经验模态分解MATLAB代码

以下是经验模态分解（Empirical Mode Decomposition，EMD）的MATLAB代码示例：

function [IMF,Residual] = emd(x)
% EMD: Empirical mode decomposition
% [IMF,Residual] = EMD(x)
% input:
% x - input signal (1-D vector)
% output:
% IMF - intrinsic mode functions (matrix)
% Residual - residual signal (1-D vector)
% Reference: Huang et al., "The empirical mode decomposition and the
% Hilbert spectrum for nonlinear and non-stationary time series analysis",
% Proc. R. Soc. Lond. A, 1998

% initialization
IMF = []; % intrinsic mode functions
Residual = x; % residual signal
N = length(x); % length of input signal

% EMD
while (1)
% find local extrema
maxtab = []; % maximum points
mintab = []; % minimum points
for i=2:N-1
if (x(i)>x(i-1) && x(i)>x(i+1))
maxtab = [maxtab; i x(i)];
end
if (x(i)<x(i-1) && x(i)<x(i+1))
mintab = [mintab; i x(i)];
end
end

if (length(maxtab)<2 || length(mintab)<2)
break;
end

% create upper and lower envelopes
x1 = zeros(N,1);
x2 = zeros(N,1);
maxidx = maxtab(:,1);
maxval = maxtab(:,2);
minidx = mintab(:,1);
minval = mintab(:,2);
x1(maxidx) = maxval;
x2(minidx) = minval;
p1 = interp1(maxidx,maxval,1:N,'spline');
p2 = interp1(minidx,minval,1:N,'spline');
upper = (p1+p2)/2;
lower = upper;
upper(p1<p2) = p1(p1<p2);
lower(p1>p2) = p2(p1>p2);

% calculate mean of envelopes
mean_env = (upper+lower)/2;

% calculate difference between signal and mean envelope
d = x-mean_env;

% check for IMF
if (isempty(find(maxtab(:,1)<N/2,1))) && (isempty(find(mintab(:,1)<N/2,1)))
IMF = [IMF d];
Residual = Residual - d;
x = d;
else
break;
end
end

% add residual to IMF
IMF = [IMF Residual];

end

该函数接受一个输入信号x，并返回其分解成的所有IMF和剩余信号Residual。该代码的基本思想是将信号分解成一系列内禀模态函数（IMF），每个IMF是一个振荡函数，其带宽随着频率的增加而减小，因此它可以看作是信号中不同频率的分量。最后的残差信号是最低频率的分量。

以下是使用该函数对信号进行EMD的示例：

% generate test signal
t = linspace(0,1,1000);
x = cos(2*pi*20*t) + sin(2*pi*50*t) + randn(size(t));

% perform EMD
[IMF,Residual] = emd(x);

% plot results
figure;
subplot(length(IMF)+1,1,1);
plot(t,x);
title('Original signal');
ylabel('Amplitude');
for i=1:length(IMF)
subplot(length(IMF)+1,1,i+1);
plot(t,IMF(:,i));
title(['IMF ' num2str(i)]);
ylabel('Amplitude');
end
subplot(length(IMF)+1,1,length(IMF)+1);
plot(t,Residual);
title('Residual signal');
ylabel('Amplitude');
xlabel('Time (s)');

该示例生成一个包含三个频率分量的测试信号，并使用emf函数将其分解成IMF和Residual信号。最后，它绘制了原始信号、每个IMF和残差信号的图形。