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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\pi/T</math> | + | <math>w_0=2\pi/T=3</math> |
<math>x(t)=3cos(3t)</math> | <math>x(t)=3cos(3t)</math> | ||
| − | <math>=\frac{3}{2}[(e^{ | + | <math>=\frac{3}{2}[(e^{j3t})+(e^{-j3t})]</math> |
| − | <math>=\frac{3}{2}(e^{ | + | <math>=\frac{3}{2}(e^{j3t})+\frac{3}{2}(e^{-j3t})</math> |
| − | so we can see that when k=1 | + | so we can see that when k=1, <math>a_1=\frac{3}{2}</math>, and when k=-1,<math>a_-1=\frac{3}{2}</math> |
| + | |||
| + | others are all zero | ||
Revision as of 15:26, 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=3 $
$ x(t)=3cos(3t) $
$ =\frac{3}{2}[(e^{j3t})+(e^{-j3t})] $
$ =\frac{3}{2}(e^{j3t})+\frac{3}{2}(e^{-j3t}) $
so we can see that when k=1, $ a_1=\frac{3}{2} $, and when k=-1,$ a_-1=\frac{3}{2} $
others are all zero
