多元变分模态分解MVMD数据重构 可输出均方根误差，信噪比，各分解分量的相关系数指标 附案例数据 可直接运行

function [u, u_hat, omega] = MVMD(signal, alpha, tau, K, DC, init, tol) % Multivariate Variational Mode Decomposition % % The function MVMD applies the "Multivariate Variational Mode Decomposition (MVMD)" algorithm to multivariate or multichannel data sets. % We have verified this code through simulations involving synthetic and real world data sets containing 2-16 channels. % However, there is no reason that it shouldn't work for data with more than 16 channels. % % % Input and Parameters: % --------------------- % signal - input multivariate signal that needs to be decomposed % alpha - the parameter that defines the bandwidth of extracted modes (low value of alpha yields higher bandwidth) % tau - time-step of the dual ascent ( pick 0 for noise-slack ) % K - the number of modes to be recovered % DC - true if the first mode is put and kept at DC (0-freq) % init - 0 = all omegas start at 0 % - 1 = all omegas start uniformly distributed % - 2 = all omegas initialized randomly % tol - tolerance value for convergence of ADMM % % % Output: % ---------------------- % u - the collection of decomposed modes % u_hat - spectra of the modes % omega - estimated mode center-frequencies % % % Syntax: % ----------------------- % [u, u_hat, omega] = MVMD(X, alpha, tau, K, DC, init, tol) % returns: % a 3D matrix 'u(K,L,C)' containing K multivariate modes, each with 'C' number of channels and length 'L', that are % computed by applying the MVMD algorithm on the C-variate signal (time-series) X of length L. % - To extract a particular channel 'c' corresponding to all extracted modes, you can use u_c = u(:,:,c). % - To extract a particular mode 'k' corresponding to all channels, you can use u_k = u(k,:,:). % - To extract a particular mode 'k' corresponding to the channel 'c', you can use u_kc = u(k,:,c). % 3D matrix 'u_hat(K,L,C)' containing K multivariate modes, each with 'C' number of channels and length 'L', that % are computed by applying the MVMD algorithm on the C-variate signal (time-series) X of length L. % 2D matrix 'omega(N,K)' estimated mode center frequencies % Usage: % ----------------------- % Example 1: Mode Alignment on Synthetic Data % T = 1000; t = (1:T)/T; % f_channel1 = (cos(2*pi*2*t)) + (1/16*(cos(2*pi*36*t))); % Channel 1 contains 2 Hz and 36Hz tones % f_channel2 = (1/4*(cos(2*pi*24*t))) + (1/16*(cos(2*pi*36*t))); % Channel 2 contains 24 Hz and 36Hz tones % f = [f_channel1;f_channel2]; % Making a bivariate signal % [u, u_hat, omega] = MVMD(f, 2000, 0, 3, 0, 1, 1e-7); % Example 2: Real World Data (EEG Data) % load('EEG_data.mat'); % [u, u_hat, omega] = MVMD(data, 2000, 0, 6, 0, 1, 1e-7); % Authors: Naveed ur Rehman and Hania Aftab % Contact Email: naveed.rehman@comsats.edu.pk % % [1] N. Rehman, H. Aftab, Multivariate Variational Mode Decomposition, arXiv:1907.04509, 2019. % [2] K. Dragomiretskiy, D. Zosso, Variational Mode Decomposition, IEEE Transactions on Signal Processing, vol. 62, pp. 531-544, 2014. %---------- Check for Input Signal % Check for getting number of channels from input signal [x, y] = size(signal); if x > y C = y;% number of channels T = x;% length of the Signal signal = signal'; else C = x;% number of channels T = y;% length of the Signal end %---------- Preparations % Sampling Frequency fs = 1/T; % Mirroring f(:,1:T/2) = signal(:,T/2:-1:1); f(:,T/2+1:3*T/2) = signal; f(:,3*T/2+1:2*T) = signal(:,T:-1:T/2+1); % Time Domain 0 to T (of mirrored signal) T = size(f,2); t = (1:T)/T; % frequencies freqs = t-0.5-1/T; % Construct and center f_hat f_hat = fftshift(fft(f,[],2),2); f_hat_plus = f_hat; f_hat_plus(:,1:T/2) = 0; %------------ Initialization % Maximum number of iterations N = 500; % For future generalizations: individual alpha for each mode Alpha = alpha*ones(1,K); % matrix keeping track of every iterant u_hat_plus_00 = zeros(length(freqs), C, K); u_hat_plus = zeros(length(freqs), C, K); omega_plus = zeros(N, K); % initialize omegas uniformly switch init case 1 omega_plus(1,:) = (0.5/K)*((1:K)-1); case 2 omega_plus(1,:) = sort(exp(log(fs) + (log(0.5)-log(fs))*rand(1,K))); otherwise omega_plus(1,:) = 0; end % if DC mode imposed, set its omega to 0 if DC omega_plus(1,1) = 0; end % start with empty dual variables lambda_hat = zeros(length(freqs), C, N); % other inits uDiff = tol+eps; % update step n = 1; % loop counter sum_uk = zeros(length(freqs), C); % accumulator %--------------- Algorithm of MVMD while ( uDiff > tol && n < N ) % not converged and below iterations limit % update modes for k = 1:K % update mode accumulator if k > 1 sum_uk = u_hat_plus(:,:,k-1) + sum_uk - u_hat_plus_00(:,:,k); else sum_uk = u_hat_plus_00(:,:,K) + sum_uk - u_hat_plus_00(:,:,k); end % update spectrum of mode through Wiener filter of residuals for c = 1:C u_hat_plus(:,c,k) = (f_hat_plus(c,:).' - sum_uk(:,c) - lambda_hat(:,c,n)/2)./(1+Alpha(1,k)*(freqs.' - omega_plus(n,k)).^2); end % update first omega if not held at 0 if DC || (k > 1) % center frequencies numerator = freqs(T/2+1:T)*(abs(u_hat_plus(T/2+1:T,:, k)).^2); denominator = sum(abs(u_hat_plus(T/2+1:T,:,k)).^2); temp1 = sum(numerator); temp2 = sum(denominator); omega_plus(n+1,k) = temp1/temp2; end end % Dual ascent lambda_hat(:,:,n+1) = lambda_hat(:,:,n) + tau*(sum(u_hat_plus,3) - f_hat_plus.'); % loop counter n = n+1; u_hat_plus_m1 = u_hat_plus_00; u_hat_plus_00 = u_hat_plus; % converged yet? uDiff = u_hat_plus_00 - u_hat_plus_m1; uDiff = 1/T*(uDiff).*conj(uDiff); uDiff = eps+abs(sum(uDiff(:))); end %------ Post-processing and cleanup % discard empty space if converged early N = min(N,n); omega = omega_plus(1:N,:); % Signal reconstruction u_hat = zeros(T, K, C); for c = 1:C u_hat((T/2+1):T,:,c) = squeeze(u_hat_plus((T/2+1):T,c,:)); u_hat((T/2+1):-1:2,:,c) = squeeze(conj(u_hat_plus((T/2+1):T,c,:))); u_hat(1,:,c) = conj(u_hat(end,:,c)); end u = zeros(K,length(t),C); for k = 1:K for c = 1:C u(k,:,c)=real(ifft(ifftshift(u_hat(:,k,c)))); end end % remove mirror part u = u(:,T/4+1:3*T/4,:); % recompute spectrum clear u_hat; for k = 1:K for c = 1:C u_hat(:,k,c)=fftshift(fft(u(k,:,c)))'; end end u_hat = permute(u_hat, [2 1 3]); end