1 | <?xml version="1.0" standalone="no"?> |
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2 | <!DOCTYPE section PUBLIC "-//OASIS//DTD DocBook XML V4.2//EN" |
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3 | "http://www.oasis-open.org/docbook/xml/4.2/docbookx.dtd" [ |
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4 | |
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5 | ]> |
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6 | |
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7 | <section id="vorbis-spec-floor0"> |
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8 | <sectioninfo> |
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9 | <releaseinfo> |
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10 | $Id: 06-floor0.xml 10424 2005-11-23 08:44:18Z xiphmont $ |
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11 | </releaseinfo> |
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12 | </sectioninfo> |
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13 | <title>Floor type 0 setup and decode</title> |
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14 | |
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15 | |
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16 | <section> |
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17 | <title>Overview</title> |
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18 | |
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19 | <para> |
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20 | Vorbis floor type zero uses Line Spectral Pair (LSP, also alternately |
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21 | known as Line Spectral Frequency or LSF) representation to encode a |
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22 | smooth spectral envelope curve as the frequency response of the LSP |
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23 | filter. This representation is equivalent to a traditional all-pole |
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24 | infinite impulse response filter as would be used in linear predictive |
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25 | coding; LSP representation may be converted to LPC representation and |
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26 | vice-versa.</para> |
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27 | |
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28 | </section> |
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29 | |
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30 | <section> |
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31 | <title>Floor 0 format</title> |
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32 | |
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33 | <para> |
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34 | Floor zero configuration consists of six integer fields and a list of |
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35 | VQ codebooks for use in coding/decoding the LSP filter coefficient |
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36 | values used by each frame. </para> |
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37 | |
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38 | <section><title>header decode</title> |
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39 | |
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40 | <para> |
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41 | Configuration information for instances of floor zero decodes from the |
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42 | codec setup header (third packet). configuration decode proceeds as |
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43 | follows:</para> |
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44 | |
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45 | <screen> |
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46 | 1) [floor0_order] = read an unsigned integer of 8 bits |
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47 | 2) [floor0_rate] = read an unsigned integer of 16 bits |
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48 | 3) [floor0_bark_map_size] = read an unsigned integer of 16 bits |
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49 | 4) [floor0_amplitude_bits] = read an unsigned integer of six bits |
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50 | 5) [floor0_amplitude_offset] = read an unsigned integer of eight bits |
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51 | 6) [floor0_number_of_books] = read an unsigned integer of four bits and add 1 |
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52 | 7) if any of [floor0_order], [floor0_rate], [floor0_bark_map_size], [floor0_amplitude_bits], |
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53 | [floor0_amplitude_offset] or [floor0_number_of_books] are less than zero, the stream is not decodable |
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54 | 8) array [floor0_book_list] = read a list of [floor0_number_of_books] unsigned integers of eight bits each; |
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55 | </screen> |
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56 | |
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57 | <para> |
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58 | An end-of-packet condition during any of these bitstream reads renders |
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59 | this stream undecodable. In addition, any element of the array |
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60 | <varname>[floor0_book_list]</varname> that is greater than the maximum codebook |
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61 | number for this bitstream is an error condition that also renders the |
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62 | stream undecodable.</para> |
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63 | |
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64 | </section> |
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65 | |
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66 | <section id="vorbis-spec-floor0-decode"> |
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67 | <title>packet decode</title> |
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68 | |
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69 | <para> |
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70 | Extracting a floor0 curve from an audio packet consists of first |
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71 | decoding the curve amplitude and <varname>[floor0_order]</varname> LSP |
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72 | coefficient values from the bitstream, and then computing the floor |
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73 | curve, which is defined as the frequency response of the decoded LSP |
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74 | filter.</para> |
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75 | |
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76 | <para> |
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77 | Packet decode proceeds as follows:</para> |
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78 | <screen> |
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79 | 1) [amplitude] = read an unsigned integer of [floor0_amplitude_bits] bits |
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80 | 2) if ( [amplitude] is greater than zero ) { |
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81 | 3) [coefficients] is an empty, zero length vector |
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82 | 4) [booknumber] = read an unsigned integer of <link linkend="vorbis-spec-ilog">ilog</link>( [floor0_number_of_books] ) bits |
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83 | 5) if ( [booknumber] is greater than the highest number decode codebook ) then packet is undecodable |
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84 | 6) [last] = zero; |
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85 | 7) vector [temp_vector] = read vector from bitstream using codebook number [floor0_book_list] element [booknumber] in VQ context. |
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86 | 8) add the scalar value [last] to each scalar in vector [temp_vector] |
