arburg.rar

function varargout = arburg( x, p) %ARBURG AR parameter estimation via Burg method. % A = ARBURG(X,ORDER) returns the polynomial A corresponding to the AR % parametric signal model estimate of vector X using Burg's method. % ORDER is the model order of the AR system. % % [A,E] = ARBURG(...) returns the final prediction error E (the variance % estimate of the white noise input to the AR model). % % [A,E,K] = ARBURG(...) returns the vector K of reflection % coefficients (parcor coefficients). % % See also PBURG, ARMCOV, ARCOV, ARYULE, LPC, PRONY. % Ref: S. Kay, MODERN SPECTRAL ESTIMATION, % Prentice-Hall, 1988, Chapter 7 % S. Orfanidis, OPTIMUM SIGNAL PROCESSING, 2nd Ed. % Macmillan, 1988, Chapter 5 % Author(s): D. Orofino and R. Losada % Copyright 1988-2004 The MathWorks, Inc. % $Revision: 1.12.4.3 $ $Date: 2007/12/14 15:03:40 $ error(nargchk(2,2,nargin,'struct')) [mx,nx] = size(x); if isempty(x) || min(mx,nx) > 1, error(generatemsgid('InvalidDimensions'),'X must be a vector with length greater than twice the model order.'); elseif isempty(p) || ~(p == round(p)) error(generatemsgid('MustBeInteger'),'Model order must be an integer.') end if issparse(x), error(generatemsgid('Sparse'),'Input signal cannot be sparse.') end x = x(:); N = length(x); % Initialization ef = x; eb = x; a = 1; % Initial error E = x'*x./N; % Preallocate 'k' for speed. k = zeros(1, p); for m=1:p % Calculate the next order reflection (parcor) coefficient efp = ef(2:end); ebp = eb(1:end-1); num = -2.*ebp'*efp; den = efp'*efp+ebp'*ebp; k(m) = num ./ den; % Update the forward and backward prediction errors ef = efp + k(m)*ebp; eb = ebp + k(m)'*efp; % Update the AR coeff. a=[a;0] + k(m)*[0;conj(flipud(a))]; % Update the prediction error E(m+1) = (1 - k(m)'*k(m))*E(m); end a = a(:).'; % By convention all polynomials are row vectors varargout{1} = a; if nargout >= 2 varargout{2} = E(end); end if nargout >= 3 varargout{3} = k(:); end