Revision as of 06:22, 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} $

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[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} $

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