invert.m

语音编码

% MATLAB SIMULATION OF FS-1015 LPC-10e
% COPYRIGHT (C) 1996-99 ANDREAS SPANIAS and TED PAINTER
%
% This Copyright applies only to this particular MATLAB implementation
% of the LPC-10e coder.  The MATLAB software is intended only for educational
% purposes.  No other use is intended or authorized.  This is not a public
% domain program and unauthorized distribution to individuals or networks 
% is prohibited. Be aware that use of the standard in any form is goverened
% by rules of the US DoD.  
% This program is free software. It is distributed in the hope that it will
% be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  There is no commitment 
% or even implied commitment on behalf of Andreas Spanias or Ted Painter
% for maintenance or support of this code.
%
% MATLAB is trademark of The Mathworks Inc
%
% ALL DERIVATIVE WORKS MUST INCLUDE THIS COPYRIGHT NOTICE.
%
% ******************************************************************
% INVERT
%
% PORTED TO MATLAB FROM LPC-55 C RELEASE
% 3-21-94
%
% ******************************************************************
%
% DESCRIPTION
%
% Invert the covariance matrix using Choleski decomposition.
%
% DESIGN NOTES
%
% Classical Cholesky decomposition is not completed because reflection
% coefficients obtained during the first back substitution correlete
% closely with actual reflection coefficients.
%
% See Also:  Version 52 release notes; Rabiner and Schafer, pp. 407-411.
%
% VARIABLES
%
% INPUTS
%   phi      -   Covariance matrix
%   psi      -   Covariance vector
%   rc       -   Pseudo reflection coefficients
%
% OUTPUTS
%   rc       -   Pseudo reflection coefficients
%
% INTERNAL
%   save     -   Intermediate result
%   eps      -   Termination tolerance
%
% CONSTANTS
%   ORDER    -   Linear prediction order
%   AF       -   Analysis frame buffer index
%
% ******************************************************************

function rc = invert( phi, psi, rc )

% DECLARE GLOBAL VARIABLES
global ORDER AF;

% INITIALIZE CONSTANTS
eps = 1.0e-10;

% DECOMPOSE PHI INTO V D V', WHERE V IS A TRIANGULAR MATRIX WHOSE
% MAIN DIAGONAL ELEMENTS ARE ALL 1, V' IS THE TRANSPOSE OF V, AND
% D IS A VECTOR.  STORE ALL RESULTS IN MODIFIED PHI MATRIX.
j = 1;
while j <= ORDER
    k = 1;
    while k < j
        save = phi(j,k) * phi(k,k);
        phi(j:ORDER,j) = phi(j:ORDER,j) - ( phi(j:ORDER,k) .* save );
        k = k + 1;
    end

    % ZERO OUT HIGHER ORDER RC'S IF ALGORITHM TERMINATES EARLY
    if abs( phi(j,j) ) < eps
        rc(j:ORDER,AF) = zeros( ORDER-j+1, 1);
        return
    end

    % COMPUTE INTERMEDIATE RESULTS, WHICH ARE SIMILAR TO RC'S ( == PSUEDO RCs)
    rc(j,AF) = psi(j);
    rc(j,AF) = rc(j,AF) - sum( rc(1:(j-1),AF) .* phi(j,1:(j-1))' );
    phi(j,j) = 1.0 / phi(j,j);
    rc(j,AF) = rc(j,AF) * phi(j,j);
    rc(j,AF) = max([min([rc(j,AF),0.999]),-0.999]);
    j = j + 1;
end