/usr/share/octave/packages/signal-1.3.2/ifht.m is in octave-signal 1.3.2-5.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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##
## 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} =} ifht (@var{d}, @var{n}, @var{dim})
## Calculate the inverse Fast Hartley Transform of real input @var{d}. If
## @var{d} is a matrix, the inverse 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();
endif
if ( nargin == 3 )
Y = ifft(d,n,dim);
elseif ( nargin == 2 )
Y = ifft(d,n);
else
Y = ifft(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)./N;
## m(K) = val;
## endfor
endfunction
%!assert(ifht(fht(1:4)),[1 2 3 4])
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