(New page: Convolution of Unit Step Function: To take a convolution, first determine whether the system is CT or DT and use the correct formula. Next it's time to simplify. Originally the bounds a...) |
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| − | Convolution of Unit Step Function: | + | ==Convolution of Unit Step Function:== |
| − | + | To take a convolution, first determine whether the system is CT or DT and use the correct formula. Next it's time to simplify. Originally the bounds are set to negative and positive infinity. The unit step function will determine the new set of bounds. Consider the following unit step function as an example: <img alt="tex:u(2t-1)" style="vertical-align: middle;" />. This function will be a zero as long as <math>(2t-1)style=vertical-align: middle</math> is less than 0. Solve for t and apply the new bounds. Next its time for the real work! | |
| − | Convolution of Delta Function: | + | ==Convolution of Delta Function:== |
| − | + | Consider <math>\delta(ax+b)style=vertical-align: middle</math>. Simplify this convolution by solving for when the delta function is set to one. (This is when the <img alt="tex:(ax+b)" style="vertical-align: middle;" /> is equal to zero). That is the only value of the integration or sum, so replace t accordingly and solve. | |
Revision as of 20:18, 16 March 2008
Convolution of Unit Step Function:
To take a convolution, first determine whether the system is CT or DT and use the correct formula. Next it's time to simplify. Originally the bounds are set to negative and positive infinity. The unit step function will determine the new set of bounds. Consider the following unit step function as an example: <img alt="tex:u(2t-1)" style="vertical-align: middle;" />. This function will be a zero as long as $ (2t-1)style=vertical-align: middle $ is less than 0. Solve for t and apply the new bounds. Next its time for the real work!
Convolution of Delta Function:
Consider $ \delta(ax+b)style=vertical-align: middle $. Simplify this convolution by solving for when the delta function is set to one. (This is when the <img alt="tex:(ax+b)" style="vertical-align: middle;" /> is equal to zero). That is the only value of the integration or sum, so replace t accordingly and solve.
