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| − | + | '''Example''' | |
| − | Given that a signal <math>\,\! x(t)=2t^2+1</math>, find the Energy and Power from | + | Given that a signal |
| + | <math>\,\! x(t)=2t^2+1</math>, find the Energy and Power from <math>\,\!t_1=1</math> to <math>\,\!t_2=4</math> | ||
| − | + | <math>\,\! E=\int_{1}^{4} |2t^2+1|^2\, dt | |
| − | + | ||
| − | + | ||
| − | <math>\,\! E=\int_{1}^{4} |2t^2+1|^2\, dt | + | |
=\int_{1}^{4} |4t^4+4t^2+1|\, dt | =\int_{1}^{4} |4t^4+4t^2+1|\, dt | ||
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=\frac{4}{5}t^5+\frac{4}{3}t^3+t\bigg]_0^3 | =\frac{4}{5}t^5+\frac{4}{3}t^3+t\bigg]_0^3 | ||
| − | =905.4</math> | + | =905.4</math>Joules. |
| − | <math>\,\! | + | <math>\,\! |
| − | P=\frac{1}{t_2-t_1}905.4=301. | + | P=\frac{1}{t_2-t_1}905.4=301.8watts. |
| − | </math> | + | </math> |
Latest revision as of 13:21, 5 September 2008
Jayanth Athreya H.w 1.5 Computation of Signal Energy and power. Source for definition Of Continuous Signal: Wikipedia.
Continuous signal:A continuous signal or a continuous-time signal is a varying quantity (a signal) that is expressed as a function of a real-valued domain, usually time. The function of time need not be continuous.
Example Given that a signal $ \,\! x(t)=2t^2+1 $, find the Energy and Power from $ \,\!t_1=1 $ to $ \,\!t_2=4 $
$ \,\! E=\int_{1}^{4} |2t^2+1|^2\, dt =\int_{1}^{4} |4t^4+4t^2+1|\, dt =\frac{4}{5}t^5+\frac{4}{3}t^3+t\bigg]_0^3 =905.4 $Joules.
$ \,\! P=\frac{1}{t_2-t_1}905.4=301.8watts. $
