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+ − 11 <title>Digital Filtering (LTPDA Toolbox)</title>
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+ − 15 "Presents an overview of the features, system requirements, and starting the toolbox.">
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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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+ − 28 <td valign="baseline" align="right"><a href=
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+ − 29 "sigproc.html"><img src="b_prev.gif" border="0" align=
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+ − 30 "bottom" alt="Signal Processing in LTPDA"></a> <a href=
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+ − 31 "sigproc_iir.html"><img src="b_next.gif" border="0" align=
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+ − 32 "bottom" alt="IIR Filters"></a></td>
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+ − 33 </tr>
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+ − 34 </table>
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+ − 36 <h1 class="title"><a name="f3-12899" id="f3-12899"></a>Digital Filtering</h1>
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+ − 39 <p>
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+ − 40 <p>
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+ − 41 A digital filter is an operation that associates an input time series x[n] into an output one, y[n]. Methods developed in the LTPDA Toolbox deal with linear digital filters, i.e. those which fulfill that a linear combination of inputs results in a linear combination of outputs with the same coefficients (provided that these are not time dependent). In these conditions, the filter can be expressed as
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+ − 42 </p>
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+ − 43 <div align="center">
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+ − 44 <IMG src="images/sigproc_1.png" width="173" height="55" align="center" border="0">
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+ − 45 </div>
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+ − 46 <p>
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+ − 47 described in these terms, the filter is completely described by the impulse response h[k], and can then be subdivided into the following classes:
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+ − 48 </p>
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+ − 50 <ul>
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+ − 51 <li> Causal: if there is no output before input is fed in.
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+ − 52 <div align="center">
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+ − 53 <IMG src="images/sigproc_2.png" width="103" height="28" align="center" border="0">
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+ − 54 </div>
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+ − 55 </li>
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+ − 56 <li> Stable: if finite input results in finite output.
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+ − 57 <div align="center">
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+ − 58 <IMG src="images/sigproc_3.png" width="105" height="55" align="center" border="0">
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+ − 59 </div>
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+ − 60 </li>
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+ − 61 <li> Shift invariant: if time shift in the input results in a time shift in the output by the same amount.
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+ − 62 <div align="center">
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+ − 63 <IMG src="images/sigproc_4.png" width="84" height="28" align="center" border="0">
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+ − 64 </div>
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+ − 65 </li>
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+ − 66 </ul>
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+ − 67 <br>
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+ − 68 <h2><a name="ARMA">Digital filters classification</a></h2>
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+ − 69 <p>
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+ − 70 Digital filters can be described as difference equations. If we consider an input time series x and an output y, three specific cases can then be distinguished:
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+ − 71 </p>
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+ − 72 <ul>
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+ − 73 <li> Autoregressive (AR) process: the difference equation in this case is given by:
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+ − 74 <div align="center">
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+ − 75 <br>
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+ − 76 <IMG src="images/sigproc_12.png" width="154" height="56" align="center" border="0">
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+ − 77 </div>
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+ − 78 <br>
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+ − 79 AR processes can be also classified as <a href="sigproc_iir.html"> IIR Filters</a>.
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+ − 80 <br>
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+ − 81 <br></li>
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+ − 82 <li> Moving Averrage (MA) process:the difference equation in this case is given by: <br>
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+ − 84 <br>
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+ − 85 <IMG src="images/sigproc_11.png" width="156" height="56" align="center" border="0">
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+ − 86 </div>
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+ − 87 <br>
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+ − 88 MA processes can be also classified as <a href="sigproc_fir.html"> FIR Filters</a>.
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+ − 89 <br>
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+ − 90 <br></li>
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+ − 91 <li>Autoregressive Moving Average (ARMA) process: the difference equation in this case contains both an AR and a MA process:
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+ − 92 <div align="center">
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+ − 93 <br>
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+ − 94 <IMG src="images/sigproc_7.png" width="283" height="56" align="center" border="0">
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+ − 95 </div>
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+ − 96 </li>
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+ − 100 </p>
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+ − 103 <br>
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+ − 104 <table class="nav" summary="Navigation aid" border="0" width=
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+ − 109 "Signal Processing in LTPDA"></a> </td>
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+ − 111 <td align="left">Signal Processing in LTPDA</td>
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+ − 113 <td> </td>
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+ − 115 <td align="right">IIR Filters</td>
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+ − 119 "bottom" alt="IIR Filters"></a></td>
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+ − 120 </tr>
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+ − 121 </table><br>
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+ − 123 <p class="copy">©LTP Team</p>
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+ − 124 </body>
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