RSFFT fft of a real symmetric spectrum X=(Y,N) Y is the "first half" of a symmetric real input signal and X is the "first half" of the symmetric real fourier transform. If the length, N, of the full signal is even, then the "first half" contains 1+N/2 elements (the first and last are excluded from the reflection). If N is odd, the "first half" conatins 0.5+N/2 elements and only the first is excluded from the reflection. If N is specified explicitly, then Y will be truncated of zero-padded accordingly. If N is omitted it will be taken to be 2*(length(Y)-1) and is always even. If Y is a matrix, the transform is performed along each column The inverse function is y=rsfft(x,n)/n

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0001 function x=rsfft(y,n) 0002 %RSFFT fft of a real symmetric spectrum X=(Y,N) 0003 % Y is the "first half" of a symmetric real input signal and X is the 0004 % "first half" of the symmetric real fourier transform. 0005 % If the length, N, of the full signal is even, then the "first half" 0006 % contains 1+N/2 elements (the first and last are excluded from the reflection). 0007 % If N is odd, the "first half" conatins 0.5+N/2 elements and only the first 0008 % is excluded from the reflection. 0009 % If N is specified explicitly, then Y will be truncated of zero-padded accordingly. 0010 % If N is omitted it will be taken to be 2*(length(Y)-1) and is always even. 0011 % 0012 % If Y is a matrix, the transform is performed along each column 0013 % 0014 % The inverse function is y=rsfft(x,n)/n 0015 0016 % Could be made faster for even n by using symmetry 0017 0018 % Copyright (C) Mike Brookes 1998 0019 % Version: $Id: rsfft.m 5024 2014-08-22 17:05:55Z dmb $ 0020 % 0021 % VOICEBOX is a MATLAB toolbox for speech processing. 0022 % Home page: http://www.ee.ic.ac.uk/hp/staff/dmb/voicebox/voicebox.html 0023 % 0024 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 0025 % This program is free software; you can redistribute it and/or modify 0026 % it under the terms of the GNU General Public License as published by 0027 % the Free Software Foundation; either version 2 of the License, or 0028 % (at your option) any later version. 0029 % 0030 % This program is distributed in the hope that it will be useful, 0031 % but WITHOUT ANY WARRANTY; without even the implied warranty of 0032 % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 0033 % GNU General Public License for more details. 0034 % 0035 % You can obtain a copy of the GNU General Public License from 0036 % http://www.gnu.org/copyleft/gpl.html or by writing to 0037 % Free Software Foundation, Inc.,675 Mass Ave, Cambridge, MA 02139, USA. 0038 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 0039 0040 if ~isreal(y) error('RSFFT: Input must be real'); end 0041 fl=size(y,1)==1; 0042 if fl y=y(:); end 0043 [m,k]=size(y); 0044 if nargin<2 n=2*m-2; 0045 else 0046 mm=1+fix(n/2); 0047 if mm>m y=[y; zeros(mm-m,k)]; 0048 elseif mm<m y(mm+1:m,:)=[]; 0049 end 0050 m=mm; 0051 end 0052 x=real(fft([y;y(n-m+1:-1:2,:)])); 0053 x(m+1:end,:)=[]; 0054 if fl x=x.'; end

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