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Diffstat (limited to 'help/en_US/sftrans.xml')
| -rw-r--r-- | help/en_US/sftrans.xml | 66 |
1 files changed, 23 insertions, 43 deletions
diff --git a/help/en_US/sftrans.xml b/help/en_US/sftrans.xml index 56aee48..3a2e0c5 100644 --- a/help/en_US/sftrans.xml +++ b/help/en_US/sftrans.xml @@ -17,7 +17,7 @@ <refnamediv> <refname>sftrans</refname> - <refpurpose>Transform band edges of a generic lowpass filter (cutoff at W=1) represented in splane zero-pole-gain form.</refpurpose> + <refpurpose>Transform band edges of a prototype filter (cutoff at W=1) represented in s-plane zero-pole-gain form (Frequency Transformation in Analog domain).</refpurpose> </refnamediv> @@ -42,59 +42,39 @@ <varlistentry><term>W:</term> <listitem><para> Edge of target filter.</para></listitem></varlistentry> <varlistentry><term>stop:</term> - <listitem><para> True for high pass and band stop filters or false for low pass and band pass filters.</para></listitem></varlistentry> + <listitem><para> True(%T or 1) for high pass and band stop filters or false (%F or 0) for low pass and band pass filters.</para></listitem></varlistentry> </variablelist> </refsection> <refsection> <title>Description</title> <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: - </para> - <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 ----------------- ------------------------- ------------------------ - </para> - <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: - </para> - <para> -H(S)=g prod(S-Xi)/prod(S-Xj) -</para> +Given a low pass filter represented by poles and zeros in the splane, can be converted into a </para> +<para> low pass (having diffrent cutoff frequency),</para> +<para> high pass,</para> +<para> band pass,</para> +<para> band stop.</para> +<para> by transforming each of the poles and zeros individually.</para> </refsection> <refsection> <title>Examples</title> <programlisting role="example"><![CDATA[ -[Sz, Sp, Sg] = sftrans (5, 10, 15, 20, 30) -Sz = 4 -Sp = 2 -Sg = 7.5000 +Sz = [1 2 3]; +Sp = [4 5 6]; +Sg = 15; +W = 20; +stop = %T; +[Sz, Sp, Sg] = sftrans (Sz, Sp, Sg, W, stop) + ]]></programlisting> </refsection> + +<refsection> +<title>Modified by :</title> +<simplelist type="vert"> +<member>Sonu Sharma, RGIT Mumbai (fellow at FOSSEE, IIT Bombay)</member> + </simplelist> +</refsection> + </refentry> |