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<math>\ h(t) = 5e^{-t} </math> | <math>\ h(t) = 5e^{-t} </math> | ||
<math>\ H(jw) = 5\int_0^{\infty} e^{-\tau}e^{-jw{\tau}}\,d{\tau} </math> | <math>\ H(jw) = 5\int_0^{\infty} e^{-\tau}e^{-jw{\tau}}\,d{\tau} </math> | ||
| − | <math>\ H(jw) = 5[-{1 | + | <math>\ H(jw) = 5[-\frac{1}{1 + jw}e^{-\tau}e^{-jwr} ]^{\infty}_0 </math><br><br> |
| − | <math>\ H(jw) = 5{ | + | <math>\ H(jw) = \frac{5}{1+ jw} </math> |
Revision as of 18:39, 26 September 2008
$ \ h(t) = 5e^{-t} $
$ \ H(jw) = 5\int_0^{\infty} e^{-\tau}e^{-jw{\tau}}\,d{\tau} $
$ \ H(jw) = 5[-\frac{1}{1 + jw}e^{-\tau}e^{-jwr} ]^{\infty}_0 $
$ \ H(jw) = \frac{5}{1+ jw} $
