diff options
Diffstat (limited to 'help/en_US/scilab_en_US_help/sftrans.html')
| -rw-r--r-- | help/en_US/scilab_en_US_help/sftrans.html | 115 |
1 files changed, 115 insertions, 0 deletions
diff --git a/help/en_US/scilab_en_US_help/sftrans.html b/help/en_US/scilab_en_US_help/sftrans.html new file mode 100644 index 0000000..2a9b8ad --- /dev/null +++ b/help/en_US/scilab_en_US_help/sftrans.html @@ -0,0 +1,115 @@ +<html><head> + <meta http-equiv="Content-Type" content="text/html; charset=utf-8"> + <title>sftrans</title> + <style type="text/css" media="all"> + @import url("scilab_code.css"); + @import url("xml_code.css"); + @import url("c_code.css"); + @import url("style.css"); + </style> + </head> + <body> + <div class="manualnavbar"> + <table width="100%"><tr> + <td width="30%"> + <span class="previous"><a href="seqperiod.html"><< seqperiod</a></span> + + </td> + <td width="40%" class="center"> + <span class="top"><a href="section_cc2bc01c47967d47fcf3507a91d572ba.html">FOSSEE Signal Processing Toolbox</a></span> + + </td> + <td width="30%" class="next"> + <span class="next"><a href="sgolay.html">sgolay >></a></span> + + </td> + </tr></table> + <hr /> + </div> + + + + <span class="path"><a href="index.html">FOSSEE Signal Processing Toolbox</a> >> <a href="section_cc2bc01c47967d47fcf3507a91d572ba.html">FOSSEE Signal Processing Toolbox</a> > sftrans</span> + + <br /><br /> + <div class="refnamediv"><h1 class="refname">sftrans</h1> + <p class="refpurpose">Transform band edges of a generic lowpass filter (cutoff at W=1) represented in splane zero-pole-gain form.</p></div> + + +<div class="refsynopsisdiv"><h3 class="title">Calling Sequence</h3> + <div class="synopsis"><pre><span class="default">[</span><span class="default">Sz</span><span class="default">, </span><span class="default">Sp</span><span class="default">, </span><span class="default">Sg</span><span class="default">] = </span><span class="functionid">sftrans</span><span class="default"> (</span><span class="default">Sz</span><span class="default">, </span><span class="default">Sp</span><span class="default">, </span><span class="default">Sg</span><span class="default">, </span><span class="default">W</span><span class="default">, </span><span class="default">stop</span><span class="default">)</span> +<span class="default">[</span><span class="default">Sz</span><span class="default">, </span><span class="default">Sp</span><span class="default">] = </span><span class="functionid">sftrans</span><span class="default"> (</span><span class="default">Sz</span><span class="default">, </span><span class="default">Sp</span><span class="default">, </span><span class="default">Sg</span><span class="default">, </span><span class="default">W</span><span class="default">, </span><span class="default">stop</span><span class="default">)</span> +<span class="default">[</span><span class="default">Sz</span><span class="default">] = </span><span class="functionid">sftrans</span><span class="default"> (</span><span class="default">Sz</span><span class="default">, </span><span class="default">Sp</span><span class="default">, </span><span class="default">Sg</span><span class="default">, </span><span class="default">W</span><span class="default">, </span><span class="default">stop</span><span class="default">)</span></pre></div></div> + +<div class="refsection"><h3 class="title">Parameters</h3> + <dl><dt><span class="term">Sz:</span> + <dd><p class="para">Zeros.</p></dd></dt> + <dt><span class="term">Sp:</span> + <dd><p class="para">Poles.</p></dd></dt> + <dt><span class="term">Sg:</span> + <dd><p class="para">Gain.</p></dd></dt> + <dt><span class="term">W:</span> + <dd><p class="para">Edge of target filter.</p></dd></dt> + <dt><span class="term">stop:</span> + <dd><p class="para">True for high pass and band stop filters or false for low pass and band pass filters.