Code covered by the BSD License

# Delta Sigma Toolbox

### Richard Schreier (view profile)

• 1 file
• 4.58904

14 Jan 2000 (Updated )

High-level design and simulation of delta-sigma modulators

### Editor's Notes:

This file was selected as MATLAB Central Pick of the Week

find2dPIS(u,ABCD,options)
```function s = find2dPIS(u,ABCD,options)
%function s = find2dPIS(u,ABCD,options)
%Find a positively invariant set for the 2nd-order binary modulator whose
%loop filter is described by ABCD and whose input is a constant u.
%Return s = [] if no invariant set is found.
%
%options = [ dbg=0 itnLimit=100 expFactor=0.005 N=1000 skip=100]
%dbg=1 causes debugging information to be displayed.

s=[];
n = size(ABCD,1)-1;
if n ~= 2
fprintf('%s: Error. The modulator must be second order.\n', mfilename);
return;
end
% Handle the options
nlev=2;
parameters = ['dbg      ';'itnLimit ';'expFactor';'N        ';'skip     '];
defaults = [ 0 100 .005 1000 100];
for i=1:length(defaults)
if i>length(options)
eval([parameters(i,:) '=defaults(i);'])
elseif isnan(options(i))
eval([parameters(i,:) '=defaults(i);'])
else
eval([parameters(i,:) '=options(i);'])
end
end

% Compute a few iterations of difference equations
if size(u)==[1 1]
un = u(ones(1,N+skip));
elseif size(u) == [2 1]
if ABCD(n+1,n+1) ~= 0	% Require D1=0
fprintf('%s: Limitation. D1 must be zero for u-ranges.\n', mfilename);
return;
end
% Make 90% of the u-values take on the extremes
un = uvar(u,skip+N);
else
fprintf('%s: Error. Argument 2 (u) has the wrong dimensions.\n', mfilename);
return
end
[v x] = simulateDSM(un,ABCD,nlev);
x = x(:,skip+1:skip+N);

xmin = min(x(1,:)); xmax = max(x(1,:)); dx = xmax-xmin;
ymin = min(x(2,:)); ymax = max(x(2,:)); dy = ymax-ymin;
axis1 = [ xmin-dx/4 xmax+dx/4 ymin-dy/4 ymax+dy/4 ];

% Take the convex hull of the result
s = hull2d(x')';
ec = mean(x')';

for i = 1:itnLimit
% Inflate the hull
shift = ec(:,ones(1,length(s)));
s = shift + (1+expFactor)*( s-shift );

% Split the set
[splus eplus sminus eminus] = dssplit2d(u,ABCD,s);
% Map the two halves
s1 = dsmap(u,ABCD,2,splus,eplus,1);
s2 = dsmap(u,ABCD,2,sminus,eminus,-1);
ns = [s1(:,1:size(s1,2)-1) s2(:,1:size(s2,2)-1)];

% Test for inclusion: ns inside s (the inflated hull)
out = outconvex2d(ns,s);
if dbg
clf; hold on; grid; axis(axis1);
set(gca,'drawmode','fast');
dotplot(x,'k.');
dotplot(ec,'o');
polyplot(s);
polyplot(s1,'m');
polyplot(s2,'c');
outi = logical(sign(out));
dotplot(ns(:,outi),'rs');
str = sprintf('Iteration %d: %d image vertices outside',i, sum(outi));
title(str);
drawnow;
end
if out == 0
break;
end
% take the hull and repeat
s = hull2d(ns')';
end
```