filterbank/filterbankdual.m

function gdout=filterbankdual(g,a,varargin)
%FILTERBANKDUAL  Dual filters
%   Usage:  gd=filterbankdual(g,a,L);
%           gd=filterbankdual(g,a);
%           
%
%   `filterbankdual(g,a,L)` computes the canonical dual filters of *g* for a
%   channel subsampling rate of *a* (hop-size) and system length *L*.
%   *L* must be compatible with subsampling rate *a* as 
%   `L==filterbanklength(L,a)`. This will create a dual frame valid for 
%   signals of length *L*. 
%
%   `filterabankrealdual(g,a)` does the same, but the filters must be FIR
%   filters, as the transform length is unspecified. *L* will be set to 
%   next suitable length equal or bigger than the longest impulse response
%   such that `L=filterbanklength(gl_longest,a)`.
%
%   The input and output format of the filters *g* are described in the
%   help of |filterbank|.
%
%   In addition, the funtion recognizes a 'forcepainless' flag which
%   forces treating the filterbank *g* and *a* as a painless case
%   filterbank.  
%
%   To actually invert the output of a filterbank, use the dual filters
%   together with the |ifilterbank| function.
%
%   REMARK: In general, perfect reconstruction can be obtained for signals 
%   of length *L*. In some cases, using dual system calculated for shorter
%   *L* might work but check the reconstruction error.
%
%   See also: filterbank, ufilterbank, ifilterbank

complainif_notenoughargs(nargin,2,'FILTERBANKDUAL');

definput.import={'filterbankdual'};
[flags,~,L]=ltfatarghelper({'L'},definput,varargin);

[g,asan,info]=filterbankwin(g,a,L,'normal');
if isempty(L) 
    if info.isfir
        % Pick shortest possible length for FIR filterbank
        L = filterbanklength(info.longestfilter,asan);
    else
        % Just thow an error, nothing reasonable can be done without L
        error(['%s: L must be specified when not working with FIR ',...'
               'filterbanks.'], upper(mfilename));
    end
end
M=info.M;

% Force usage of the painless algorithm 
if flags.do_forcepainless
    info.ispainless = 1;
end

% Check user defined L
if L~=filterbanklength(L,a)
     error(['%s: Specified length L is incompatible with the length of ' ...
            'the time shifts.'],upper(mfilename));
end;

% Prioritize painless over uniform algorithm if both are suitable
if info.isuniform && info.ispainless
    info.isuniform = 0;
end

% Factorization of frame operator to block-diagonal matrix
if info.isuniform
  % Uniform filterbank, use polyphase representation
  a=a(1);
  
  % Transfer functions of individual filters as cols
  G = filterbankfreqz(g,a,L);
  
  N=L/a;
  
  gd=zeros(M,N,class(G));
  
  for w=0:N-1
    idx = mod(w-(0:a-1)*N,L)+1;
    H = G(idx,:);
    
    H=pinv(H)';
    
    gd(:,idx)=H.';
  end;
  % gd was created transposed because the indexing gd(:,idx_a)
  % is much faster than gd(idx_a,:)
  gd =  gd.';
  
  gd=ifft(gd)*a;
  
  % Matrix cols to cell elements + cast
  gdout = cellfun(@(gdEl) cast(gdEl,class(G)), num2cell(gd,1),...
                  'UniformOutput',0);
  % All filters in gdout will be treated as FIR of length L. Convert them
  % to a struct with .h and .offset format.
  gdout = filterbankwin(gdout,a); 
  
elseif info.ispainless
   % Factorized frame operator is diagonal.
   gdout = comp_painlessfilterbank(g,asan,L,'dual',0);
else
        error(['%s: The canonical dual frame of this system is not a ' ...
               'filterbank. You must either call an iterative ' ...
               'method to perform the desired inverstion or transform ',...
               'or transform the filterbank to uniform one. Please see ' ...
               'FRANAITER or FRSYNITER for the former and ',...
               'NONU2UFILTERBANK for the latter case.'],upper(mfilename));        

    
end;