You are an expert in writing code in many different languages. Your goal is to perform code completion for the following code, keeping in mind the rest of the code and the file meta data.
    Metadata details:
    filename: VMD.m
    path of file: ./repos/University_project_vmd_majorization/woa
    
    the code of the file until where you have to start completion: function [u, u_hat, omega] = VMD(signal, alpha, tau, K, DC, init, tol)
% Variational Mode Decomposition VMD变分模态分解  经验模式分解（EMD）
%EMD分解经常被用作信号特征提取的一个预先处理手段，将各IMF分量作为后续分析方法的输入，以完成更加复杂的工作。
% 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输入和参数:
% ---------------------
% signal  - 此参数为一个信号，从表中读取的参数 the time domain signal (1D) to be decomposed
% -----alpha   -输入为     带宽限制，经验取值为抽样点长度1.5-2.0 倍；数据保真约束的平衡参数the balancing parameter of the data-fidelity constraint
% tau     - 输入为0    双爬升的时间步长(噪声松弛选0)time-step of the dual ascent ( pick 0 for noise-slack )
% -----K       - 输入为       需要恢复的模式个数，分解模态（IMF）个数the number of modes to be recovered
%DC      - 输入为0   如果将第一模态设置为DC(0频率)则为真true if the first mode is put and kept at DC (0-freq)
% init    - 输入为1      0 = all omegas start at 0  从零开始
%                    1 = all omegas start uniformly distributed   均匀分布
%                    2 = all omegas initialized randomly  随机分布
% tol     -输入为1e-5     收敛准则的容差;通常大约e-6tolerance of convergence criterion; typically around 1e-6
%迭代次数是反复迭代的次数，迭代次数越大，结果越准确。容差是计算结果和设定结果（期望结果）之间的误差值。

% Output:
% -------
% u       -分解模式的集合 the collection of decomposed modes
% u_hat   - 模谱spectra of the modes
% omega   - 估计模式中心频率 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
%signal=load('moni_noise.dat');alpha=3.216578811729743e+03;tau=0;K=5;DC=0;init=1;tol=1e-5

    
function [u, u_hat, omega] = VMD(signal, alpha, tau, K, DC, init, tol)
% Variational Mode Decomposition VMD变分模态分解  经验模式分解（EMD）
%EMD分解经常被用作信号特征提取的一个预先处理手段，将各IMF分量作为后续分析方法的输入，以完成更加复杂的工作。
% 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输入和参数:
% ---------------------
% signal  - 此参数为一个信号，从表中读取的参数 the time domain signal (1D) to be decomposed
% -----alpha   -输入为     带宽限制，经验取值为抽样点长度1.5-2.0 倍；数据保真约束的平衡参数the balancing parameter of the data-fidelity constraint
% tau     - 输入为0    双爬升的时间步长(噪声松弛选0)time-step of the dual ascent ( pick 0 for noise-slack )
% -----K       - 输入为       需要恢复的模式个数，分解模态（IMF）个数the number of modes to be recovered
%DC      - 输入为0   如果将第一模态设置为DC(0频率)则为真true if the first mode is put and kept at DC (0-freq)
% init    - 输入为1      0 = all omegas start at 0  从零开始
%                    1 = all omegas start uniformly distributed   均匀分布
%                    2 = all omegas initialized randomly  随机分布
% tol     -输入为1e-5     收敛准则的容差;通常大约e-6tolerance of convergence criterion; typically around 1e-6
%迭代次数是反复迭代的次数，迭代次数越大，结果越准确。容差是计算结果和设定结果（期望结果）之间的误差值。

% Output:
% -------
% u       -分解模式的集合 the collection of decomposed modes
% u_hat   - 模谱spectra of the modes
% omega   - 估计模式中心频率 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
%signal=load('moni_noise.dat');alpha=3.216578811729743e+03;tau=0;K=5;DC=0;init=1;tol=1e-5

% 输入信号的周期和采样频率Period and sampling frequency of input signal
save_T = length(signal);%信号的时间2048
fs = 1/save_T;%信号的频率

% 通过镜像扩展信号extend