function [music_data,msg] = music(x,p,varargin)%MUSIC Implements the heart of the MUSIC algorithm of line spectra estimation.% MUSIC is called by both PMUSIC and ROOTMUSIC.% % Inputs:% % x - vector or matrix. If vector it is a signal, if matrix it may be either a data% matrix such that x'*x=R, or a correlation matrix R.% p - scalar or two element vector. If scalar, it indicates the dimension of the % signal subspace. If vector, p(2) is a threshold used to determine the % aforementioned dimension.% nfft - (optional) to be used only with PMUSIC. A scalar indicating the number of% points used in the evaluation of the pseudospectrum.% Fs - (optional) a scalar specifying the sampling frequency. If omitted, we work% in rad/sample; if empty it defaults to 1 Hz.% nw - (optional) a scalar or vector indicating either the order of the correlation% matrix or (when a vector) a window whose length is the order of the matrix% and whose values are used to window each column of the data matrix.% noverlap - (optional) a integer indicating the number of samples to overlap from% column to column.% strings - Optional input strings are: 'corr', 'EV' and range ('half' or 'whole').%% Outputs:%% msg - a possible error message.%% music_data - a structure with the following fields:% % noise_eigenvects - a matrix whose columns are the noise subspace eigenvectors.% signal_eigenvects - a matrix whose columns are the signal subspace eigenvectors.% eigenvals - the eigenvalues of the correlation matrix.% p_eff - the effective dimension of the signal subspace.% nfft - number of points used to evaluate the pseudospectrum (only used in PMUSIC).% Fs - sampling freq.% range - string indicating whether 'half' or the 'whole' pseudospectrum should be% computed. (Only used in PMUSIC.)% EVFlag - flag, 0 = MUSIC method; 1 = EigenVector method.% Author(s): R. Losada% Copyright 1988-2006 The MathWorks, Inc.% $Revision: 1.1 $ $Date: 2010/02/18 11:16:20 $ % References:% [1] Petre Stoica and Randolph Moses, Introduction To Spectral% Analysis, Prentice-Hall, 1997, pg. 15% [2] S. J. Orfanidis, Optimum Signal Processing. An Introduction. % 2nd Ed., Macmillan, 1988.xIsReal = isreal(x);msg = '';music_data = [];if isempty(p), msg = 'The signal subspace dimension cannot be empty.'; returnend[opts,msg] = music_options(xIsReal,p,varargin{:});if ~isempty(msg), returnend% Compute the eigenvalues and eigenvectors of the correlation matrix[eigenvals,eigenvects] = computeeig(x,opts.CorrFlag,opts.CorrMatrOrd,opts.nw,opts.noverlap,opts.window,opts.EVFlag);% Determine the effective dimension of the signal subspacep_eff = determine_signal_space(p,eigenvals);% Separate the signal and noise eigenvectorssignal_eigenvects = eigenvects(:,1:p_eff);noise_eigenvects = eigenvects(:,p_eff+1:end);% Generate the output structuremusic_data.noise_eigenvects = noise_eigenvects;music_data.signal_eigenvects = signal_eigenvects;music_data.eigenvals = eigenvals;music_data.p_eff = p_eff;music_data.nfft = opts.nfft;music_data.Fs = opts.Fs;music_data.EVFlag = opts.EVFlag;music_data.range = opts.range;%--------------------------------------------------------------------------------------function [options,msg] = music_options(xIsReal,p,varargin)%MUSIC_OPTIONS Parse the optional inputs to the MUSIC function.% MUSIC_OPTIONS returns a structure, OPTIONS, with the following fields:%% options.nfft - number of freq. points at which the psd is estimated% options.Fs - sampling freq. if any% options.range - 'onesided' or 'twosided' pseudospectrum (they correspond to% 'half' and 'whole' respectively, but are returned as is by% psdoptions.m% options.nw - number of columns in the data matrix % options.noverlap - number of samples to overlap% options.window - a vector with window coefficients% options.CorrFlag - a flag indicating whether the input is a correlation matrix% options.EVFlag - flag, 0 = MUSIC method ; 1 = EigenVector method% options.CorrMatrOrd - order of the correlation matrix to be used in computations% Assign Defaultsmsg = '';options.nw = [];options.noverlap = [];options.window = [];options.nfft = 256;options.Fs = [];options.CorrFlag = 0;options.EVFlag = 0;% Determine if frequency vector specifiedfreqVecSpec = false;if (length(varargin) > 0 && isnumeric(varargin{1}) && length(varargin{1}) > 1) freqVecSpec = true;end if xIsReal && ~freqVecSpec, options.range = 'onesided';else options.range = 'twosided';end[options,msg] = psdoptions(xIsReal,options,varargin{:});if length(options.nfft) > 1, if strcmpi(options.range,'onesided') warning(generatemsgid('InconsistentRangeOption'),... 