function?[u?u_hat?omega]?=?VMD（signal?alpha?tau?K?DC?init?tol）
%?Variational?Mode?Decomposition
%?Authors:?Konstantin?Dragomiretskiy?and?Dominique?Zosso
%?zosso@math.ucla.edu?---?http://www.math.ucla.edu/~zosso
%?Initial?release?2013-12-12?（c）?2013
%
%?Input?and?Parameters:
%?---------------------
%?signal??-?the?time?domain?signal?（1D）?to?be?decomposed
%?alpha???-?the?balancing?parameter?of?the?data-fidelity?constraint
%?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?of?convergence?criterion;?typically?around?1e-6
%
%?Output:
%?-------
%?u???????-?the?collection?of?decomposed?modes
%?u_hat???-?spectra?of?the?modes
%?omega???-?estimated?mode?center-frequencies
%
%?When?using?this?code?please?do?cite?our?paper:
%?-----------------------------------------------
%?K.?Dragomiretskiy?D.?Zosso?Variational?Mode?Decomposition?IEEE?Trans.
%?on?Signal?Processing?（in?press）
%?please?check?here?for?update?reference:?
%??????????http://dx.doi.org/10.1109/TSP.2013.2288675



%----------?Preparations

%?Period?and?sampling?frequency?of?input?signal
save_T?=?length（signal）;
fs?=?1/save_T;

%?extend?the?signal?by?mirroring
T?=?save_T;
f_mirror（1:T/2）?=?signal（T/2:-1:1）;
f_mirror（T/2+1:3*T/2）?=?signal;
f_mirror（3*T/2+1:2*T）?=?signal（T:-1:T/2+1）;
f?=?f_mirror;

%?Time?Domain?0?to?T?（of?mirrored?signal）
T?=?length（f）;
t?=?（1:T）/T;

%?Spectral?Domain?discretization
freqs?=?t-0.5-1/T;

%?Maximum?number?of?iterations?（if?not?converged?yet?then?it?won‘t?anyway）
N?=?500;

%?For?future?generalizations:?individual?alpha?for?each?mode
Alpha?=?alpha*ones（1K）;

%?Construct?and?center?f_hat
f_hat?=?fftshift（（fft（f）））;
f_hat_plus?=?f_hat;
f_hat_plus（1:T/2）?=?0;

%?matrix?keeping?track?of?every?iterant?//?could?be?discarded?for?mem
u_hat_plus?=?zeros（N?length（freqs）?K）;

%?Initialization?of?omega_k
omega_plus?=?zeros（N?K）;
switch?init
????case?1
????????for?i?=?1:K
????????????omega_plus（1i）?=?（0.5/K）*（i-1）;
????????end
????case?2
????????omega_plus（1:）?=?sort（exp（log（fs）?+?（log（0.5）-log（fs））*rand（1K）））;
????otherwise
????????omega_plus（1:）?=?0;
end

%?if?DC?mode?imposed?set?its?omega?to?0
if?DC
????omega_plus（11）?=?0;
end

%?start?with?empty?dual?variables
lambda_hat?=?zeros（N?length（freqs））;

%?other?inits
uDiff?=?tol+eps;?%?update?step
n?=?1;?%?loop?counter
sum_uk?=?0;?%?accumulator



%?-----------?Main?loop?for?iterative?updates




while?（?uDiff?>?tol?&&??n?????
????%?update?first?mode?accumulator
????k?=?1;
????sum_uk?=?u_hat_plus（n:K）?+?sum_uk?-?u_hat_plus（n:1）;
????
????%?update?spectrum?of?first?mode?through?Wiener?filter?of?residuals
????u_hat_plus（n+1:k）?=?（f_hat_plus?-?sum_uk?-?la

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----
?????文件????????4645??2014-02-12?14:40??VMD.m