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[[Category:z-transform]] | [[Category:z-transform]] | ||
| − | =Relationship between DTFT and z-transform= | + | =Relationship between DTFT and [[Info_z-transform|z-transform]]= |
<math>X(w) = F{x[n]} = \sum_{n=-\infty}^\infty x[n]e^{-jwn}</math> | <math>X(w) = F{x[n]} = \sum_{n=-\infty}^\infty x[n]e^{-jwn}</math> | ||
Revision as of 13:49, 30 April 2015
Relationship between DTFT and z-transform
$ X(w) = F{x[n]} = \sum_{n=-\infty}^\infty x[n]e^{-jwn} $
$ X(z)|_{z=e^{jw}} = X(e^{jw}) $
Can compute Z-Transform as a DTFT write $ X(z)=X(re^{jw}) $
then $ X(z)= \sum_{-\infty}^\infty x[n]z^{-n} $
$ X(z)= \sum_{-\infty}^\infty x[n](re^{jw})^{-n} $
$ X(z)= \sum_{-\infty}^\infty x[n]r^{-n}e^{-jwn} $
$ = F{x[n]r^{-n}} $
