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According to the following equations : | According to the following equations : | ||
| − | <math>exp(2jt)=t | + | <math>exp(2jt)=t* exp(-2jt)</math> |
and | and | ||
| − | <math>exp(-2jt)=t | + | <math>exp(-2jt)=t * exp(2jt)</math> |
| + | we see that the system equation is: | ||
| + | |||
| + | <math>x(-t)->t*x(t)</math> | ||
| + | in case of cosine function | ||
| + | <math>cos(t)->t*cos(t)</math> | ||
| + | <math>cos(-t)->*cos(-t)</math> | ||
| + | thus | ||
| + | <math>cos(-t)=t*cos(t)</math>hence it is an even function | ||
Latest revision as of 21:26, 17 September 2008
According to the following equations :
$ exp(2jt)=t* exp(-2jt) $
and
$ exp(-2jt)=t * exp(2jt) $
we see that the system equation is:
$ x(-t)->t*x(t) $
in case of cosine function
$ cos(t)->t*cos(t) $
$ cos(-t)->*cos(-t) $ thus $ cos(-t)=t*cos(t) $hence it is an even function
