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-rw-r--r--macros/sftrans.sci244
1 files changed, 175 insertions, 69 deletions
diff --git a/macros/sftrans.sci b/macros/sftrans.sci
index 916d44d..2dfd2bb 100644
--- a/macros/sftrans.sci
+++ b/macros/sftrans.sci
@@ -1,74 +1,180 @@
-function [Sz, Sp, Sg] = sftrans (Sz, Sp, Sg, W, stop)
-//Transform band edges of a generic lowpass filter (cutoff at W=1) represented in splane zero-pole-gain form.
-//Calling Sequence
-//[Sz, Sp, Sg] = sftrans (Sz, Sp, Sg, W, stop)
-//[Sz, Sp] = sftrans (Sz, Sp, Sg, W, stop)
-//[Sz] = sftrans (Sz, Sp, Sg, W, stop)
-//Parameters
-//Sz: Zeros.
-//Sp: Poles.
-//Sg: Gain.
-//W: Edge of target filter.
-//stop: True for high pass and band stop filters or false for low pass and band pass filters.
-//Description
-//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:
-//
-// 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
-// ---------------- ------------------------- ------------------------
-//
-//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:
+// Copyright (C) 2018 - IIT Bombay - FOSSEE
//
-// H(S)=g prod(S-Xi)/prod(S-Xj)
-//Examples
-//[Sz, Sp, Sg] = sftrans (5, 10, 15, 20, 30)
-//Sz = 4
-//Sp = 2
-//Sg = 7.5000
+// This file must be used under the terms of the CeCILL.
+// This source file is licensed as described in the file COPYING, which
+// you should have received as part of this distribution. The terms
+// are also available at
+// http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
+// Original Source : https://octave.sourceforge.io/signal/
+// Modifieded by:Sonu Sharma, RGIT Mumbai
+// Organization: FOSSEE, IIT Bombay
+// Email: toolbox@scilab.in
+
+function [Sz, Sp, Sg] = sftrans (Sz, Sp, Sg, W, stop)
+ //Transform band edges of a prototype filter (cutoff at W=1) represented in s-plane zero-pole-gain form (Frequency Transformation in Analog domain).
+
+ //Calling Sequence
+ //[Sz, Sp, Sg] = sftrans (Sz, Sp, Sg, W, stop)
+ //[Sz, Sp] = sftrans (Sz, Sp, Sg, W, stop)
+ //[Sz] = sftrans (Sz, Sp, Sg, W, stop)
+
+ //Parameters
+ //Sz: Zeros.
+ //Sp: Poles.
+ //Sg: Gain.
+ //W: Edge freuency of target filter.
+ //stop: True(%T or 1) for high pass and band stop filters or false (%F or 0) for low pass and band pass filters.
+
+ //Description
+ //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:
+
+ // 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
+ // ---------------- ------------------------- ------------------------
+ //
+ //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:
+ //
+ // H(S)=g prod(S-Xi)/prod(S-Xj)
+
+
+ //Examples
+ //[Sz, Sp, Sg] = sftrans([1 2 3], [4 5 6], 15, 20, %T)
+ // Output
+ // Sg =
+ //
+ // 0.75
+ // Sp =
+ //
+ // 5. 4. 3.3333333
+ // Sz =
+ //
+ // 20. 10. 6.6666667
+
+ funcprot(0);
+ [nargout nargin]= argn();
+
+ if (nargin ~= 5)
+ error("sftrans: Wrong number of input arguments.")
+ end
-funcprot(0);
-lhs = argn(1)
-rhs = argn(2)
-if (rhs < 5 | rhs > 5)
-error("Wrong number of input arguments.")
