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=ECE301_S11_Exam_3_more_practice= | =ECE301_S11_Exam_3_more_practice= | ||
| + | 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 === | ||
| + | |||
| + | <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>2) \begin{align} x(t) &= r(t) - r(t-1) \\ y(t) &= r(t+2) - r(t-2) \\ z(t) &= x(t) * y(t) \end{align}</math> | ||
| + | |||
| + | <math>3) \begin{align} x(t) &= e^{jwt} \\ y(t) &= e^{jwt} \\ z(t) &= x(t) * y(t) \end{align}</math> | ||
| + | |||
| + | <math>4) \begin{align} x(t) &= sin(t) \\ y(t) &= cos(t) \\ z(t) &= x(t) * y(t) \end{align}</math> | ||
| + | |||
| + | <math>5) \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>6) \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 === | ||
| + | <math>7) \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>8) \begin{align} x[t] &= r[t] - r[t-1] \\ y[t] &= r[t+2] - r[t-2] \\ z[t] &= x[t] * y[t] \end{align}</math> | ||
| + | |||
| + | <math>9) \begin{align} x[t] &= e^{jwt} \\ y[t] &= e^{jwt} \\ z[t] &= x[t] * y[t] \end{align}</math> | ||
| + | |||
| + | <math>10) \begin{align} x[t] &= sin[t] \\ y[t] &= cos[t] \\ z[t] &= x[t] * y[t] \end{align}</math> | ||
| + | |||
| + | <math>11) \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>12) \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 05:18, 21 April 2011
ECE301_S11_Exam_3_more_practice
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) &= r(t) - r(t-1) \\ y(t) &= r(t+2) - r(t-2) \\ z(t) &= x(t) * y(t) \end{align} $
$ 3) \begin{align} x(t) &= e^{jwt} \\ y(t) &= e^{jwt} \\ z(t) &= x(t) * y(t) \end{align} $
$ 4) \begin{align} x(t) &= sin(t) \\ y(t) &= cos(t) \\ z(t) &= x(t) * y(t) \end{align} $
$ 5) \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} $
$ 6) \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
$ 7) \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} $
$ 8) \begin{align} x[t] &= r[t] - r[t-1] \\ y[t] &= r[t+2] - r[t-2] \\ z[t] &= x[t] * y[t] \end{align} $
$ 9) \begin{align} x[t] &= e^{jwt} \\ y[t] &= e^{jwt} \\ z[t] &= x[t] * y[t] \end{align} $
$ 10) \begin{align} x[t] &= sin[t] \\ y[t] &= cos[t] \\ z[t] &= x[t] * y[t] \end{align} $
$ 11) \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} $
$ 12) \begin{align} x[t] &= \frac{e^{jwt}}{2} \\ y[t] &= u[t+2] - u[t-2] \\ z[t] &= x[t] * y[t] \end{align} $
