Mercurial > hg > ltpda
diff m-toolbox/html_help/help/ug/sigproc_dfilt.html @ 0:f0afece42f48
Import.
| author | Daniele Nicolodi <nicolodi@science.unitn.it> |
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| date | Wed, 23 Nov 2011 19:22:13 +0100 |
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--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/m-toolbox/html_help/help/ug/sigproc_dfilt.html Wed Nov 23 19:22:13 2011 +0100 @@ -0,0 +1,125 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/1999/REC-html401-19991224/loose.dtd"> + +<html lang="en"> +<head> + <meta name="generator" content= + "HTML Tidy for Mac OS X (vers 1st December 2004), see www.w3.org"> + <meta http-equiv="Content-Type" content= + "text/html; charset=us-ascii"> + + <title>Digital Filtering (LTPDA Toolbox)</title> + <link rel="stylesheet" href="docstyle.css" type="text/css"> + <meta name="generator" content="DocBook XSL Stylesheets V1.52.2"> + <meta name="description" content= + "Presents an overview of the features, system requirements, and starting the toolbox."> + </head> + +<body> + <a name="top_of_page" id="top_of_page"></a> + + <p style="font-size:1px;"> </p> + + <table class="nav" summary="Navigation aid" border="0" width= + "100%" cellpadding="0" cellspacing="0"> + <tr> + <td valign="baseline"><b>LTPDA Toolbox</b></td><td><a href="../helptoc.html">contents</a></td> + + <td valign="baseline" align="right"><a href= + "sigproc.html"><img src="b_prev.gif" border="0" align= + "bottom" alt="Signal Processing in LTPDA"></a> <a href= + "sigproc_iir.html"><img src="b_next.gif" border="0" align= + "bottom" alt="IIR Filters"></a></td> + </tr> + </table> + + <h1 class="title"><a name="f3-12899" id="f3-12899"></a>Digital Filtering</h1> + <hr> + + <p> + <p> + 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 +</p> +<div align="center"> +<IMG src="images/sigproc_1.png" width="173" height="55" align="center" border="0"> +</div> +<p> +described in these terms, the filter is completely described by the impulse response h[k], and can then be subdivided into the following classes: +</p> + +<ul> +<li> Causal: if there is no output before input is fed in. +<div align="center"> +<IMG src="images/sigproc_2.png" width="103" height="28" align="center" border="0"> +</div> + </li> +<li> Stable: if finite input results in finite output. +<div align="center"> +<IMG src="images/sigproc_3.png" width="105" height="55" align="center" border="0"> +</div> +</li> +<li> Shift invariant: if time shift in the input results in a time shift in the output by the same amount. +<div align="center"> +<IMG src="images/sigproc_4.png" width="84" height="28" align="center" border="0"> +</div> +</li> +</ul> +<br> +<h2><a name="ARMA">Digital filters classification</a></h2> +<p> +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: +</p> +<ul> +<li> Autoregressive (AR) process: the difference equation in this case is given by: +<div align="center"> +<br> +<IMG src="images/sigproc_12.png" width="154" height="56" align="center" border="0"> +</div> +<br> +AR processes can be also classified as <a href="sigproc_iir.html"> IIR Filters</a>. + <br> + <br></li> +<li> Moving Averrage (MA) process:the difference equation in this case is given by: <br> +<div align="center"> +<br> +<IMG src="images/sigproc_11.png" width="156" height="56" align="center" border="0"> +</div> +<br> +MA processes can be also classified as <a href="sigproc_fir.html"> FIR Filters</a>. + <br> + <br></li> +<li>Autoregressive Moving Average (ARMA) process: the difference equation in this case contains both an AR and a MA process: +<div align="center"> +<br> +<IMG src="images/sigproc_7.png" width="283" height="56" align="center" border="0"> +</div> + </li> + + + + </p> + + <br> + <br> + <table class="nav" summary="Navigation aid" border="0" width= + "100%" cellpadding="0" cellspacing="0"> + <tr valign="top"> + <td align="left" width="20"><a href="sigproc.html"><img src= + "b_prev.gif" border="0" align="bottom" alt= + "Signal Processing in LTPDA"></a> </td> + + <td align="left">Signal Processing in LTPDA</td> + + <td> </td> + + <td align="right">IIR Filters</td> + + <td align="right" width="20"><a href= + "sigproc_iir.html"><img src="b_next.gif" border="0" align= + "bottom" alt="IIR Filters"></a></td> + </tr> + </table><br> + + <p class="copy">©LTP Team</p> +</body> +</html>