</p></dd></dt></dl></div> + +<div class="refsection"><h3 class="title">Description</h3> + <p class="para">This is an Octave function. +Theory: Given a low pass filter represented by poles and zeros in the splane, you can convert it to a low pass, high pass, band pass or band stop by transforming each of the poles and zeros +individually. The following table summarizes the transformation:</p> + <p class="para">Transform Zero at x Pole at x +---------------- ------------------------- ------------------------ +Low Pass zero: Fc x/C pole: Fc x/C +S -> C S/Fc gain: C/Fc gain: Fc/C +---------------- ------------------------- ------------------------ +High Pass zero: Fc C/x pole: Fc C/x +S -> C Fc/S pole: 0 zero: 0 +gain: -x gain: -1/x +---------------- ------------------------- ------------------------ +Band Pass zero: b +- sqrt(b^2-FhFl) pole: b +- sqrt(b^2-FhFl) +S^2+FhFl pole: 0 zero: 0 +S -> C -------- gain: C/(Fh-Fl) gain: (Fh-Fl)/C +S(Fh-Fl) b=x/C (Fh-Fl)/2 b=x/C (Fh-Fl)/2 +---------------- ------------------------- ------------------------ +Band Stop zero: b +- sqrt(b^2-FhFl) pole: b +- sqrt(b^2-FhFl) +S(Fh-Fl) pole: +-sqrt(-FhFl) zero: +-sqrt(-FhFl) +S -> C -------- gain: -x gain: -1/x +S^2+FhFl b=C/x (Fh-Fl)/2 b=C/x (Fh-Fl)/2 +---------------- ------------------------- ------------------------ +Bilinear zero: (2+xT)/(2-xT) pole: (2+xT)/(2-xT) +2 z-1 pole: -1 zero: -1 +S -> - --- gain: (2-xT)/T gain: (2-xT)/T +T z+1 +---------------- ------------------------- ------------------------</p> + <p class="para">where C is the cutoff frequency of the initial lowpass filter, Fc is the edge of the target low/high pass filter and [Fl,Fh] are the edges of the target band pass/stop filter. With abundant tedious +algebra, you can derive the above formulae yourself by substituting the transform for S into H(S)=S-x for a zero at x or H(S)=1/(S-x) for a pole at x, and converting the result into the form:</p> + <p class="para">H(S)=g prod(S-Xi)/prod(S-Xj)</p></div> + +<div class="refsection"><h3 class="title">Examples</h3> + <div class="programlisting"><table border="0" width="100%"><tr><td width="98%"><pre class="scilabcode"><span class="scilabopenclose">[</span><span class="scilabid">Sz</span><span class="scilabdefault">,</span> <span class="scilabid">Sp</span><span class="scilabdefault">,</span> <span class="scilabid">Sg</span><span class="scilabopenclose">]</span> <span class="scilaboperator">=</span> <span class="scilabid">sftrans</span> <span class="scilabopenclose">(</span><span class="scilabnumber">5</span><span class="scilabdefault">,</span> <span class="scilabnumber">10</span><span class="scilabdefault">,</span> <span class="scilabnumber">15</span><span class="scilabdefault">,</span> <span class="scilabnumber">20</span><span class="scilabdefault">,</span> <span class="scilabnumber">30</span><span class="scilabopenclose">)</span> +<span class="scilabid">Sz</span> <span class="scilaboperator">=</span> <span class="scilabnumber">4</span> +<span class="scilabid">Sp</span> <span class="scilaboperator">=</span> <span class="scilabnumber">2</span> +<span class="scilabid">Sg</span> <span class="scilaboperator">=</span> <span class="scilabnumber">7.5000</span></pre></td><td valign="top"><a href="scilab://scilab.execexample/"><img src="ScilabExecute.png" border="0"/></a></td><td valign="top"><a href="scilab://scilab.editexample/"><img src="ScilabEdit.png" border="0"/></a></td><td></td></tr></table></div></div> + <br /> + + <div class="manualnavbar"> + <table width="100%"> + <tr><td colspan="3" class="next"><a href="http://bugzilla.scilab.org/enter_bug.cgi?product=Scilab%20software&component=Documentation%20pages" class="ulink">Report an issue</a></td></tr> +<tr> + <td width="30%"> + <span class="previous"><a href="seqperiod.html"><< seqperiod</a></span> + + </td> + <td width="40%" class="center"> + <span class="top"><a href="section_cc2bc01c47967d47fcf3507a91d572ba.html">FOSSEE Signal Processing Toolbox</a></span> + + </td> + <td width="30%" class="next"> + <span class="next"><a href="sgolay.html">sgolay >></a></span> + + </td> + </tr></table> + <hr /> + </div> + </body> +</html> |