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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:
//
// 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
funcprot(0);
lhs = argn(1)
rhs = argn(2)
if (rhs < 5 | rhs > 5)
error("Wrong number of input arguments.")
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
end
endfunction
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