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ifht.m

## Copyright (C) 2008 Muthiah Annamalai <gnumuthu@users.sf.net>
## 
## This program is free software; you can redistribute it and/or modify
## it under the terms of the GNU General Public License as published by
## the Free Software Foundation; either version 2 of the License, or
## (at your option) any later version.
##
## This program is distributed in the hope that it will be useful,
## but WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
## GNU General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with this program; If not, see <http://www.gnu.org/licenses/>.
##

## -*- texinfo -*-
## @deftypefn{Function File} {m = } ifht ( d, n, dim )
## @cindex linear algebra 
##  The function ifht calculates  Fast Hartley Transform
##  where @var{d} is the real input vector (matrix), and @var{m}
## is the real-transform vector. For matrices the hartley transform
## is calculated along the columns by default. The options @var{n},
## and @var{dim} are similar to the options of FFT function.
## 
## The forward and inverse hartley transforms are the same (except for a
## scale factor of 1/N for the inverse hartley transform), but
## implemented using different functions .
##
## The definition of the forward hartley transform for vector d,
## @math{
## m[K] = 1/N \sum_{i=0}^{N-1} d[i]*(cos[K*2*pi*i/N] + sin[K*2*pi*i/N]), for  0 <= K < N.
## m[K] = 1/N \sum_{i=0}^{N-1} d[i]*CAS[K*i], for  0 <= K < N. }
## 
## @example
## ifht(1:4)
## @end example
## @seealso{fht,fft}
## @end deftypefn

function m = ifht( d, n, dim )

  if ( nargin < 1 )
    print_usage();
  end

  if ( nargin == 3 )
    Y = ifft(d,n,dim);
  elseif ( nargin == 2 )
    Y = ifft(d,n);
  else
    Y = ifft(d);
  end
  
  m = real(Y) + imag(Y);

#   -- Traditional --
#   N = length(d);
#   for K = 1:N
#     i = 0:N-1;
#     t = (2*pi*(K-1).*i/N);
#     ker = (cos(t) + sin(t));
#     val = dot(d,ker)./N;
#     m(K) = val;
#   end

end
%!
%!assert(ifht(fht(1:4)),[1 2 3 4])
%!

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