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<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 | One Solution]] | [[ECE301S11_more_practice_CT_conv_1 | One Solution]] | ||
| − | <math>2) \begin{align} x(t) &= e^{jwt} \\ y(t) &= e^{jwt} \\ z(t) &= x(t) * y(t) \end{align}</math> | + | <math>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}</math> |
| − | <math>3) \begin{align} x(t) &= sin(t) \\ y(t) &= cos(t) \\ z(t) &= x(t) * y(t) \end{align}</math> | + | [[ECE301S11_more_practice_CT_conv_2 | One Solution]] |
| + | |||
| + | <math>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}</math> | ||
| + | |||
| + | [[ECE301S11_more_practice_CT_conv_3 | One Solution]] | ||
<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>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> | ||
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=== DT === | === DT === | ||
| − | <math>6) \begin{align} x[ | + | <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> |
| + | |||
| + | [[ECE301S11_more_practice_DT_conv_1_ekhall | One Solution]] | ||
| + | |||
| + | <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> | ||
| − | + | [[ECE301S11_more_practice_DT_conv_7_ekhall | One Solution ]] | |
| − | <math>8) \begin{align} x[ | + | <math>8) \begin{align} x[n] &= sin[n] \\ y[n] &= cos[n] \\ z[n] &= x[n] * y[n] \end{align}</math> |
| − | <math>9) \begin{align} x[ | + | <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[ | + | <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> |
Latest revision as of 08:23, 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!
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} $
