Digital Control Systems: Difference between revisions

Revision as of 12:57, 8 April 2014

Relationship between the Laplace and Z transforms
Convolution and Z Transforms
- Z Transforms and Convolution
- Polynomial Multiplication is the same as Convolution
- [http://www-rohan.sdsu.edu/~jiracek/DAGSAW/4.3.html Here is an animation of discrete convolution. You flip shift $h(t)->h(t-t_{0})$ , then you multiply the two, $x(t_{0})h(t-t_{0})$ , then you integrate with respect to $t_{0}$ , so that the convolution is: $\int _{-\infty }^{\infty }x(t_{0})h(t-t_{0})dt_{0}$ .

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 **[http://www.ualberta.ca/~msacchi/GEOPH426/chapter2.pdf Z Transforms and Convolution]
 **[http://www.mathworks.com/help/matlab/ref/conv.html Polynomial Multiplication is the same as Convolution]
-**[http://www-rohan.sdsu.edu/~jiracek/DAGSAW/4.3.html Here is an animation of discrete convolution.  You flip shift <math>h(t)->h(t-t_0)</math>, then you multiply the two, <math>x(t_0)h(t-t_0)</math>, then you integrate with respect to <math>t_0</math>, <math>\int \from -\infty to \infty x(t_0)h(t-t_0) dt_0</math>.
+**[http://www-rohan.sdsu.edu/~jiracek/DAGSAW/4.3.html Here is an animation of discrete convolution.  You flip shift <math>h(t)->h(t-t_0)</math>, then you multiply the two, <math>x(t_0)h(t-t_0)</math>, then you integrate with respect to <math>t_0</math>, so that the convolution is:  <math>\int_{-\infty}^\infty x(t_0)h(t-t_0) dt_0</math>.