/usr/share/octave/packages/signal-1.3.0/fht.m is in octave-signal 1.3.0-1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 | ## Copyright (C) 2008 Muthiah Annamalai <muthiah.annamalai@uta.edu>
##
## 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 3 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} {@var{m} =} fht (@var{d})
## @deftypefnx {Function File} {@var{m} =} fht (@var{d}, @var{n})
## @deftypefnx {Function File} {@var{m} =} fht (@var{d}, @var{n}, @var{dim})
## Calculate the Fast Hartley Transform of real input @var{d}. If @var{d} is
## a matrix, 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] = \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] = \sum_{i=0}^{N-1} d[i]*CAS[K*i], for 0 <= K < N. }
##
## @example
## fht(1:4)
## @end example
## @seealso{ifht, fft}
## @end deftypefn
function m = fht( d, n, dim )
if ( nargin < 1 )
print_usage();
endif
if ( nargin == 3 )
Y = fft(d,n,dim);
elseif ( nargin == 2 )
Y = fft(d,n);
else
Y = fft(d);
endif
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);
## m(K) = val;
## endfor
endfunction
%!
%!assert( fht([1 2 3 4]),[10 -4 -2 0] )
%!
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