(→Energy) |
(→cos(t-2)) |
||
| Line 1: | Line 1: | ||
== cos(t-2) == | == cos(t-2) == | ||
A time shift should not effect the energy or power of periodic function over one period. | A time shift should not effect the energy or power of periodic function over one period. | ||
| − | u=(t-2) | + | |
| + | |||
| + | <math>u = (t-2)</math> | ||
== Energy == | == Energy == | ||
Revision as of 05:53, 5 September 2008
cos(t-2)
A time shift should not effect the energy or power of periodic function over one period.
$ u = (t-2) $
Energy
$ E=\int_{-2}^{2\pi-2}{|cos(u)|^2du} $
$ E=\frac{1}{2}\int_{-2}^{2\pi-2}(1+cos(2(u)))du $
$ E=\frac{1}{2}((u+\frac{1}{2}sin(2(u)))|_{u=-2}^{u=2\pi-2} $
$ E=\frac{1}{2}(2\pi-2 + .378 -(-2 - .378)) $
$ E=\pi $
Power
$ E=\frac{1}{2\pi-0}\int_{-2}^{2\pi-2}{|cos(u)|^2du} $
$ =\frac{1}{2\pi-0} *{\frac{1}{2}}\int_{-2}^{2\pi-2}(1+cos(2u))du $
$ =\frac{1}{4\pi}((u)+\frac{1}{2}sin(2u))|_{u=-2}^{u=2\pi-2} $
$ =\frac{1}{4\pi}(2\pi-2+.378-(-2+.378)) $
$ =\frac{1}{2} $
