The Grandke paper looks interesting based on your description. Since I am not a member of IEEE, I don't have a copy. Quite possibly a similar scheme was developed by Bruel and Kjear and reported by Randall as shown in the attachment. I have used the scheme for more accurate frequencies, but have not used the amplitude correction feature. Only used it in matlab however.

A quick note regarding the hanning, or any other window. Anders Brandt wrote a signal processing toolbox for matlab or octave called abravibe. This is an open source toolbox. A copy of his hanning window code is shown:

Code:

function w = ahann(N);
%AHANN Calculate a Hanning window
%
% w = ahann(N);
%
% w Hanning time window
%
% N Blocksize, length of w
%
% Calculates a (correct!) Hanning window with length(N), in a column
% vector. The ENBW is 1.5*df.
%
% See also aflattop winacf winenbw
% Copyright (c) 2009-2011 by Anders Brandt
% Email: abra@iti.sdu.dk
% Version: 1.0 2011-06-23
% This file is part of ABRAVIBE Toolbox for NVA
a0=.5;
a1=.5;
t=(0:pi/N:pi-pi/N)';
w=a0-a1*cos(2*t);

This would be the same as the matlab or octave hanning window with the 'periodic' option. This makes the window start with the first non zero term and end with a zero in the time domain. According to Anders (and his book) this is the correct way to do it. Realistically, I don't expect there to be much difference, but we might as well do it right if we have the option.

The hanning window from octave is:

Code:

## Copyright (C) 1995-2015 Andreas Weingessel
##
## This file is part of Octave.
##
## Octave 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.
##
## Octave 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 Octave; see the file COPYING. If not, see
## <http://www.gnu.org/licenses/>.
## -*- texinfo -*-
## @deftypefn {Function File} {} hanning (@var{m})
## @deftypefnx {Function File} {} hanning (@var{m}, "periodic")
## @deftypefnx {Function File} {} hanning (@var{m}, "symmetric")
## Return the filter coefficients of a Hanning window of length @var{m}.
##
## If the optional argument @qcode{"periodic"} is given, the periodic form
## of the window is returned. This is equivalent to the window of length
## @var{m}+1 with the last coefficient removed. The optional argument
## @qcode{"symmetric"} is equivalent to not specifying a second argument.
##
## For a definition of the Hanning window see, e.g.,
## @nospell{A.V. Oppenheim & R. W. Schafer},
## @cite{Discrete-Time Signal Processing}.
## @end deftypefn
## Author: AW <Andreas.Weingessel@ci.tuwien.ac.at>
## Description: Coefficients of the Hanning window
function c = hanning (m, opt)
if (nargin < 1 || nargin > 2)
print_usage ();
endif
if (! (isscalar (m) && (m == fix (m)) && (m > 0)))
error ("hanning: M must be a positive integer");
endif
N = m - 1;
if (nargin == 2)
switch (opt)
case "periodic"
N = m;
case "symmetric"
## Default option, same as no option specified.
otherwise
error ('hanning: window type must be either "periodic" or "symmetric"');
endswitch
endif
if (m == 1)
c = 1;
else
m = m - 1;
c = 0.5 - 0.5 * cos (2 * pi * (0 : m)' / N);
endif
endfunction
%!assert (hanning (1), 1);
%!assert (hanning (2), zeros (2,1));
%!assert (hanning (15), flip (hanning (15)), 5*eps);
%!assert (hanning (16), flip (hanning (16)), 5*eps);
%!test
%! N = 15;
%! A = hanning (N);
%! assert (A(ceil (N/2)), 1);
%!assert (hanning (15), hanning (15, "symmetric"));
%!assert (hanning (16)(1:15), hanning (15, "periodic"));
%!test
%! N = 16;
%! A = hanning (N, "periodic");
%! assert (A(N/2 + 1), 1);
%!error hanning ()
%!error hanning (0.5)
%!error hanning (-1)
%!error hanning (ones (1,4))
%!error hanning (1, "invalid");

I am interested in hearing back how the Bruel & Kjear technique for frequency line interpolation compares with the DerekR/Grandke10 one mentioned above. It may be identical?