## Copyright (C) 2012 Benjamin Lewis <benjf5@gmail.com>

##

## 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{a} =} cubicwgt (@var{series})

## Return @var{series} as windowed by a cubic polynomial,

## 1 + ( x ^ 2 * ( 2 x - 3 ) ), assuming x is in [-1,1].

## This function implements the windowing function on page 10 of the paper.

## if t is in [-1,1] then the windowed term is a = 1 + ( |t|^2 * ( 2|t| - 3 )

## else the windowed term is 0.

## @end deftypefn

function a = cubicwgt (s)

## s is the value to be windowed

a = abs (s);

a = ifelse ((a < 1), 1 + ((a .^ 2) .* (2 .* a - 3)), 0);

endfunction

%!shared h, m, k

%! h = 2;

%! m = 0.01;

%! k = [0, 3, 1.5, -1, -0.5, -0.25, 0.75];

%!assert (cubicwgt (h), 0 );

%!assert (cubicwgt (m), 1 + m ^ 2 * (2 * m - 3));

%!assert (cubicwgt (k), [1.00000, 0.00000, 0.00000, 0.00000, ...

%! 0.50000, 0.84375, 0.15625], 1e-6);

%! ## Tests cubicwgt on two scalars and two vectors; cubicwgt will work

%! ## on any array input.