(New page: Category:ECE438Spring2009mboutinCategory:ECE438Spring2009mboutin:CourseNotes:Lecture4 == ECE438 Course Notes January 28, 2009 == <h3>Properties of L.T. (Continuous Time)</h3> <u...) |
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| − | == | + | [[Category:ECE438]] |
| + | [[Category:signal processing]] | ||
| + | [[Category:ECE438Spring2009mboutin]] | ||
| + | [[Category:lecture notes]] | ||
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| + | == [[ECE_438_Spring_2009_mboutin_Course_Notes|Course Notes]], January 28, 2009 == | ||
| + | [[ECE438_%28BoutinSpring2009%29|ECE438, Spring 2009]] | ||
| + | ---- | ||
<h3>Properties of L.T. (Continuous Time)</h3> | <h3>Properties of L.T. (Continuous Time)</h3> | ||
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<li>Scaling and Shifting | <li>Scaling and Shifting | ||
<ul> | <ul> | ||
| − | <li><math>x(\frac{t-t_0}{a} \Rightarrow |a|*X(af)*e^{-j2\ | + | <li><math>x(\frac{t-t_0}{a}) \Rightarrow |a|*X(af)*e^{-j2\pi ft_0}</math></li> |
| + | </ul> | ||
| + | </li> | ||
| + | <li>Modulation | ||
| + | <ul> | ||
| + | <li><math>x(t)e^{j2\pi f_0t} \Rightarrow x(f*f_0)</math></li> | ||
| + | </ul> | ||
| + | </li> | ||
| + | <li>Reciprocity (Duality) | ||
| + | <ul> | ||
| + | <li><math>X(t) \Rightarrow X(-f)</math></li> | ||
| + | </ul> | ||
| + | </li> | ||
| + | <li>Parsevals Relation | ||
| + | <ul> | ||
| + | <li><math></math></li> | ||
</ul> | </ul> | ||
</li> | </li> | ||
</ul> | </ul> | ||
Latest revision as of 06:44, 16 September 2013
Course Notes, January 28, 2009
Properties of L.T. (Continuous Time)
- Scaling and Shifting
- $ x(\frac{t-t_0}{a}) \Rightarrow |a|*X(af)*e^{-j2\pi ft_0} $
- Modulation
- $ x(t)e^{j2\pi f_0t} \Rightarrow x(f*f_0) $
- Reciprocity (Duality)
- $ X(t) \Rightarrow X(-f) $
- Parsevals Relation