'Ignoring the ''onesided'' option. When a frequency vector is specified, a ''twosided'' PSD is computed'); end options.range = 'twosided';end% psdoptions doesn't handle this field, assign it separetelyoptions.CorrMatrOrd = 2*p(1);%-----------------------------------------------------------------------------------------function [eigenvals,eigenvects] = computeeig(x,CorrFlag,CorrMatrOrd,nw,noverlap,window,EVFlag)%COMPUTEEIG Compute eigenvalues and eigenvectors of correlation matrix.%% Inputs:% % x - input vector or matrix% CorrFlag - (flag) indicates whether x is a correlation matrix% nw - (integer) length of the rows of the data matrix % (only used if x is vector)% noverlap - (integer) overlap between the rows of the data matrix% (used in conjunction with nw) % window - (vector) window to be applied to each column of data% matrix (not used if x is a correlation matrix)% EVFlag - True if eigenvector method, false if MUSIC.% %% Outputs:% % eigenvals% eigenvects%% If x is a matrix, % If CorrFlag = 1, input x is a correlation matrix, we compute the% eigendecomposition and order the eigenvalues and eigenvectors.%% If x is a vector,% a data matrix is formed by calling corrmtx unless a custom nw% and noverlap are specified. In that case, we use buffer to form% the data matrix. %% If window is not empty, each row of the data matrix will be% multiplied by the window.% Determine if the input is a matrixxIsMatrix = ~any(size(x)==1);if xIsMatrix && CorrFlag, % Input is Correlation matrix % Compute the eigenvectors and eigenvalues [E,D] = eig((x+x')/2); % Ensure hermitian [eigenvals,indx] = sort(diag(D),'descend'); eigenvects = E(:,indx);else if xIsMatrix % Input is already a data matrix [Mx,Nx] = size(x); % Determine size of data matrix if EVFlag && (Nx > Mx), errmsg = 'The number of columns in the data matrix cannot exceed the number of rows.'; error(generatemsgid('invalidDataMatrix'),errmsg); end else % x is a vector x = x(:); % Make it a column if isempty(nw), x = corrmtx(x,CorrMatrOrd-1,'cov'); else if EVFlag && nw > (ceil((length(x)-nw)/(nw-noverlap))+1), errmsg = sprintf(['The segment length and overlap specified result in\n',... 'a data matrix with more columns than rows.']); error(generatemsgid('invalidDataMatrix'),errmsg); end Lx = length(x); x = buffer(x,nw,noverlap,'nodelay'); if Lx <= nw, error(generatemsgid('invalidSegmentLength'),'The segment length, NW, must be smaller than the signal length.'); end x = x'./sqrt(Lx-nw); % Scale appropriately such that X'*X is a scaled estimate of R end end if ~isempty(window), % Apply window to each row of data matrix if length(window) ~= size(x,2), error(generatemsgid('InvalidDimensions'),'Window length must equal the number of columns in the data matrix.'); end window = repmat(window(:).',size(x,1),1); x = x.*window; end % Compute the eigenvectors and eigenvalues via the SVD [U,S,eigenvects] = svd(x,0); eigenvals = diag(S).^2; % We need to square the singular values hereend%--------------------------------------------------------------------------------------------function p_eff = determine_signal_space(p,eigenvals)%DETERMINE_SIGNAL_SPACE Determines the effective dimension of the signal subspace.% % Inputs:%% p - (scalar or vector) signal subspace dimension % (but may contain a desired threshold).% eigenvals - (vector) contains the eigenvalues (sorted in decreasing order)% of the correlation matrix%% Outputs:%% p_eff - The effective dimension of the signal subspace. If a threshold% is given as p(2), the signal subspace will be equal to the number% of eigenvalues, NEIG, greater than the threshold times the smallest% eigenvalue. However, the dimension of the signal subspace is at most% p(1), so that if NEIG is greater than p(1), p_eff will be equal to% p(1). If the threshold criteria results in an empty signal subspace,% once again we make p_eff = p(1).% Use the signal space dimension or the threshold to separate the noise subspace eigenvectorsif length(p) == 2, % The threshold will be the input threshold times the smallest eigenvalue thresh = p(2)*eigenvals(end); indx = find(eigenvals > thresh); if ~isempty(indx) p_eff = min( p(1), length(indx) ); else p_eff = p(1); endelse p_eff = p;end% [EOF] - music.m