clear?all;
close?all;
clc;

%?Time?Domain?0?to?T
T?=?1000;
fs?=?1/T;
t?=?（1:T）/T;
freqs?=?2*pi*（t-0.5-1/T）/（fs）;

%?center?frequencies?of?components
f_1?=?2;
f_2?=?24;
f_3?=?288;

%?modes
v_1?=?（cos（2*pi*f_1*t））;
v_2?=?1/4*（cos（2*pi*f_2*t））;
v_3?=?1/16*（cos（2*pi*f_3*t））;

%?for?visualization?purposes
fsub?=?{};
wsub?=?{};
fsub{1}?=?v_1;
fsub{2}?=?v_2;
fsub{3}?=?v_3;
wsub{1}?=?2*pi*f_1;
wsub{2}?=?2*pi*f_2;
wsub{3}?=?2*pi*f_3;

%?composite?signal?including?noise
f?=?v_1?+?v_2?+?v_3?+?0.1*randn（size（v_1））;
f_hat?=?fftshift（（fft（f）））;

%?some?sample?parameters?for?VMD
alpha?=?2000;????????%?moderate?bandwidth?constraint
tau?=?0;????????????%?noise-tolerance?（no?strict?fidelity?enforcement）
K?=?3;??????????????%?3?modes
DC?=?0;?????????????%?no?DC?part?imposed
init?=?1;???????????%?initialize?omegas?uniformly
tol?=?1e-7;


%---------------?Run?actual?VMD?code

[u?u_hat?omega]?=?VMD（f?alpha?tau?K?DC?init?tol）;

%---------------?Visualization

%?For?convenience?here:?Order?omegas?increasingly?and?reindex?u/u_hat
[~?sortIndex]?=?sort（omega（end:））;
omega?=?omega（:sortIndex）;
u_hat?=?u_hat（:sortIndex）;
u?=?u（sortIndex:）;
linestyles?=?{‘b‘?‘g‘?‘m‘?‘c‘?‘c‘?‘r‘?‘k‘};

figure（‘Name‘?‘Composite?input?signal‘?）;
plot（tf?‘k‘）;
set（gca?‘XLim‘?[0?1]）;

f