-end
+ if stop == %T then
+ elseif stop == %F
+ elseif stop == 1
+ elseif stop == 0
+ else
+ error("sftrans: stop must be true (%T or 1) or false (%F or 0)")
+ end
-select(rhs)
-
- case 5 then
- if(lhs==1)
- Sz = callOctave("sftrans",Sz, Sp, Sg, W, stop)
- elseif(lhs==2)
- [Sz, Sp] = callOctave("sftrans",Sz, Sp, Sg, W, stop)
- elseif(lhs==3)
- [Sz, Sp, Sg] = callOctave("sftrans",Sz, Sp, Sg, W, stop)
- else
- error("Wrong number of output argments.")
- end
+ C = 1;
+ p = length(Sp);
+ z = length(Sz);
+ if z > p | p == 0
+ error("sftrans: must have at least as many poles as zeros in s-plane");
+ end
- end
+ if length(W)==2
+ Fl = W(1);
+ Fh = W(2);
+ if stop
+ // ---------------- ------------------------- ----------------------
+ // 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
+ // ---------------- ------------------------- ----------------------
+ if (isempty(Sz))
+ Sg = Sg * real (1 ./ prod(-Sp));
+ elseif (isempty(Sp))
+ Sg = Sg * real(prod(-Sz));
+ else
+ Sg = Sg * real(prod(-Sz)/prod(-Sp));
+ end
+ b = (C*(Fh-Fl)/2)./Sp;
+ Sp = [b+sqrt(b.^2-Fh*Fl), b-sqrt(b.^2-Fh*Fl)];
+ extend = [sqrt(-Fh*Fl), -sqrt(-Fh*Fl)];
+ if isempty(Sz)
+ Sz = [extend(1+rem([1:2*p],2))];
+ else
+ b = (C*(Fh-Fl)/2)./Sz;
+ Sz = [b+sqrt(b.^2-Fh*Fl), b-sqrt(b.^2-Fh*Fl)];
+ if (p > z)
+ Sz = [Sz, extend(1+rem([1:2*(p-z)],2))];
+ end
+ end
+ else
+ // ---------------- ------------------------- ----------------------
+ // 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
+ // ---------------- ------------------------- ----------------------
+ Sg = Sg * (C/(Fh-Fl))^(z-p);
+ b = Sp*((Fh-Fl)/(2*C));
+ Sp = [b+sqrt(b.^2-Fh*Fl), b-sqrt(b.^2-Fh*Fl)];
+ if isempty(Sz)
+ Sz = zeros(1,p);
+ else
+ b = Sz*((Fh-Fl)/(2*C));
+ Sz = [b+sqrt(b.^2-Fh*Fl), b-sqrt(b.^2-Fh*Fl)];
+ if (p>z)
+ Sz = [Sz, zeros(1, (p-z))];
+ end
+ end
+ end
+ else
+ Fc = W;
+ if stop
+ // ---------------- ------------------------- ----------------------
+ // High Pass zero: Fc C/x pole: Fc C/x
+ // S -> C Fc/S pole: 0 zero: 0
+ // gain: -x gain: -1/x
+ // ---------------- ------------------------- ----------------------
+ if (isempty(Sz))
+ Sg = Sg * real (1 ./ prod(-Sp));
+ elseif (isempty(Sp))
+ Sg = Sg * real(prod(-Sz));
+ else
+ Sg = Sg * real(prod(-Sz)/prod(-Sp));
+ end
+ Sp = C * Fc ./ Sp;
+ if isempty(Sz)
+ Sz = zeros(1,p);
+ else
+ Sz = [C * Fc ./ Sz];
+ if (p > z)
+ Sz = [Sz, zeros(1,p-z)];
+ end
+ end
+ else
+ // ---------------- ------------------------- ----------------------
+ // Low Pass zero: Fc x/C pole: Fc x/C
+ // S -> C S/Fc gain: C/Fc gain: Fc/C
+ // ---------------- ------------------------- ----------------------
+ Sg = Sg * (C/Fc)^(z-p);
+ Sp = Fc * Sp / C;
+ Sz = Fc * Sz / C;
+ end
+ end
endfunction
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