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[Octave-cvsupdate] SF.net SVN: octave:[5386] trunk/octave-forge/main/signal/inst
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From: <pki...@us...> - 2008-10-27 10:01:15
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Revision: 5386
http://octave.svn.sourceforge.net/octave/?rev=5386&view=rev
Author: pkienzle
Date: 2008-10-27 09:56:54 +0000 (Mon, 27 Oct 2008)
Log Message:
-----------
signal: undoing change from T->Fs in iir filters
Modified Paths:
--------------
trunk/octave-forge/main/signal/inst/bilinear.m
trunk/octave-forge/main/signal/inst/butter.m
trunk/octave-forge/main/signal/inst/buttord.m
trunk/octave-forge/main/signal/inst/cheb1ord.m
trunk/octave-forge/main/signal/inst/cheb2ord.m
trunk/octave-forge/main/signal/inst/cheby1.m
trunk/octave-forge/main/signal/inst/cheby2.m
trunk/octave-forge/main/signal/inst/ellip.m
trunk/octave-forge/main/signal/inst/ellipord.m
Modified: trunk/octave-forge/main/signal/inst/bilinear.m
===================================================================
--- trunk/octave-forge/main/signal/inst/bilinear.m 2008-10-25 09:09:50 UTC (rev 5385)
+++ trunk/octave-forge/main/signal/inst/bilinear.m 2008-10-27 09:56:54 UTC (rev 5386)
@@ -13,20 +13,20 @@
## You should have received a copy of the GNU General Public License
## along with this program; If not, see <http://www.gnu.org/licenses/>.
-## usage: [Zz, Zp, Zg] = bilinear(Sz, Sp, Sg, Fs)
-## [Zb, Za] = bilinear(Sb, Sa, Fs)
+## usage: [Zz, Zp, Zg] = bilinear(Sz, Sp, Sg, T)
+## [Zb, Za] = bilinear(Sb, Sa, T)
##
## Transform a s-plane filter specification into a z-plane
## specification. Filters can be specified in either zero-pole-gain or
## transfer function form. The input form does not have to match the
-## output form. Fs is the sampling frequency represented in the z plane.
+## output form. T is the sampling frequency represented in the z plane.
##
## Theory: Given a piecewise flat filter design, you can transform it
## from the s-plane to the z-plane while maintaining the band edges by
## means of the bilinear transform. This maps the left hand side of the
## s-plane into the interior of the unit circle. The mapping is highly
## non-linear, so you must design your filter with band edges in the
-## s-plane positioned at 2/Fs tan(w*Fs/2) so that they will be positioned
+## s-plane positioned at 2/T tan(w*T/2) so that they will be positioned
## at w after the bilinear transform is complete.
##
## The following table summarizes the transformation:
@@ -35,9 +35,9 @@
## | Transform | Zero at x | Pole at x |
## | H(S) | H(S) = S-x | H(S)=1/(S-x) |
## +---------------+-----------------------+----------------------+
-## | 2 z-1 | zero: (2+xFs)/(2-xFs) | zero: -1 |
-## | S -> -- --- | pole: -1 | pole: (2+xFs)/(2-xFs)|
-## | Fs z+1 | gain: (2-xFs)/Fs | gain: (2-xFs)/Fs |
+## | 2 z-1 | zero: (2+xT)/(2-xT) | zero: -1 |
+## | S -> - --- | pole: -1 | pole: (2+xT)/(2-xT) |
+## | T z+1 | gain: (2-xT)/T | gain: (2-xT)/T |
## +---------------+-----------------------+----------------------+
##
## With tedious algebra, you can derive the above formulae yourself by
@@ -69,13 +69,13 @@
## Author: Paul Kienzle <pki...@us...>
-function [Zz, Zp, Zg] = bilinear(Sz, Sp, Sg, Fs)
+function [Zz, Zp, Zg] = bilinear(Sz, Sp, Sg, T)
if nargin==3
- Fs = Sg;
+ T = Sg;
[Sz, Sp, Sg] = tf2zp(Sz, Sp);
elseif nargin!=4
- usage("[Zz, Zp, Zg]=bilinear(Sz,Sp,Sg,Fs) or [Zb, Za]=blinear(Sb,Sa,Fs)");
+ usage("[Zz, Zp, Zg]=bilinear(Sz,Sp,Sg,T) or [Zb, Za]=blinear(Sb,Sa,T)");
end;
p = length(Sp);
@@ -85,17 +85,17 @@
end
