# v_lpcpf2cc

## PURPOSE V_LPCPF2CC Convert power spectrum to complex cepstrum CC=(PF,NP)

## SYNOPSIS function [cc,c0]=v_lpcpf2cc(pf,np,f)

## DESCRIPTION ```V_LPCPF2CC Convert power spectrum to complex cepstrum CC=(PF,NP)

Inputs: pf(nf,n)    Power spectrum, uniformly spaced DC to Nyquist
np          Number of cepstral coefficients to calculate [n-1]
f(1,n)      Frequencies of pf columns [linspace(0,0.5,n)]

Outputs: cc(nf,np)  Complex spectrum from DC to Nyquist
c0(nf,1)   The zeroth cepstral coefficient, c(0)

Note since the log spectrum is not normally bandlimited, this conversion is not exact unless n >> np```

## CROSS-REFERENCE INFORMATION This function calls:
• v_rsfft V_RSFFT fft of a real symmetric spectrum X=(Y,N)
This function is called by:
• v_lpcpf2ff V_LPCPF2FF Convert power spectrum to complex spectrum [FF,FO]=(PF,NP,FI)

## SOURCE CODE ```0001 function [cc,c0]=v_lpcpf2cc(pf,np,f)
0002 %V_LPCPF2CC Convert power spectrum to complex cepstrum CC=(PF,NP)
0003 %
0004 %  Inputs: pf(nf,n)    Power spectrum, uniformly spaced DC to Nyquist
0005 %          np          Number of cepstral coefficients to calculate [n-1]
0006 %          f(1,n)      Frequencies of pf columns [linspace(0,0.5,n)]
0007 %
0008 % Outputs: cc(nf,np)  Complex spectrum from DC to Nyquist
0009 %          c0(nf,1)   The zeroth cepstral coefficient, c(0)
0010 %
0011 % Note since the log spectrum is not normally bandlimited, this conversion is not exact unless n >> np
0012
0013 %      Copyright (C) Mike Brookes 1998-2014
0014 %      Version: \$Id: v_lpcpf2cc.m 10865 2018-09-21 17:22:45Z dmb \$
0015 %
0016 %   VOICEBOX is a MATLAB toolbox for speech processing.
0018 %
0019 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0020 %   This program is free software; you can redistribute it and/or modify
0022 %   the Free Software Foundation; either version 2 of the License, or
0023 %   (at your option) any later version.
0024 %
0025 %   This program is distributed in the hope that it will be useful,
0026 %   but WITHOUT ANY WARRANTY; without even the implied warranty of
0027 %   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
0028 %   GNU General Public License for more details.
0029 %
0030 %   You can obtain a copy of the GNU General Public License from
0031 %   http://www.gnu.org/copyleft/gpl.html or by writing to
0032 %   Free Software Foundation, Inc.,675 Mass Ave, Cambridge, MA 02139, USA.
0033 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0034 [nf,nq]=size(pf);
0035 if nargin<2 || ~numel(np) np=nq-1; end
0036 if nargin<3 || ~numel(f)
0037     cc=v_rsfft(log(pf.')).'/(2*nq-2);
0038     c0=cc(:,1)*0.5;
0039     cc(:,nq)=cc(:,nq)*0.5;
0040     if np>nq-1
0041         cc=[cc(:,2:nq) zeros(nf,np-nq+1)];
0042     else
0043         cc=cc(:,2:np+1);
0044     end
0045 else
0046     cc=0.5*(log(pf)/cos(2*pi*f(:)*(0:min(np,nq-1))));
0047     c0=cc(:,1);
0048     cc=cc(:,2:end);
0049     if np>nq-1
0050         cc(1,np)=0;
0051     end
0052 end
0053
0054```