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−<p>
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−  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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−<div align="center">
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−<IMG src="images/sigproc_1.png" width="173" height="55" align="center" border="0">
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−<p>
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−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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−</p>
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−<ul>
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−<li> Causal: if there is no output before input is fed in.
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−<IMG src="images/sigproc_2.png" width="103" height="28" align="center" border="0">
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−  </li>
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−<li> Stable: if finite input results in finite output.  
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−<IMG src="images/sigproc_3.png" width="105" height="55" align="center" border="0">
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−</li>
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−<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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−<IMG src="images/sigproc_4.png" width="84" height="28" align="center" border="0">
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−</li>
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−</ul>
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−<br>
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−<h2><a name="ARMA">Digital filters classification</a></h2>
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−<p>
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−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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−</p>
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−<ul>
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−<li> Autoregressive (AR) process: the difference equation in this case is given by:  
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−<IMG src="images/sigproc_12.png" width="154" height="56" align="center" border="0">
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−<br>
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−AR processes can be also classified as <a href="sigproc_iir.html"> IIR Filters</a>.
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−    <br>
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−    <br></li>
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−<li> Moving Averrage (MA) process:the difference equation in this case is given by: <br>  
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−<IMG src="images/sigproc_11.png" width="156" height="56" align="center" border="0">
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−<br>
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−MA processes can be also classified as <a href="sigproc_fir.html"> FIR Filters</a>.
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−    <br>
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−    <br></li>
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−<li>Autoregressive Moving Average (ARMA) process: the difference equation in this case contains both an AR and a MA process:   
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−<IMG src="images/sigproc_7.png" width="283" height="56" align="center" border="0">
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− </li>
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