function [a,e]=lpc(x,N)%LPC Linear Predictor Coefficients.% A = LPC(X,N) finds the coefficients, A=[ 1 A(2) ... A(N+1) ], of an Nth% order forward linear predictor.%% Xp(n) = -A(2)*X(n-1) - A(3)*X(n-2) - ... - A(N+1)*X(n-N)%% such that the sum of the squares of the errors%% err(n) = X(n) - Xp(n)%% is minimized. X can be a vector or a matrix. If X is a matrix% containing a separate signal in each column, LPC returns a model% estimate for each column in the rows of A. N specifies the order of% the polynomial A(z) which must be a positive integer. N must be less% or equal to the length of X. If X is a matrix, N must be less or equal% to the length of each column of X.%% If you do not specify a value for N, LPC uses a default N =% length(X)-1.%% [A,E] = LPC(X,N) returns the variance (power) of the prediction error.%% LPC uses the Levinson-Durbin recursion to solve the normal equations% that arise from the least-squares formulation. This computation of the% linear prediction coefficients is often referred to as the% autocorrelation method.%% See also LEVINSON, ARYULE, PRONY, STMCB.% Author(s): T. Krauss, 9-21-93% Modified: T. Bryan 11-14-97% Copyright 1988-2004 The MathWorks, Inc.% $Revision: 1.12.4.6 $ $Date: 2009/08/11 15:47:46 $error(nargchk(1,2,nargin,'struct'))if isempty(x) error(generatemsgid('Empty'),'Input vector X should not be empty');end[m,n] = size(x);if (n>1) && (m==1)x = x(:);[m,n] = size(x);endif nargin < 2, N = m-1; elseif N < 0, % Check for N positive error(generatemsgid('negativeOrder'), ... 'Order of the predictor should be a positive integer.');end% Check the input data type. Single precision is not supported.try chkinputdatatype(x,N);catch ME throwAsCaller(ME);endif (N > m), error(generatemsgid('orderTooLarge'), '%s\n%s\n%s', ... 'X must be a vector with length greater or equal to the prediction order.', ... 'If X is a matrix, the length of each column must be greater or equal to', ... 'the prediction order.');end% Compute autocorrelation vector or matrixX = fft(x,2^nextpow2(2*size(x,1)-1));R = ifft(abs(X).^2);R = R./m; % Biased autocorrelation estimate[a,e] = levinson(R,N);% Return only real coefficients for the predictor if the input is realfor k = 1:n, if isreal(x(:,k)) a(k,:) = real(a(k,:)); endend