(New page: == Signal Energy and Power Calculations == == Background == The energy of a signal within specific time limits is defined as: <math>E=\int_{t_1}^{t_2} |x(t)|^2\, dt</math> The average...) |
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<math>P=\frac{1}{t_2-t_1}\int_{t_1}^{t_2} |x(t)|^2\, dt</math> | <math>P=\frac{1}{t_2-t_1}\int_{t_1}^{t_2} |x(t)|^2\, dt</math> | ||
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| + | |||
| + | === Example === | ||
| + | Given that a signal <math>\,\! x(t)=4t^2+2</math>, find the Energy and Power from <math>\,\!t_1=0</math> to <math>\,\!t_2=3</math> | ||
| + | |||
| + | <math>\,\! E=\int_{0}^{3} |4t+2|^2\, dt | ||
| + | |||
| + | =\int_{0}^{3} |16t^4+16t^2+4|\, dt | ||
| + | |||
| + | =\frac{16}{5}t^5+\frac{16}{3}t^3+4t\bigg]_0^3 | ||
| + | |||
| + | =933.6</math> | ||
| + | |||
| + | <math>\,\! | ||
| + | P=\frac{1}{t_2-t_1}933.6=311.2 | ||
| + | |||
| + | |||
| + | </math> | ||
Latest revision as of 15:50, 4 September 2008
Signal Energy and Power Calculations
Background
The energy of a signal within specific time limits is defined as:
$ E=\int_{t_1}^{t_2} |x(t)|^2\, dt $
The average power of a signal between specific time limits is defined as:
$ P=\frac{1}{t_2-t_1}\int_{t_1}^{t_2} |x(t)|^2\, dt $
Example
Given that a signal $ \,\! x(t)=4t^2+2 $, find the Energy and Power from $ \,\!t_1=0 $ to $ \,\!t_2=3 $
$ \,\! E=\int_{0}^{3} |4t+2|^2\, dt =\int_{0}^{3} |16t^4+16t^2+4|\, dt =\frac{16}{5}t^5+\frac{16}{3}t^3+4t\bigg]_0^3 =933.6 $
$ \,\! P=\frac{1}{t_2-t_1}933.6=311.2 $
