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# lpccc2pf

## PURPOSE

LPCCC2PF Convert complex cepstrum to power spectrum PF=(CC,NP,NC)

## SYNOPSIS

function [pf,f]=lpccc2pf(cc,np,nc,c0)

## DESCRIPTION

```LPCCC2PF Convert complex cepstrum to power spectrum PF=(CC,NP,NC)

Inputs: cc(nf,n)     Complex ceptral coefficients excluding c(0), one frame per row
np           Size of output spectrum is np+1 [n]
Alternatively, np can be a vector of output frequencies in the range 0 to 0.5
nc           Highest cepstral coefficient to use [np or, if np is a vector, n]
Set nc=-1 to use n coefficients
c0(nf,1)     Cepstral coefficient cc(0) [0]

Outputs: pf(nf,np+1)  Power spectrum from DC to Nyquist
f(1,np+1)    Normalized frequencies (0 to 0.5)

The "complex cepstral coefficients", cc(n), are the inverse discrete-time Fourier transform
of the log of the complex-valued spectrum. The cc(n) are real-valued and, for n<0, cc(n)=0.
The "real cepstral coeffcients", rc(n), are the inverse discrete-time Fourier transform
of the log of the magnitude spectrum; rc(0)=cc(0) and rc(n)=0.5*cc(n) for n~=0.
For highest speed, choose np to be a power of 2.```

## CROSS-REFERENCE INFORMATION

This function calls:
• lpccc2cc LPCCC2PF Extrapolate complex cepstrum C=(CC)
• rfft RFFT Calculate the DFT of real data Y=(X,N,D)
This function is called by:
• lpcar2cc LPCAR2CC LPC: Convert AR filter to complex cepstrum [CC,C0]=(AR,NP)

## SOURCE CODE

```0001 function [pf,f]=lpccc2pf(cc,np,nc,c0)
0002 %LPCCC2PF Convert complex cepstrum to power spectrum PF=(CC,NP,NC)
0003 %
0004 %  Inputs: cc(nf,n)     Complex ceptral coefficients excluding c(0), one frame per row
0005 %          np           Size of output spectrum is np+1 [n]
0006 %                       Alternatively, np can be a vector of output frequencies in the range 0 to 0.5
0007 %          nc           Highest cepstral coefficient to use [np or, if np is a vector, n]
0008 %                       Set nc=-1 to use n coefficients
0009 %          c0(nf,1)     Cepstral coefficient cc(0) [0]
0010 %
0011 % Outputs: pf(nf,np+1)  Power spectrum from DC to Nyquist
0012 %          f(1,np+1)    Normalized frequencies (0 to 0.5)
0013 %
0014 % The "complex cepstral coefficients", cc(n), are the inverse discrete-time Fourier transform
0015 % of the log of the complex-valued spectrum. The cc(n) are real-valued and, for n<0, cc(n)=0.
0016 % The "real cepstral coeffcients", rc(n), are the inverse discrete-time Fourier transform
0017 % of the log of the magnitude spectrum; rc(0)=cc(0) and rc(n)=0.5*cc(n) for n~=0.
0018 % For highest speed, choose np to be a power of 2.
0019
0020 %      Copyright (C) Mike Brookes 1998-2014
0021 %      Version: \$Id: lpccc2pf.m 5026 2014-08-22 17:47:43Z dmb \$
0022 %
0023 %   VOICEBOX is a MATLAB toolbox for speech processing.
0025 %
0026 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0027 %   This program is free software; you can redistribute it and/or modify
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 [nf,mc]=size(cc);
0042 if nargin<2 || ~numel(np)
0043     if nargout
0044         np=mc;
0045     else
0046         np=128;
0047     end
0048 end
0049 if nargin>=3 && numel(nc)==1 && nc==-1 nc=mc; end
0050 if nargin<4 || ~numel(c0) c0=zeros(nf,1); end
0051 if numel(np)>1 || np(1)<1
0052     if nargin<3 || ~numel(nc) nc=mc; end
0053     f=np(:)';
0054     if nc==mc
0055         pf=exp(2*[c0 cc]*cos(2*pi*(0:mc)'*f));
0056     else
0057         pf=exp(2*[c0 lpccc2cc(cc,nc)]*cos(2*pi*(0:nc)'*f));
0058     end
0059 else
0060     if nargin<3 || ~numel(nc) nc=np; end
0061     if nc==mc
0062         pf=exp(2*real(rfft([c0 cc].',2*np).'));
0063     else
0064         pf=exp(2*real(rfft([c0 lpccc2cc(cc,nc)].',2*np).'));
0065     end
0066     f=linspace(0,0.5,np+1);
0067 end
0068 if ~nargout
0069     plot(f,db(pf.')/2);
0070     xlabel('Normalized frequency f/f_s');
0071     ylabel('Gain (dB)');
0072 end
0073
0074
0075
0076
0077```

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