tfr_dualnorm.m

linear time－frequency toolbox

function cnr=tfr_dualnorm(self,L);
%TFR_DUALNORM  Measure of how close a window is to be a dual window. 
%   Usage:  dn=tfr_dualnorm(tfr,L);
%
%   Input parameters:
%         tfr   : Time/frequency representation handle.
%         L     : Length of transform to consider.
%   Output parameters:
%         dn    : dual norm.
%
%   TFR_DUALNORM(tfr) calculates how the analysis and synthesis windows
%   are to being duals of each other for a transform length of
%
%   TFR_DUALNORM can be used to get the maximum relative reconstruction
%   error. Consider the following code for some signal f.
% 
%      fr=tfr_s(tfr,tfr_a(tfr,f));
%      er=norm(f-fr)/norm(f);
%      eest=tfr_dualnorm(tfr);
% 
%   Then  er < eest for all possible input signals f.
%
%   SEE ALSO:  TFR_CREATE, TFR_A, TFR_S, TFR_CLEAR


if nargin<1
  error('Too few arguments.');
end;

if nargin>2
  error('Too many arguments.');
end;

global TF_STORAGE;

% Verify that TF_STORAGE has been initialized
if prod(size(TF_STORAGE))==0
  error('Please run TFR_CREATE to obtain a valid handle.');
end;

% Easy references
a=TF_STORAGE.data{self}.a;
M=TF_STORAGE.data{self}.M;
dgtinfo=TF_STORAGE.data{self}.dgtinfo;


% XXX This is not right.
[awinpos,L]=assert_winready(self,L,1,1,0,'TFR_DUALNORM');
[swinpos,L]=assert_winready(self,L,2,1,0,'TFR_DUALNORM');
 
awininfo=TF_STORAGE.data{self}.w{awinpos};
swininfo=TF_STORAGE.data{self}.w{swinpos};

L_dgt=L*dgtinfo.Lmul;
a_dgt=dgtinfo.a;
M_dgt=dgtinfo.M;
N_dgt=L_dgt/a_dgt;

%  XXX What to do instead of this??
%  g=firextend(g,L);
%  gamma=firextend(gamma,L);
  
% Calculate the right-hand side of the Wexler-Raz equations.
rhs=dgt(TF_STORAGE.data{self}.w{swinpos}.g, ...
	TF_STORAGE.data{self}.w{awinpos}.g,M_dgt,a_dgt);

% Subtract from the very first element.
rhs(1,1)=rhs(1,1)-a_dgt/M_dgt;  

% Calculate 1-norm.
cnr=norm(rhs(:),1);