 function y=v_rfft(x,n,d)
 %V_RFFT     Calculate the DFT of real data Y=(X,N,D)
 % Data is truncated/padded to length N if specified.
 %   N even:    (N+2)/2 points are returned with
 %             the first and last being real
 %   N odd:    (N+1)/2 points are returned with the
 %             first being real
 % In all cases fix(1+N/2) points are returned
 % D is the dimension along which to do the DFT
 
 
 
 %      Copyright (C) Mike Brookes 1998
 %      Version: $Id: v_rfft.m 10865 2018-09-21 17:22:45Z dmb $
 %
 %   VOICEBOX is a MATLAB toolbox for speech processing.
 %   Home page: http://www.ee.ic.ac.uk/hp/staff/dmb/voicebox/voicebox.html
 %
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 %   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 2 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 can obtain a copy of the GNU General Public License from
 %   http://www.gnu.org/copyleft/gpl.html or by writing to
 %   Free Software Foundation, Inc.,675 Mass Ave, Cambridge, MA 02139, USA.
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 s=size(x);
 if prod(s)==1
     y=x
 else
     if nargin <3 || isempty(d)
         d=find(s>1,1);
         if nargin<2
             n=s(d);
         end
     end
     if isempty(n) 
         n=s(d);
     end
     y=fft(x,n,d);
     y=reshape(y,prod(s(1:d-1)),n,prod(s(d+1:end))); 
     s(d)=1+fix(n/2);
     y(:,s(d)+1:end,:)=[];
     y=reshape(y,s);
 end