(New page: == Signal == We will compute the Power and Energy of a 440HZ sin wave, also known as an "A". <math>x(t)=sin(2\pi440t)\!</math>. == Average Power == Average power of the 440 Hz sine wav...) |
(→Average Power) |
||
| Line 15: | Line 15: | ||
| − | <math>=\frac{1}{4\pi}(t | + | <math>=\frac{1}{4\pi}(t-\frac{1}{4\pi440}sin(4\pi440t))|_{t=0}^{t=2\pi}</math> |
| − | <math>=\frac{1}{4\pi}(2\pi | + | <math>=\frac{1}{4\pi}(2\pi-(1.7305e^-4)-0-0)</math> |
<math>=\frac{1}{2}</math> | <math>=\frac{1}{2}</math> | ||
Revision as of 09:13, 4 September 2008
Signal
We will compute the Power and Energy of a 440HZ sin wave, also known as an "A".
$ x(t)=sin(2\pi440t)\! $.
Average Power
Average power of the 440 Hz sine wave.
$ E=\frac{1}{2\pi-0}\int_0^{2\pi}{|sin(2\pi440t)|^2dt} $
$ =\frac{1}{2\pi-0}\frac{1}{2}\int_0^{2\pi}(|1-cos(4\pi440t)|)dt $
$ =\frac{1}{4\pi}(t-\frac{1}{4\pi440}sin(4\pi440t))|_{t=0}^{t=2\pi} $
$ =\frac{1}{4\pi}(2\pi-(1.7305e^-4)-0-0) $
$ =\frac{1}{2} $
