# v_rsfft

## PURPOSE

V_RSFFT fft of a real symmetric spectrum X=(Y,N)

## SYNOPSIS

function x=v_rsfft(y,n)

## DESCRIPTION

    V_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=v_rsfft(x,n)/n

## CROSS-REFERENCE INFORMATION

This function calls:

This function is called by:

- v_lpcpf2cc V_LPCPF2CC Convert power spectrum to complex cepstrum CC=(PF,NP)
- v_pow2cep V_POW2CEP convert power domain means and variances to the cepstral domain

## SOURCE CODE

    0001 function x=v_rsfft(y,n)
    0002 %V_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=v_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: v_rsfft.m 10865 2018-09-21 17:22:45Z 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 Lesser General Public License as published by
    0027 %   the Free Software Foundation; either version 3 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 Lesser General Public License for more details.
    0034 %
    0035 %   You can obtain a copy of the GNU Lesser General Public License from
    0036 %   https://www.gnu.org/licenses/ .
    0037 %
    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