c_syn.m

Sparse Signal Representation using Overlapping Frames (matlab toolbox)

function X = C_syn(Y,a0,a1)
% C_syn     The synthesis part of an IIR filter bank based on allpass filters
%           Two and two columns of Y are filtered independently of the other columns
% to give one column in X.
% Block diagram, x is a column of X. y0 and y1 are columns of Y.
%                      
%     y0              v0  +----------+   even x           
%   ----------->(+)------>| A0(z^-1) |-----------+
%          \   /          +----------+           |       x
%            x                                   +--->--->                                      
%     y1   /   \      v1  +----------+           |  0.5
%   -------->-->(+)------>| A1(z^-1) |-----------+
%           -1            +----------+   odd x    
%   
% X = C_syn(Y,a0,a1);
% ---------------------------------------------------------------------------
% arguments:
%  Y        the subband signal to be filtered, number of columns should be even.
%  a0,a1    the values of a0 and a1 used in the IIR filterbank.
% ---------------------------------------------------------------------------

%----------------------------------------------------------------------
% Copyright (c) 1998.  Karl Skretting.  All rights reserved.
% Hogskolen in Stavanger (Stavanger University), Signal Processing Group
% Mail:  [e-mail]   Homepage:  http://www.ux.his.no/~karlsk/
% 
% HISTORY:
% Ver. 1.0  27.03.1998  Karl Skretting, used in Master thesis 1998, HIS: 
%                       "Kompresjon av seismiske data"
% Ver. 1.1  20.07.2000  KS: added optional arguments a0, a1
% Ver. 1.2  02.12.2002  KS: moved from ..\Frames to ..\FrameTools
%----------------------------------------------------------------------

Mfile='C_syn';

% check input and output arguments, and assign values to arguments
if (nargin < 1); 
   error([Mfile,': function must have one input argument, see help.']); 
end
if (nargin < 3)
   % the default values
   a0=0.1576056086;
   a1=0.6148404766;
end
% periodic extension of the signal in the ends by "ekstra" samples 
ekstra=50;		

N2=size(Y,1);
kol=size(Y,2);
if (rem(kol,2) ~= 0)
   error([Mfile,': Y should have an even number of columns, see help.']); 
end
N=N2*2;
X=zeros(N,kol/2);

for kol=1:2:size(Y,2)
   y0=Y(:,kol);
   y1=Y(:,kol+1);
   v0=y0+y1;
   v1=y0-y1;
   x=zeros(N,1);
   % filtering backwards using A0
   i=mod(ekstra,N2);
   if (i==0); i=N2; end
   temp=0;
   last=0;					% last v
   for k=1:ekstra
      temp=a0*(v0(i)-temp)+last;
      last=v0(i);
      i=i-1; if (i<1); i=i+N2; end;
   end
   if (i~=N2)
      error([Mfile,': logical error, (v0), i ~= N2.']); 
   end
   for k=N:-2:2
      temp=a0*(v0(i)-temp)+last;
      last=v0(i);
      i=i-1; % if (i<1); i=i+N2; end;
      x(k)=temp;
   end
   % filtering backwards using A1
   i=mod(ekstra,N2);
   if (i==0); i=N2; end
   temp=0;
   last=0;					% last v
   for k=1:ekstra
      temp=a1*(v1(i)-temp)+last;
      last=v1(i);
      i=i-1; if (i<1); i=i+N2; end;
   end
   if (i~=N2)
      error([Mfile,': logical error, (v1), i ~= N2.']); 
   end
   for k=(N-1):-2:1
      temp=a1*(v1(i)-temp)+last;
      last=v1(i);
      i=i-1; % if (i<1); i=i+N2; end;
      x(k)=temp;
   end
   X(:,(kol+1)/2)=0.5*x;
end

return