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Source page: http://commons.wikimedia.org/wiki/File:DCT_Forumla_.jpg
 This image shows some kind of formula that could be converted to TeX. The MediaWiki TeX interpreter generates either PNG images or simple HTML markup, depending on user preferences and the complexity of the expression. In future, as more browsers are smarter, it will be able to generate enhanced HTML or even MathML in many cases. Storing formulas as images makes it harder to change them. TeX also helps making sure that they all use the same font and size. A replacement has been proposed: $\begin{array}{l}B_{pq}=\alpha_p \alpha_q \sum_{m=0}^{M-1} \sum_{n=0}^{N-1} A_{mn} \cos\frac{\pi(2m+1)p}{2M} \cos\frac{\pi(2n+1)q}{2N},\qquad 0 \le p \le M-1,\; 0 \le q \le N-1 \\ \alpha_p=\begin{cases}\frac{1}{\sqrt{M} },&p=0 \\ \sqrt{\frac{2}{M} },&1\le p\le M-1\end{cases} \qquad \alpha_q=\begin{cases}\frac{1}{\sqrt{N} },&q=0 \\ \sqrt{\frac{2}{N} },&1\le q\le N-1\end{cases}\end{array}$ $\begin{array}{l}B_{pq}=\alpha_p \alpha_q \sum_{m=0}^{M-1} \sum_{n=0}^{N-1} A_{mn} \cos\frac{\pi(2m+1)p}{2M} \cos\frac{\pi(2n+1)q}{2N},\qquad 0 \le p \le M-1,\; 0 \le q \le N-1 \\ \alpha_p=\begin{cases}\frac{1}{\sqrt{M} },&p=0 \\ \sqrt{\frac{2}{M} },&1\le p\le M-1\end{cases} \qquad \alpha_q=\begin{cases}\frac{1}{\sqrt{N} },&q=0 \\ \sqrt{\frac{2}{N} },&1\le q\le N-1\end{cases}\end{array}$

## Summary

 Description English: Formula used to calculate the DCT in a 2D array. Español: Formula utilizada para realizar el calculo de la DCT en una matriz 2D. Date 20 October 2009 Source UPCommons Author Sergi Laencina Verdaguer

## Licensing

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Creative Commons Attribution 3.0 Unported