From c257cd7a7e766fb89332cca4fb367904767362ed Mon Sep 17 00:00:00 2001 From: Brijeshcr Date: Thu, 30 Nov 2017 18:27:20 +0530 Subject: Help files and functions --- help/en_US/sftrans.xml | 100 +++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 100 insertions(+) create mode 100644 help/en_US/sftrans.xml (limited to 'help/en_US/sftrans.xml') diff --git a/help/en_US/sftrans.xml b/help/en_US/sftrans.xml new file mode 100644 index 0000000..56aee48 --- /dev/null +++ b/help/en_US/sftrans.xml @@ -0,0 +1,100 @@ + + + + + + + + sftrans + 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 + + + -- cgit