(→Example) |
(→Example) |
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Let's look at: <math>x(t)=3*cos(3t)</math>, we know that the fudamental period of x(t) is | Let's look at: <math>x(t)=3*cos(3t)</math>, we know that the fudamental period of x(t) is | ||
| − | <math>w_0=2 | + | <math>w_0=2\pi/T</math> |
| − | <math>x(t)= | + | <math>x(t)=3cos(3t)</math> |
<math>=\frac{3}{2}[(e^{j*3*t})+(e^{-j*3*t})]</math> | <math>=\frac{3}{2}[(e^{j*3*t})+(e^{-j*3*t})]</math> | ||
Revision as of 15:19, 26 September 2008
Definition of Periodic CT Signal
x(t) is periodic if there existes T>0 such that x(t)=x(T+t)
Example
Let's look at: $ x(t)=3*cos(3t) $, we know that the fudamental period of x(t) is
$ w_0=2\pi/T $
$ x(t)=3cos(3t) $
$ =\frac{3}{2}[(e^{j*3*t})+(e^{-j*3*t})] $
$ =\frac{3}{2}(e^{j*3*t})+\frac{3}{2}(e^{-j*3*t}) $
so we can see that when k=1
