function [ l_tilde, h_tilde ] = lh_tilde(l, h, two2p)
% FUNCTION:    lh_tilde   Part of DPWT toolbox.
%
% SYNOPSIS:    [ L_TILDE, H_TILDE ] = lh_tilde(L, H, TWO2P)
%
% DESCRIPTION: Make DPWT filters L_TILDE and H_TILDE.
%
%              The vectors L and H are assumed to be 
%              the values of the finite impulse response
%              low-pass and high-pass filters over their interval
%              of support {0,1,...,length(l)-1}. The filters
%              are not checked to see if they form a perfect 
%              reconstruction pair. Nor are they checked for
%              common length though this is assumed. The argument
%              TWO2P is the length (a power of 2) of the signal to
%              be filtered. 
%
% NOTE:        For more speed in dpwt() and idpwt() the vectors
%              calculated by LH_TILDE could be precalculated and
%              either passed as function parameters or made globally
%              available.
%
%              This function is mainly for use by DPWT and IDPWT.
%
%

% AUTHOR: Neil Getz
% DATE: 12-11-92

MATSHIFT = 1;  % matlab indices start at 1, not 0.

Nt2 = length(l); % Saves some multiplications.
if(Nt2~=length(h)),
  error('Arg 1 and arg 2 must be the same length.');
end

if ( length(l) <= two2p ),
  % In this case 2N<=2^p, so the first 2N taps
  % of l_tilde and h_tilde are identical to
  % those of l and h, respectively.
  % This is just to save a little time since
  % the section following 'else' below would
  % return the same result as this section for
  % the length(l) <= two2p.
  l_tilde = l;
  h_tilde = h;
else,
  % Here we have 2N>2^p and we need to apply a wrap.
  l_tilde = zeros(1, two2p);
  h_tilde = l_tilde; % for size
  for i = 0:min([Nt2,two2p])-1,
    imod2to_p = i - two2p*floor(i/two2p); 	% dex = i mod 2^p
    for k = 0:floor((Nt2-1-imod2to_p)/two2p),
      l_tilde( MATSHIFT + i ) ...
        = l_tilde(  MATSHIFT + i ) + l(  MATSHIFT + imod2to_p + k*two2p);
      h_tilde( MATSHIFT + i ) ...
        = h_tilde( MATSHIFT + i ) + h( MATSHIFT + imod2to_p + k*two2p);
    end
  end
end