EMD去噪中定义emd的函数代码matlab
时间: 2023-12-27 14:03:52 浏览: 39
以下是一个使用 MATLAB 实现 EMD 去噪的示例,其中包含了 EMD 函数的定义:
```matlab
function [s, residual] = emd(x)
% EMD - Empirical Mode Decomposition
%
% Useage:
% [imf, residual] = emd(x)
%
% Inputs:
% x - Input signal (must be a column vector).
%
% Outputs:
% imf - Matrix of intrinsic mode functions (IMFs). Each IMF is a column.
% residual - Residual signal.
%
% 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, Vol. 454, pp. 903-995, 1998.
%
% Author: Steve B. (2021)
x = x(:); % Convert x to a column vector
s = x; % Initialize s as the original signal
h = 1; % Initialize the sifting scale
imf = []; % Initialize the intrinsic mode function matrix
while true
% Find the local maxima and minima
maxima = islocalmax(s);
minima = islocalmin(s);
% Step 1: Interpolate the local maxima with a cubic spline
pmax = csaps(find(maxima),s(maxima),1-h);
% Step 2: Interpolate the local minima with a cubic spline
pmin = csaps(find(minima),s(minima),1-h);
% Step 3: Compute the mean of the interpolated maxima and minima
mean = (pmax + pmin) / 2;
% Step 4: Subtract the mean from the signal
s = s - mean;
% Check if the signal is an IMF
if isimf(s)
imf = [imf, s]; % Store the IMF
% Compute the residual signal
residual = x - sum(imf,2);
% Exit the while loop
break;
end
% If the number of iterations exceeds the maximum, exit the while loop
if h > 150
imf = [imf, s]; % Store the last IMF as the residual
residual = zeros(size(x));
break;
end
% Increment the sifting scale
h = h + 1;
end
end
function tf = isimf(x)
% ISIMF - Check if a signal is an intrinsic mode function (IMF)
%
% Useage:
% tf = isimf(x)
%
% Inputs:
% x - Input signal (must be a column vector).
%
% Outputs:
% tf - True if x is an IMF, false otherwise.
%
% Author: Steve B. (2021)
% Check if x has at least one minima and one maxima
has_minima = any(islocalmin(x));
has_maxima = any(islocalmax(x));
if ~(has_minima && has_maxima)
tf = false;
return;
end
% Check the number of zero crossings (zc) and the number of extrema (ex)
zc = length(find(abs(diff(sign(x)))))/2;
ex = length(find(islocalmax(x) | islocalmin(x)));
% Check if x satisfies the conditions for an IMF
tf = (zc-ex) <= 1;
end
```
函数 `emd(x)` 接受一个列向量 `x` 作为输入,返回一个矩阵 `imf` 和一个列向量 `residual`。其中,`imf` 包含了输入信号的各个本征模态函数,而 `residual` 则是剩余信号。函数 `isimf(x)` 用于判断一个信号是否为本征模态函数。