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irfft

PURPOSE ^

IRFFT Inverse fft of a conjugate symmetric spectrum X=(Y,N,D)

SYNOPSIS ^

function x=irfft(y,n,d)

DESCRIPTION ^

IRFFT    Inverse fft of a conjugate symmetric spectrum X=(Y,N,D)

 Inputs:  Y(M)   The first half of a complex spectrum
          N      The number of output points to generate (default: 2M-2)
          D      The dimension along which to perorm the transform
                 (default: first non-singleton dimension of Y)

 Outputs: X(N)   Real inverse dft of Y

 This routine calculates the inverse DFT of a conjugate-symmetric to give a real-valued
 output of dimension N. Only the first half of the spectrum need be supplied: if N is even,
 this includes the Nyquist term and is of dimension M=N/2 + 1 whereas if N is odd then there is
 no Nyquist term and the input is of dimension M=(N+1)/2.
 Note that the default value of N is always even so that N must be given explicitly
 if it is odd.

 See also the forward transform: RFFT

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 function x=irfft(y,n,d)
0002 %IRFFT    Inverse fft of a conjugate symmetric spectrum X=(Y,N,D)
0003 %
0004 % Inputs:  Y(M)   The first half of a complex spectrum
0005 %          N      The number of output points to generate (default: 2M-2)
0006 %          D      The dimension along which to perorm the transform
0007 %                 (default: first non-singleton dimension of Y)
0008 %
0009 % Outputs: X(N)   Real inverse dft of Y
0010 %
0011 % This routine calculates the inverse DFT of a conjugate-symmetric to give a real-valued
0012 % output of dimension N. Only the first half of the spectrum need be supplied: if N is even,
0013 % this includes the Nyquist term and is of dimension M=N/2 + 1 whereas if N is odd then there is
0014 % no Nyquist term and the input is of dimension M=(N+1)/2.
0015 % Note that the default value of N is always even so that N must be given explicitly
0016 % if it is odd.
0017 %
0018 % See also the forward transform: RFFT
0019 
0020 %      Copyright (C) Mike Brookes 2009
0021 %      Version: $Id: irfft.m 2460 2012-10-29 22:20:45Z dmb $
0022 %
0023 %   VOICEBOX is a MATLAB toolbox for speech processing.
0024 %   Home page: http://www.ee.ic.ac.uk/hp/staff/dmb/voicebox/voicebox.html
0025 %
0026 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0027 %   This program is free software; you can redistribute it and/or modify
0028 %   it under the terms of the GNU General Public License as published by
0029 %   the Free Software Foundation; either version 2 of the License, or
0030 %   (at your option) any later version.
0031 %
0032 %   This program is distributed in the hope that it will be useful,
0033 %   but WITHOUT ANY WARRANTY; without even the implied warranty of
0034 %   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
0035 %   GNU General Public License for more details.
0036 %
0037 %   You can obtain a copy of the GNU General Public License from
0038 %   http://www.gnu.org/copyleft/gpl.html or by writing to
0039 %   Free Software Foundation, Inc.,675 Mass Ave, Cambridge, MA 02139, USA.
0040 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0041 
0042 s=size(y);
0043 ps=prod(s);
0044 ns=length(s);
0045 if ps==1
0046     x=y;
0047 else
0048     if nargin <3 || isempty(d)
0049         d=find(s>1,1);
0050     end
0051     m=s(d);
0052     k=ps/m;     % number of fft's to do
0053     if d==1
0054         v=reshape(y,m,k);
0055     else
0056         v=reshape(permute(y,[d:ns 1:d-1]),m,k);
0057     end
0058     if nargin<2 || isempty(n)
0059         n=2*m-2;        % default output length
0060     else
0061         mm=1+fix(n/2);          % expected input length
0062         if mm>m v=[v; zeros(mm-m,k)];   % zero pad
0063         elseif mm<m v(mm+1:m,:)=[];     % or truncate
0064         end
0065         m=mm;
0066     end
0067     if rem(n,2)        % odd output length
0068         x=real(ifft([v;conj(v(m:-1:2,:))],[],1));    % do it the long way
0069     else            % even output length
0070         v(m,:)=real(v(m,:));    % force nyquist element real
0071         w=ones(1,k);
0072         %  t=[cumprod([-0.5i; exp(2i*pi/n)*ones(m-2,1)]); 0.5i];
0073         t=-0.5i* exp((2i*pi/n)*(0:m-1)).';
0074         z=(t(:,w)+0.5).*(conj(flipud(v))-v)+v;
0075         z(m,:)=[];
0076         zz=ifft(z,[],1);
0077         x=zeros(n,k);
0078         x(1:2:n,:)=real(zz);
0079         x(2:2:n,:)=imag(zz);
0080     end
0081     s(d)=n;         % change output dimension
0082     if d==1
0083         x=reshape(x,s);
0084     else
0085         x=permute(reshape(x,s([d:ns 1:d-1])),[ns+2-d:ns 1:ns+1-d]);
0086     end
0087 end

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