## ---------------- ------------------------- ------------------------
-## Bilinear zero: (2+xFs)/(2-xFs) pole: (2+xFs)/(2-xFs)
-## 2 z-1 pole: -1 zero: -1
-## S -> -- --- gain: (2-xFs)/Fs gain: (2-xFs)/Fs
-## Fs z+1
+## 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
## ---------------- ------------------------- ------------------------
- Zg = real(Sg * prod((2-Sz*Fs)/Fs) / prod((2-Sp*Fs)/Fs));
- Zp = (2+Sp*Fs)./(2-Sp*Fs);
+ Zg = real(Sg * prod((2-Sz*T)/T) / prod((2-Sp*T)/T));
+ Zp = (2+Sp*T)./(2-Sp*T);
if isempty(Sz)
Zz = -ones(size(Zp));
else
- Zz = [(2+Sz*Fs)./(2-Sz*Fs)];
+ Zz = [(2+Sz*T)./(2-Sz*T)];
Zz = postpad(Zz, p, -1);
end
Modified: trunk/octave-forge/main/signal/inst/butter.m
===================================================================
--- trunk/octave-forge/main/signal/inst/butter.m 2008-10-25 09:09:50 UTC (rev 5385)
+++ trunk/octave-forge/main/signal/inst/butter.m 2008-10-27 09:56:54 UTC (rev 5386)
@@ -87,8 +87,8 @@
## Prewarp to the band edges to s plane
if digital
- Fs = 2; # sampling frequency of 2 Hz
- W = 2/Fs*tan(pi*W/Fs);
+ T = 2; # sampling frequency of 2 Hz
+ W = 2/T*tan(pi*W/T);
endif
## Generate splane poles for the prototype butterworth filter
@@ -104,7 +104,7 @@
## Use bilinear transform to convert poles to the z plane
if digital
- [zero, pole, gain] = bilinear(zero, pole, gain, Fs);
+ [zero, pole, gain] = bilinear(zero, pole, gain, T);
endif
## convert to the correct output form
Modified: trunk/octave-forge/main/signal/inst/buttord.m
===================================================================
--- trunk/octave-forge/main/signal/inst/buttord.m 2008-10-25 09:09:50 UTC (rev 5385)
+++ trunk/octave-forge/main/signal/inst/buttord.m 2008-10-27 09:56:54 UTC (rev 5386)
@@ -55,7 +55,7 @@
warning("buttord: seems to overdesign bandpass and bandreject filters");
end
- Fs = 2;
+ T = 2;
## if high pass, reverse the sense of the test
stop = find(Wp > Ws);
@@ -63,8 +63,8 @@
Ws(stop) = 1-Ws(stop); # subtract from ones(1,length(stop))
## warp the target frequencies according to the bilinear transform
- Ws = (2/Fs)*tan(pi*Ws./Fs);
- Wp = (2/Fs)*tan(pi*Wp./Fs);
+ Ws = (2/T)*tan(pi*Ws./T);
+ Wp = (2/T)*tan(pi*Wp./T);
## compute minimum n which satisfies all band edge conditions
## the factor 1/length(Wp) is an artificial correction for the
@@ -77,7 +77,7 @@
Wc = exp(log(Wp) - qp/2/n);
## unwarp the returned frequency
- Wc = atan(Fs/2*Wc)*Fs/pi;
+ Wc = atan(T/2*Wc)*T/pi;
## if high pass, reverse the sense of the test
Wc(stop) = 1-Wc(stop);
Modified: trunk/octave-forge/main/signal/inst/cheb1ord.m
===================================================================
--- trunk/octave-forge/main/signal/inst/cheb1ord.m 2008-10-25 09:09:50 UTC (rev 5385)
+++ trunk/octave-forge/main/signal/inst/cheb1ord.m 2008-10-27 09:56:54 UTC (rev 5386)
@@ -44,14 +44,14 @@
error("cheb1ord: Wp(1)<Ws(1)<Ws(2)<Wp(2) or Ws(1)<Wp(1)<Wp(2)<Ws(2)");
end
- Fs = 2;
+ T = 2;
## returned frequency is the same as the input frequency
Wc = Wp;
## warp the target frequencies according to the bilinear transform
- Ws = (2/Fs)*tan(pi*Ws./Fs);
- Wp = (2/Fs)*tan(pi*Wp./Fs);
+ Ws = (2/T)*tan(pi*Ws./T);
+ Wp = (2/T)*tan(pi*Wp./T);
if (Wp(1) < Ws(1))
## low pass
Modified: trunk/octave-forge/main/signal/inst/cheb2ord.m
===================================================================
--- trunk/octave-forge/main/signal/inst/cheb2ord.m 2008-10-25 09:09:50 UTC (rev 5385)
+++ trunk/octave-forge/main/signal/inst/cheb2ord.m 2008-10-27 09:56:54 UTC (rev 5386)
@@ -44,14 +44,14 @@
error("cheb2ord: Wp(1)<Ws(1)<Ws(2)<Wp(2) or Ws(1)<Wp(1)<Wp(2)<Ws(2)");
end
- Fs = 2;
+ T = 2;
