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<span class="path"><a href="index.html">FOSSEE Signal Processing Toolbox</a> >> <a href="section_e54aa8aac34aa55341e8b4b782fe1a74.html">FOSSEE Signal Processing Toolbox</a> > sftrans</span>
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<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>
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