\ y[t] &= cos[t] \\ z[t] &= x[t] * y[t] \end{align} $
$ 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} $
$ 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} $