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87 | 9) [last] = the value of the last scalar in vector [temp_vector] |
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88 | 10) concatenate [temp_vector] onto the end of the [coefficients] vector |
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89 | 11) if (length of vector [coefficients] is less than [floor0_order], continue at step 6 |
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90 | |
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91 | } |
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92 | |
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93 | 12) done. |
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94 | |
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95 | </screen> |
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96 | |
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97 | <para> |
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98 | Take note of the following properties of decode: |
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99 | <itemizedlist> |
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100 | <listitem><simpara>An <varname>[amplitude]</varname> value of zero must result in a return code that indicates this channel is unused in this frame (the output of the channel will be all-zeroes in synthesis). Several later stages of decode don't occur for an unused channel.</simpara></listitem> |
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101 | <listitem><simpara>An end-of-packet condition during decode should be considered a |
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102 | nominal occruence; if end-of-packet is reached during any read |
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103 | operation above, floor decode is to return 'unused' status as if the |
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104 | <varname>[amplitude]</varname> value had read zero at the beginning of decode.</simpara></listitem> |
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105 | |
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106 | <listitem><simpara>The book number used for decode |
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107 | can, in fact, be stored in the bitstream in <link linkend="vorbis-spec-ilog">ilog</link>( <varname>[floor0_number_of_books]</varname> - |
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108 | 1 ) bits. Nevertheless, the above specification is correct and values |
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109 | greater than the maximum possible book value are reserved.</simpara></listitem> |
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110 | |
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111 | <listitem><simpara>The number of scalars read into the vector <varname>[coefficients]</varname> |
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112 | may be greater than <varname>[floor0_order]</varname>, the number actually |
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113 | required for curve computation. For example, if the VQ codebook used |
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114 | for the floor currently being decoded has a |
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115 | <varname>[codebook_dimensions]</varname> value of three and |
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116 | <varname>[floor0_order]</varname> is ten, the only way to fill all the needed |
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117 | scalars in <varname>[coefficients]</varname> is to to read a total of twelve |
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118 | scalars as four vectors of three scalars each. This is not an error |
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119 | condition, and care must be taken not to allow a buffer overflow in |
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120 | decode. The extra values are not used and may be ignored or discarded.</simpara></listitem> |
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121 | </itemizedlist> |
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122 | </para> |
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123 | |
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124 | </section> |
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125 | |
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126 | <section id="vorbis-spec-floor0-synth"> |
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127 | <title>curve computation</title> |
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128 | |
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129 | <para> |
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130 | Given an <varname>[amplitude]</varname> integer and <varname>[coefficients]</varname> |
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131 | vector from packet decode as well as the [floor0_order], |
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132 | [floor0_rate], [floor0_bark_map_size], [floor0_amplitude_bits] and |
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133 | [floor0_amplitude_offset] values from floor setup, and an output |
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134 | vector size <varname>[n]</varname> specified by the decode process, we compute a |
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135 | floor output vector.</para> |
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136 | |
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137 | <para> |
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138 | If the value <varname>[amplitude]</varname> is zero, the return value is a |
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139 | length <varname>[n]</varname> vector with all-zero scalars. Otherwise, begin by |
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140 | assuming the following definitions for the given vector to be |
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141 | synthesized:</para> |
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142 | |
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143 | <informalequation> |
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144 | <mediaobject> |
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145 | <textobject><phrase>[lsp map equation]</phrase></textobject> |
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146 | <textobject role="tex"><phrase> |
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147 | <![CDATA[ |
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148 | \begin{math} |
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149 | \mathrm{map}_i = \left\{ |
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150 | \begin{array}{ll} |
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151 | \min ( |
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152 | \mathtt{floor0\_bark\_map\_size} - 1, |
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153 | foobar |
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154 | ) & \textrm{for } i \in [0,n-1] \\ |
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155 | -1 & \textrm{for } i = n |
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156 | \end{array} |
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157 | \right. |
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158 | \end {math} |
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159 | |
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160 | where |
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161 | |
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162 | \begin{math} |
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163 | foobar = |
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164 | \left\lfloor |
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165 | \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})} |
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166 | \right\rfloor |
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167 | \end{math} |
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168 | |
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169 | and |
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170 | |
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171 | \begin{math} |
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172 | \mathrm{bark}(x) = 13.1 \arctan (.00074x) + 2.24 \arctan (.0000000185x^2 + .0001x) |
