Revision as of 15:09, 18 September 2008 by Thouliha (Talk)

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

The Basics of Linearity

This example is solved using the following trigonometric identity:

$ cos(\omega t)=\frac{e^{\omega jt}+e^{-\omega jt}}{2}\, $.

We are told that the system has the following inputs and outputs:

$ x_1(t)=e^{2jt} \to y_1(t)=te^{2jt} $ , and

$ x_2(t)=e^{-2jt} \to y_2(t)=te^{-2jt} $

So what is the systems response to cos(2t)?

Using the identity:

$ x(t)=cos(2t)=\frac{e^{2jt}+e^{-2jt}}{2} \to y(t)=\frac{te^{2jt}+te^{-2jt}}{2}\, $

$ y(t)=t\frac{e^{2jt}+e^{-2jt}}{2}=tcos(2t)\, $

Alumni Liaison

Ph.D. on Applied Mathematics in Aug 2007. Involved on applications of image super-resolution to electron microscopy

Francisco Blanco-Silva