Commit 65a4ae98 by Ralph Giles

### Add latex versions of the lsp equations.

svn path=/trunk/vorbis/; revision=3999
parent 1c23ffc1

$Id: 06-floor0.xml,v 1.1 2002/10/12 20:37:11 giles Exp$ $Id: 06-floor0.xml,v 1.2 2002/10/13 14:32:16 giles Exp$ Last update to this document: July 19, 2002 ... ... @@ -137,7 +137,35 @@ assuming the following definitions for the given vector to be synthesized: [latex for lspmap goes here] [lsp map equation] \begin{math} \mathrm{map}_i = \left\{ \begin{array}{ll} \min ( \mathtt{floor0\_bark\_map\_size} - 1, foobar ) & \textrm{for } i \in [0,n-1] \\ -1 & \textrm{for } i = n \end{array} \right. \end {math} where \begin{math} foobar = \left\lfloor \mathrm{bark}\left(\frac{\mathtt{floor0\_rate} \cdot i}{2n}\right) \cdot \frac{\mathtt{floor0\_bark\_map\_size}} {\mathrm{bark}(.5 \cdot \mathtt{floor0\_rate})} \right\rfloor \end{math} and \begin{math} \mathrm{bark}(x) = 13.1 \arctan (.00074x) + 2.24 \arctan (.0000000158x^2)+.0001x \end{math} ... ... @@ -153,7 +181,13 @@ Similarly, the below calculation synthesizes the output LSP curve [outp calculate [p] and [q] according to: [latex for oddlsp here] [equation for odd lsp] \begin{eqnarray*} p & = & (1 - \cos^2\omega)\prod_{j=0}^{(\mathtt{order}-3)/2} 4 (\cos c_{2j+1} - \cos \omega)^2 \\ q & = & \frac{1}{4} \prod_{j=0}^{(\mathtt{order}-1)/2} 4 (\cos c_{2j+1} - \cos \omega)^2 \end{eqnarray*} ... ... @@ -162,7 +196,13 @@ Similarly, the below calculation synthesizes the output LSP curve [outp calculate [p] and [q] according to: [latex for evenlsp here] [equation for even lsp] \begin{eqnarray*} p & = & \frac{(1 - \cos^2\omega)}{2} \prod_{j=0}^{(\mathtt{order}-2)/2} 4 (\cos c_{2j} - \cos \omega)^2 \\ q & = & \frac{(1 + \cos^2\omega)}{2} \prod_{j=0}^{(\mathtt{order}-2)/2} 4 (\cos c_{2j} - \cos \omega)^2 \end{eqnarray*} ... ... @@ -171,7 +211,13 @@ Similarly, the below calculation synthesizes the output LSP curve [outp calculate [linear_floor_value] according to: [latex for floorval here] [expression for floorval] \begin{math} \exp \left( .11512925 \left(\frac{\mathtt{amplitude} \cdot \mathtt{floor0\_amplitute\_offset}}{(2^{\mathtt{floor0\_amplitude\_bits}}-1)\sqrt{p+q}} - \mathtt{floor0\_amplitude\_offset} \right) \right) \end{math} ... ...
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