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#Introduction | #Introduction | ||
| + | #Definition <br> | ||
#Derivation<br> | #Derivation<br> | ||
#Example | #Example | ||
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\end{array}\right. = {\frac{1}{D}} \sum_{k = -\infty}^{D-1} e^{jk {\frac{2 \pi}{D} m}}</math> | \end{array}\right. = {\frac{1}{D}} \sum_{k = -\infty}^{D-1} e^{jk {\frac{2 \pi}{D} m}}</math> | ||
| − | == Derivation == | + | == Derivation l == |
== Example<br> == | == Example<br> == | ||
Revision as of 20:38, 9 October 2014
Downsampling
A slecture by ECE student Yerkebulan Yeshmukhanbetov
Partly based on the ECE438 Fall 2014 lecture material of Prof. Mireille Boutin.
Outline
- Introduction
- Definition
- Derivation
- Example
- Conclusion
- References
Introduction
where
$ s_D [m]=\left\{ \begin{array}{ll} 1,& \text{ if } n \text{ is a multiple of } 4,\\ 0, & \text{ else}. \end{array}\right. = {\frac{1}{D}} \sum_{k = -\infty}^{D-1} e^{jk {\frac{2 \pi}{D} m}} $
Derivation l
Example
Example
Conclusion
To summarize, the Nyquist theorem states that any bandlimited signal can be perfectly reconstructed from its sampling if sampled at a rate greater than twice its bandwidth (fs > 2fM). However, the Nyquist condition is not necessary for perfect reconstruction as shown in the example above.
