EMD算法的matlab程序介绍.pdf

%此版本为ALAN 版本的整合注释版 function imf = emd(x) % Empiricial Mode Decomposition (Hilbert-Huang Transform) % imf = emd(x) % Func :findpeaks x= transpose(x(:));%转置为行矩阵 imf = []; while ~ismonotonic(x) %当x 不是单调函数，分解终止条件 x1 = x; sd = Inf;%均值 %直到x1 满足IMF 条件，得c1 while (sd 0.1) |~isimf(x1) %当标准偏差系数sd 大于0.1 或x1 不是固有模态函数时，分 量终止条件 s1 = getspline(x1);%上包络线 s2 = -getspline(-x1);%下包络线 x2 = x1-(s1+s2)/2;%此处的x2 为文章中的h sd = sum((x1-x2).^2)/sum(x1.^2); x1 = x2; end imf{end+1} = x1; x = x-x1; end imf{end+1} = x; % FUNCTIONS function u = ismonotonic(x) %u=0 表示x 不是单调函数，u=1 表示x 为单调的 u1 = length(findpeaks(x))*length(findpeaks(-x)); if u1 0, u = 0; else, u = 1; end function u = isimf(x) %u=0 表示x 不是固有模式函数，u=1 表示x 是固有模式函数 N = length(x); u1 = sum(x(1:N-1).*x(2:N) 0); u2 = length(findpeaks(x))+length(findpeaks(-x)); if abs(u1-u2) 1, u = 0; else, u = 1; end function s = getspline(x) %三次样条函数拟合成元数据包络线 N = length(x); p = findpeaks(x); s = spline([0 p N+1],[0 x(p) 0],1:N); function n = findpeaks(x) % Find peaks.找到极值 ,n 为极值点所在位置 % n = findpeaks(x) n = find(diff(diff(x) 0) 0); u = find(x(n+1) x(n)); n(u) = n(u)+1; function plot_hht00(x,Ts) % 双边带调幅信号的EMD 分解 % Plot the HHT. % plot_hht(x,Ts) % % :: Syntax % The array （列） x is the input signal and Ts is the sampling period （取样周期）. % Example on use: [x,Fs] = wavread(Hum.wav); % plot_hht(x(1:6000),1/Fs); % Func : emd % Get HHT. clear all; close all; Ts=0.0005; t=0:Ts:10; % 采样率2000HZ % 调幅信号 %x=sin(2*pi*t).*sin(40*pi*t); x=sin(2*pi*t); s1 = getspline(x);%上包络线 s2 = -getspline(-x);%上包络线 x1 = (s1+s2)/2;%此处的x2 为文章中的h figure; plot(t,x);xlabel(Time), ylabel(Amplitude);title(双边带调幅信号);hold on; plot(t,s1,-r); plot(t,s2,-r); plot(t,x1,g); imf = emd(x); for k = 1:length(imf) b(k) = sum(imf{k}.*imf{k});