## Copyright (C) 2000 Paul Kienzle <pkienzle@users.sf.net>
## Copyright (C) 2007 Peter L. Soendergaard
##
## 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; see the file COPYING. If not, see
## <https://www.gnu.org/licenses/>.

## -*- texinfo -*-
## @deftypefn {Function File} {@var{h} =} hilbert (@var{f}, @var{N}, @var{dim})
## Analytic extension of real valued signal.
##
## @code{@var{h} = hilbert (@var{f})} computes the extension of the real
## valued signal @var{f} to an analytic signal. If @var{f} is a matrix,
## the transformation is applied to each column. For N-D arrays,
## the transformation is applied to the first non-singleton dimension.
##
## @code{real (@var{h})} contains the original signal @var{f}.
## @code{imag (@var{h})} contains the Hilbert transform of @var{f}.
##
## @code{hilbert (@var{f}, @var{N})} does the same using a length @var{N}
## Hilbert transform. The result will also have length @var{N}.
##
## @code{hilbert (@var{f}, [], @var{dim})} or
## @code{hilbert (@var{f}, @var{N}, @var{dim})} does the same along
## dimension @var{dim}.
## @end deftypefn

function f=hilbert(f, N = [], dim = [])

  ## ------ PRE: initialization and dimension shifting ---------

  if (nargin<1 || nargin>3)
    print_usage;
  endif

  if ~isreal(f)
    warning ('HILBERT: ignoring imaginary part of signal');
    f = real (f);
  endif

  D=ndims(f);

  ## Dummy assignment.
  order=1;

  if isempty(dim)
    dim=1;

    if sum(size(f)>1)==1
      ## We have a vector, find the dimension where it lives.
      dim=find(size(f)>1);
    endif

  else
    if (numel(dim)~=1 || ~isnumeric(dim))
      error('HILBERT: dim must be a scalar.');
    endif
    if rem(dim,1)~=0
      error('HILBERT: dim must be an integer.');
    endif
    if (dim<1) || (dim>D)
      error('HILBERT: dim must be in the range from 1 to %d.',D);
    endif

  endif

  if (numel(N)>1 || ~isnumeric(N))
    error('N must be a scalar.');
  elseif (~isempty(N) && rem(N,1)~=0)
    error('N must be an integer.');
  endif

  if dim>1
    order=[dim, 1:dim-1,dim+1:D];

    ## Put the desired dimension first.
    f=permute(f,order);

  endif

  Ls=size(f,1);

  ## If N is empty it is set to be the length of the transform.
  if isempty(N)
    N=Ls;
  endif

  ## Remember the exact size for later and modify it for the new length
  permutedsize=size(f);
  permutedsize(1)=N;

  ## Reshape f to a matrix.
  f=reshape(f,size(f,1),numel(f)/size(f,1));
  W=size(f,2);

  if ~isempty(N)
    f=postpad(f,N);
  endif

  ## ------- actual computation -----------------
  if N>2
    f=fft(f);

    if rem(N,2)==0
      f=[f(1,:);
         2*f(2:N/2,:);
         f(N/2+1,:);
         zeros(N/2-1,W)];
    else
      f=[f(1,:);
         2*f(2:(N+1)/2,:);
         zeros((N-1)/2,W)];
    endif

    f=ifft(f);
  endif

  ## ------- POST: Restoration of dimensions ------------

  ## Restore the original, permuted shape.
  f=reshape(f,permutedsize);

  if dim>1
    ## Undo the permutation.
    f=ipermute(f,order);
  endif

endfunction

%!demo
%! ## notice that the imaginary signal is phase-shifted 90 degrees
%! t=linspace(0,10,256);
%! z = hilbert(sin(2*pi*0.5*t));
%! grid on; plot(t,real(z),';real;',t,imag(z),';imag;');

%!demo
%! ## the magnitude of the hilbert transform eliminates the carrier
%! t=linspace(0,10,1024);
%! x=5*cos(0.2*t).*sin(100*t);
%! grid on; plot(t,x,'g;z;',t,abs(hilbert(x)),'b;|hilbert(z)|;');