## returned frequency is the same as the input frequency
Wc = Ws;
## warp the target frequencies according to the bilinear transform
- Ws = (2/Fs)*tan(pi*Ws./Fs);
- Wp = (2/Fs)*tan(pi*Wp./Fs);
+ Ws = (2/T)*tan(pi*Ws./T);
+ Wp = (2/T)*tan(pi*Wp./T);
if (Wp(1) < Ws(1))
## low pass
Modified: trunk/octave-forge/main/signal/inst/cheby1.m
===================================================================
--- trunk/octave-forge/main/signal/inst/cheby1.m 2008-10-25 09:09:50 UTC (rev 5385)
+++ trunk/octave-forge/main/signal/inst/cheby1.m 2008-10-27 09:56:54 UTC (rev 5386)
@@ -89,8 +89,8 @@
## Prewarp to the band edges to s plane
if digital
- Fs = 2; # sampling frequency of 2 Hz
- W = 2/Fs*tan(pi*W/Fs);
+ T = 2; # sampling frequency of 2 Hz
+ W = 2/T*tan(pi*W/T);
endif
## Generate splane poles and zeros for the chebyshev type 1 filter
@@ -114,7 +114,7 @@
## Use bilinear transform to convert poles to the z plane
if digital
- [zero, pole, gain] = bilinear(zero, pole, gain, Fs);
+ [zero, pole, gain] = bilinear(zero, pole, gain, T);
endif
## convert to the correct output form
Modified: trunk/octave-forge/main/signal/inst/cheby2.m
===================================================================
--- trunk/octave-forge/main/signal/inst/cheby2.m 2008-10-25 09:09:50 UTC (rev 5385)
+++ trunk/octave-forge/main/signal/inst/cheby2.m 2008-10-27 09:56:54 UTC (rev 5386)
@@ -13,7 +13,7 @@
## You should have received a copy of the GNU General Public License
## along with this program; If not, see <http://www.gnu.org/licenses/>.
-## Generate an Chebyshev type II filter with Rs dB of stop band ripple.
+## Generate an Chebyshev type II filter with Rs dB of stop band attenuation.
##
## [b, a] = cheby2(n, Rs, Wc)
## low pass filter with cutoff pi*Wc radians
@@ -90,8 +90,8 @@
## Prewarp to the band edges to s plane
if digital
- Fs = 2; # sampling frequency of 2 Hz
- W = 2/Fs*tan(pi*W/Fs);
+ T = 2; # sampling frequency of 2 Hz
+ W = 2/T*tan(pi*W/T);
endif
## Generate splane poles and zeros for the chebyshev type 2 filter
@@ -123,7 +123,7 @@
## Use bilinear transform to convert poles to the z plane
if digital
- [zero, pole, gain] = bilinear(zero, pole, gain, Fs);
+ [zero, pole, gain] = bilinear(zero, pole, gain, T);
endif
## convert to the correct output form
Modified: trunk/octave-forge/main/signal/inst/ellip.m
===================================================================
--- trunk/octave-forge/main/signal/inst/ellip.m 2008-10-25 09:09:50 UTC (rev 5385)
+++ trunk/octave-forge/main/signal/inst/ellip.m 2008-10-27 09:56:54 UTC (rev 5386)
@@ -102,8 +102,8 @@
##Prewarp the digital frequencies
if digital
- Fs = 2; # sampling frequency of 2 Hz
- W = tan(pi*W/Fs);
+ T = 2; # sampling frequency of 2 Hz
+ W = tan(pi*W/T);
endif
##Generate s-plane poles, zeros and gain
@@ -114,7 +114,7 @@
## Use bilinear transform to convert poles to the z plane
if digital
- [zero, pole, gain] = bilinear(zero, pole, gain, Fs);
+ [zero, pole, gain] = bilinear(zero, pole, gain, T);
endif
Modified: trunk/octave-forge/main/signal/inst/ellipord.m
===================================================================
--- trunk/octave-forge/main/signal/inst/ellipord.m 2008-10-25 09:09:50 UTC (rev 5385)
+++ trunk/octave-forge/main/signal/inst/ellipord.m 2008-10-27 09:56:54 UTC (rev 5386)
@@ -55,10 +55,10 @@
# sampling frequency of 2 Hz
-Fs = 2;
+T = 2;
-Wpw = tan(pi.*Wp./Fs); # prewarp
-Wsw = tan(pi.*Ws./Fs); # prewarp
+Wpw = tan(pi.*Wp./T); # prewarp
+Wsw = tan(pi.*Ws./T); # prewarp
##pass/stop band to low pass filter transform:
if (length(Wpw)==2 && length(Wsw)==2)
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