Revision as of 18:52, 4 September 2008 by Bchanyas (Talk)

Suppose a signal is defined by $ cos(t) $

The energy can be computed using the formula:

$ E = \int_{b}^{a}{|x(t)|^2}dt\, $


Suppose we want to compute the energy of the signal $ cos(t) $ in the interval $ 0 $ to $ 2\pi $.

The formula then becomes:


$ E = \int_{0}^{2\pi}{|cos(t)|^2}dt\, $


Using trigonometric identity, $ cos^2(t) = \frac{1}{2} + \frac{1}{2}cos(2t)\, $

This implies:


$ E = \frac{1}{2}\int_{0}^{2\pi}1 + cos(2t)dt\, $


Integrating yields


$ E = \frac{1}{2}\left(t + \frac{1}{2}sin(2t)\right)\, $

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BSEE 2004, current Ph.D. student researching signal and image processing.

Landis Huffman