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author Daniele Nicolodi <nicolodi@science.unitn.it>
date Mon, 05 Dec 2011 16:20:06 +0100
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1 <!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
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2 "http://www.w3.org/TR/1999/REC-html401-19991224/loose.dtd">
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3
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4 <html lang="en">
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5 <head>
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6 <meta name="generator" content=
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7 "HTML Tidy for Mac OS X (vers 1st December 2004), see www.w3.org">
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8 <meta http-equiv="Content-Type" content=
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9 "text/html; charset=us-ascii">
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10
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11 <title>Upsampling a time-series AO (LTPDA Toolbox)</title>
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12 <link rel="stylesheet" href="docstyle.css" type="text/css">
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13 <meta name="generator" content="DocBook XSL Stylesheets V1.52.2">
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14 <meta name="description" content=
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15 "Presents an overview of the features, system requirements, and starting the toolbox.">
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16 </head>
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17
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18 <body>
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19 <a name="top_of_page" id="top_of_page"></a>
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20
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21 <p style="font-size:1px;">&nbsp;</p>
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22
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23 <table class="nav" summary="Navigation aid" border="0" width=
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24 "100%" cellpadding="0" cellspacing="0">
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25 <tr>
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26 <td valign="baseline"><b>LTPDA Toolbox</b></td><td><a href="../helptoc.html">contents</a></td>
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27
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28 <td valign="baseline" align="right"><a href=
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29 "ltpda_training_topic_2_1.html"><img src="b_prev.gif" border="0" align=
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30 "bottom" alt="Downsampling a time-series AO"></a>&nbsp;&nbsp;&nbsp;<a href=
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31 "ltpda_training_topic_2_3.html"><img src="b_next.gif" border="0" align=
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32 "bottom" alt="Resampling a time-series AO"></a></td>
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33 </tr>
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34 </table>
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35
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36 <h1 class="title"><a name="f3-12899" id="f3-12899"></a>Upsampling a time-series AO</h1>
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37 <hr>
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38
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39 <p>
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40 <p>
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41 Upsampling increases the sampling rate of the input AOs by an integer factor
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42 </p>
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43
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44 <p>The <tt>ao/upsample</tt> method can take the following parameters:
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45 <table cellspacing="0" class="body" cellpadding="2" border="0" width="80%">
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46 <colgroup>
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47 <col width="25%"/>
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48 <col width="75%"/>
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49 </colgroup>
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50 <thead>
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51 <tr valign="top">
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52 <th class="categorylist">Key</th>
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53 <th class="categorylist">Description</th>
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54 </tr>
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55 </thead>
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56 <tbody>
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57 <!-- Key 'N' -->
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58 <tr valign="top">
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59 <td bgcolor="#f3f4f5">
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60 <p><tt>N</tt></p>
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61 </td>
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62 <td bgcolor="#f3f4f5">
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63 <p>The upsample factor. The algorithm places 'N-1' zeros between each of the original samples.</p>
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64 </td>
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65 </tr>
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66 <!-- Key 'offset' -->
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67 <tr valign="top">
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68 <td bgcolor="#f3f4f5">
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69 <p><tt>PHASE</tt></p>
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70 </td>
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71 <td bgcolor="#f3f4f5">
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72 <p>This parameter specifies an additional sample offet. The value must be between 0 and N-1.</p>
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73 </td>
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74 </tr>
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75 </tbody>
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76 </table>
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77 </p>
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78 <h2>Example 1</h2>
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79 <p>
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80 We will upsample a sine-wave by a factor of 3 with no initial phase offset.
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81 </p>
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82 <p>
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83 Start by creating a sine-wave at 1Hz with a 30Hz sample rate and 10 seconds long. We can use
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84 the <tt>ao</tt> "From Waveform" parameter set to do this. (Equally, we can do this with the "From Time-series Function"
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85 parameter set.)
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86 </p>
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87 <div class="fragment"><pre>
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88 pl = plist(<span class="string">'Waveform'</span>, <span class="string">'sine wave'</span>, <span class="string">'f'</span>, 1, <span class="string">'fs'</span>, 30, <span class="string">'nsecs'</span>, 10);
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89 x = ao(pl);</pre></div>
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90 <p>
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91 Now we can proceed to upsample this data by a factor 3. This will place 2 zero samples between each of the
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92 original samples.
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93 </p>
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94 <div class="fragment"><pre>
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95 pl_up = plist(<span class="string">'N'</span>, 3); <span class="comment">% increase the sampling frequency by a factor of 10</span>
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96 x_up = upsample(x, pl_up); <span class="comment">% resample the input AO (x) to obtain the upsampled AO (y) </span>
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97 iplot(x, x_up, plist(<span class="string">'XRanges'</span>, [0 1], <span class="string">'Markers'</span>, {<span class="string">'o'</span>, <span class="string">'s'</span>})) <span class="comment">% plot original and upsampled data</span>
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98 </pre>
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99 </div>
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100 <img src="images/ltpda_training_1/topic2/up1.png" alt="Upsample" border="3">
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101 <br>
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102 <br>
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103 <h2>Example 2</h2>
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104
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105 <p>
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106 In this second example, we will upsample some random noise by a factor 4 with a phase offset of 2 samples.
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107 </p>
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108 <p>
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109 Again, start by constructing some test data, in this case a white-noise data stream. We can do this
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110 again using the "From Waveform" parameter set with an <tt>ao</tt> constructor.
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111 </p>
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112 <div class="fragment"><pre>
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113 pl = plist(<span class="string">'Waveform'</span>, <span class="string">'noise'</span>, <span class="string">'fs'</span>, 10, <span class="string">'nsecs'</span>, 10, <span class="string">'yunits'</span>, <span class="string">'m'</span>);
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114 x = ao(pl);
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115 pl_upphase = plist(<span class="string">'N'</span>, 4,<span class="string">'phase'</span>, 2); <span class="comment">% increase the sampling frequency and add phase of 2 samples to the upsampled data</span>
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116 x_upphase = upsample(x, pl_upphase); <span class="comment">% resample the input AO (x) to obtain the upsampled and delayed AO</span>
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117 iplot(x, x_upphase, plist(<span class="string">'XRanges'</span>, [0 1], <span class="string">'Markers'</span>, {<span class="string">'o'</span>, <span class="string">'s'</span>})) <span class="comment">% plot original and upsampled data</span>
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118 </pre>
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119 </div>
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120 <img src="images/ltpda_training_1/topic2/up2.png" alt="Upsample" border="3">
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121
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122
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123 </p>
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124
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125 <br>
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126 <br>
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127 <table class="nav" summary="Navigation aid" border="0" width=
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128 "100%" cellpadding="0" cellspacing="0">
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129 <tr valign="top">
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130 <td align="left" width="20"><a href="ltpda_training_topic_2_1.html"><img src=
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131 "b_prev.gif" border="0" align="bottom" alt=
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132 "Downsampling a time-series AO"></a>&nbsp;</td>
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133
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134 <td align="left">Downsampling a time-series AO</td>
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135
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136 <td>&nbsp;</td>
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137
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138 <td align="right">Resampling a time-series AO</td>
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139
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140 <td align="right" width="20"><a href=
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141 "ltpda_training_topic_2_3.html"><img src="b_next.gif" border="0" align=
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142 "bottom" alt="Resampling a time-series AO"></a></td>
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143 </tr>
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144 </table><br>
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145
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146 <p class="copy">&copy;LTP Team</p>
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147 </body>
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148 </html>