function ff = showbylevel( w, L, levels)
% FUNCTION: showbylevel
%
% SYNOPSIS: FF = showbylevel( W, L, [LEVELS])
%
% DESCRIPTION: Given a vector of wavelet coefficients W and 
%              a low-pass wavelet filter L, SHOWBYLEVEL plots the
%              components at each level of the inverse DPWT
%              of W from coarsest down to finest resolution. 
%
%              LEVELS is an optional argument specifying the 
%              levels the use wishes to be reconstructed and 
%              plotted. If only the first 2 arguments are 
%              used reconstructions at all levels are 
%              plotted. level numbers must be integers 
%              between -1 and log2(length(w)) - 1.
%
%              FF is a length(W) by length(LEVELS)
%              matrix (If LEVELS is not specified then 
%              length(LEVELS) = log2(length(w)).
%
% EXAMPLE:     figure,
%              f = sin(pi*[0:(2^7 - 1)]/2^5)';
%              w = dpwt(f,daubcofs(2));
%              ff = showbylevel(w,daubcofs(2));
%
%              To see the cumulative result of adding the 
%              contributions of decreasing levels together
%              enter, after the above:
%	
%              figure, waterfall(cumsum(ff'))
%
% NOTE:        The run time of this function can take awhile since
%              log2(length(w)) IDPWT's are being performed on sequences
%              of length length(w).

% 
% AUTHOR: Neil Getz
% DATE: 5-4-92
%
% COPYRIGHT 1992, Neil Getz
%

if (nargin > 3 | nargin <2 ),
  help showbylevel;
  return;
end

lenw = length(w);
p = log(lenw)/log(2);

if(nargin==2), 
  levels = ( p - 1 ):-1:-1;   % default
else  % nargin is 3. Check for legitimate level numbers
  Validlevels = ( rem(levels,1) == 0 ) & (levels >= -1) ...
                & ( levels <= p-1 );
  if ( sum(~Validlevels ~= 0 ) ),
     error('showbylevel: Invalid level numbers (arg4).');
  end
end

ff = zeros(lenw, length(levels));

for i = 1:length(levels),
  z = zeros(size(w));
  coordsati = getlevel( w, levels(i) );
  wffi = putlevel( z, coordsati, levels(i) );
  ff(:,i) = column(idpwt(  wffi , L ));
end 


S = waterfall(ff');
view([142,30])