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173 | \end{math} |
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174 | ]]> |
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175 | </phrase></textobject> |
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176 | <imageobject><imagedata fileref="lspmap.png"/></imageobject> |
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177 | </mediaobject> |
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178 | </informalequation> |
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179 | |
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180 | <para> |
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181 | The above is used to synthesize the LSP curve on a Bark-scale frequency |
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182 | axis, then map the result to a linear-scale frequency axis. |
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183 | Similarly, the below calculation synthesizes the output LSP curve <varname>[output]</varname> on a log |
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184 | (dB) amplitude scale, mapping it to linear amplitude in the last step:</para> |
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185 | |
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186 | <orderedlist> |
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187 | <listitem><simpara> <varname>[i]</varname> = 0 </simpara></listitem> |
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188 | <listitem><para>if ( <varname>[floor0_order]</varname> is odd ) { |
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189 | <orderedlist> |
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190 | <listitem><para>calculate <varname>[p]</varname> and <varname>[q]</varname> according to: |
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191 | <informalequation> |
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192 | <mediaobject> |
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193 | <textobject><phrase>[equation for odd lsp]</phrase></textobject> |
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194 | <textobject role="tex"><phrase> |
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195 | <![CDATA[ |
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196 | \begin{eqnarray*} |
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197 | p & = & (1 - \cos^2\omega)\prod_{j=0}^{(\mathtt{order}-3)/2} 4 (\cos c_{2j+1} - \cos \omega)^2 \\ |
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198 | q & = & \frac{1}{4} \prod_{j=0}^{(\mathtt{order}-1)/2} 4 (\cos c_{2j+1} - \cos \omega)^2 |
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199 | \end{eqnarray*} |
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200 | ]]> |
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201 | </phrase></textobject> |
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202 | <imageobject><imagedata fileref="oddlsp.png"/></imageobject> |
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203 | </mediaobject> |
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204 | </informalequation> |
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205 | </para></listitem> |
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206 | </orderedlist> |
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207 | } else <varname>[floor0_order]</varname> is even { |
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208 | <orderedlist> |
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209 | <listitem><para>calculate <varname>[p]</varname> and <varname>[q]</varname> according to: |
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210 | <informalequation> |
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211 | <mediaobject> |
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212 | <textobject><phrase>[equation for even lsp]</phrase></textobject> |
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213 | <textobject role="tex"><phrase> |
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214 | <![CDATA[ |
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215 | \begin{eqnarray*} |
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216 | p & = & \frac{(1 - \cos^2\omega)}{2} \prod_{j=0}^{(\mathtt{order}-2)/2} 4 (\cos c_{2j} - \cos \omega)^2 \\ |
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217 | q & = & \frac{(1 + \cos^2\omega)}{2} \prod_{j=0}^{(\mathtt{order}-2)/2} 4 (\cos c_{2j} - \cos \omega)^2 |
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218 | \end{eqnarray*} |
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219 | ]]> |
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220 | </phrase></textobject> |
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221 | <imageobject><imagedata fileref="evenlsp.png"/></imageobject> |
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222 | </mediaobject> |
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223 | </informalequation> |
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224 | </para></listitem> |
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225 | </orderedlist> |
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226 | } |
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227 | </para></listitem> |
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228 | <listitem><para>calculate <varname>[linear_floor_value]</varname> according to: |
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229 | <informalequation> |
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230 | <mediaobject> |
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231 | <textobject><phrase>[expression for floorval]</phrase></textobject> |
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232 | <textobject role="tex"><phrase> |
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233 | <![CDATA[ |
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234 | \begin{math} |
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235 | \exp \left( .11512925 \left(\frac{\mathtt{amplitude} \cdot \mathtt{floor0\_amplitute\_offset}}{(2^{\mathtt{floor0\_amplitude\_bits}}-1)\sqrt{p+q}} |
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236 | - \mathtt{floor0\_amplitude\_offset} \right) \right) |
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237 | \end{math} |
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238 | ]]> |
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239 | </phrase></textobject> |
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240 | <imageobject><imagedata fileref="floorval.png"/></imageobject> |
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241 | </mediaobject> |
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242 | </informalequation> |
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243 | </para></listitem> |
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244 | <listitem><simpara><varname>[iteration_condition]</varname> = map element <varname>[i]</varname></simpara></listitem> |
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245 | <listitem><simpara><varname>[output]</varname> element <varname>[i]</varname> = <varname>[linear_floor_value]</varname></simpara></listitem> |
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246 | <listitem><simpara>increment <varname>[i]</varname></simpara></listitem> |
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247 | <listitem><simpara>if ( map element <varname>[i]</varname> is equal to <varname>[iteration_condition]</varname> ) continue at step 5</simpara></listitem> |
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248 | <listitem><simpara>if ( <varname>[i]</varname> is less than <varname>[n]</varname> ) continue at step 2</simpara></listitem> |
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249 | <listitem><simpara>done</simpara></listitem> |
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250 | </orderedlist> |
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251 | |
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252 | </section> |
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253 | |
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254 | </section> |
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255 | |
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256 | </section> |
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257 | |
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