求助：找包络线的方法

yizhendong · 发表于 2012-4-20 11:19

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大家帮我看下这样的曲线如何求包络线，换句话说，对于任意曲线如何找到包络线，谢谢。

眉间尺 · 发表于 2012-4-20 12:25

如果周期已知的话, 不知是否可以按照周期分段找出最大值与最小值.

hustxyong · 发表于 2012-4-20 15:20

1、先分别找到极大值和极小值（利用diff函数和极值点的特点）
2、用曲线拟合函数拟合所有极大值点即为上包络线，拟合所有极小值点即为下包络线

yizhendong · 发表于 2012-4-20 18:32

hustxyong 发表于 2012-4-20 15:20

登录/注册后可看大图

1、先分别找到极大值和极小值（利用diff函数和极值点的特点）
2、用曲线拟合函数拟合所有极大值点即为上包 ...

用什么曲线拟合呢？（高次多项式？）
我的这个曲线是用数值计算得出来的，没法用diff函数来球，极值得一个个的找。

yizhendong · 发表于 2012-4-20 18:32

眉间尺发表于 2012-4-20 12:25

登录/注册后可看大图

如果周期已知的话, 不知是否可以按照周期分段找出最大值与最小值.

这是个非周期运动。

syxqq123 · 发表于 2012-4-21 06:13

可以参考EMD分解中使用三次样条拟合上下包络
，具体看看EMD分解，可能给你一些思路

ChaChing · 发表于 2012-4-22 01:45

Ref: 6.一种有效的包络线算法 http://forum.vibunion.com/thread-32967-1-1.html
求画出振荡的包络线图 http://forum.vibunion.com/thread-28736-1-1.html
http://www.mathworks.com/matlabc ... ange/24902-envelope
求非线性曲线波峰和波谷的坐标 http://forum.vibunion.com/thread-95495-1-1.html
Detect zero level crossing of signals http://www.mathworks.com/matlabcentral/fileexchange/2432

321forever · 发表于 2012-4-22 03:11

这个以前做过一次，一个个找极值是不需要的，用个for函数就解决了，在cftool中可以自己试下有多种方法的

yizhendong · 发表于 2012-4-24 19:24

本帖最后由 yizhendong 于 2012-4-24 19:27 编辑

我用matlab二次开发的envelope函数，得到的包络线如下。估计envelope的精度有限，所以包络线并不正确。

fzwxjtu · 发表于 2012-4-24 22:21

本帖最后由 fzwxjtu 于 2012-4-24 22:23 编辑

EMD中的包络方法还是比较理想的，下面是我仿真做的代码，楼主可以试试能用不？其实用Hilbert包络同样可以解调的，效果没这个好，就不贴了。

clear;
fs=12800;
t=0:1/fs:10-1/fs;t=t';
f1=5;f2=100;
x=cos(2*pi*f1*t).*sin(2*pi*f2*t);
n=length(x);
s=x;
t=0:length(s)-1;
s1=s;
sd=1;
if(sd>0.3)
jd=find(diff(sign(diff(s1)))==-2)+1; %找h1极大值的位置
jx=find(diff(sign(diff(s1)))==2)+1; %找h1极小值的位置
ah=length(jd);
al=length(jx);
jdz(ah)=0;
for i=1:ah
bh=jd(i);
jdz(i)=s1(bh);
end %找出h1极大值对应函数值
jxz(al)=0;
for i=1:al
bl=jx(i);
jxz(i)=s1(bl);
end %找出h1极小值对应函数值
jsbl=spline(jd,jdz,t); %极大值拟和的上包络
jxbl=spline(jx,jxz,t); %极小值拟和的下包络
m1=(jsbl+jxbl)/2; %上下包络均值
m1=m1';
h1=s1-m1;
sd=sum(((s1-h1)./h1).^2);
end
figure(1)
plot(x);
hold on;
plot(jsbl,'r');
title('采用EMD中的包络方法');

复制代码

下面是效果图，红线是包络线。

ChaChing · 发表于 2012-4-25 00:02

用matlab二次开发的envelope函数

什麼意思? 那个函数?

眉间尺 · 发表于 2012-4-25 00:55

试着将楼主的图片还原成了数据, 大家方便的话先在自己的机器上试试包络生成程序:

眉间尺 · 发表于 2012-4-25 00:57

findenv.rar中含有存储下列数据的各种类型文件:
=================
0.091954023 -4.857142857
0.137931034 -5.80952381
0.183908046 -0.857142857
0.229885057 6.285714286
0.275862069 9.714285714
0.32183908 6.666666667
0.367816092 1.619047619
0.413793103 -1.238095238
0.459770115 -2.19047619
0.505747126 -5.142857143
0.551724138 -10.38095238
0.597701149 -12
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0.689655172 5.619047619
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6.896551724 -7.714285714
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7.08045977 3.333333333
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7.172413793 10
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7.770114943 0
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8 -0.857142857
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8.643678161 8.666666667
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8.735632184 -3.142857143
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14.71264368 0.380952381
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17.70114943 -0.19047619
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18.3908046 -0.19047619
18.43678161 -0.19047619
18.48275862 -0.380952381
18.52873563 -0.380952381
18.57471264 -0.19047619
18.62068966 -0.19047619
18.66666667 -0.19047619
18.71264368 -0.380952381
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18.89655172 -0.380952381
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19.31034483 -0.19047619
19.35632184 -0.380952381
19.40229885 -0.380952381
19.44827586 -0.19047619
19.49425287 -0.19047619
19.54022989 -0.19047619
19.5862069 -0.380952381
19.63218391 -0.380952381
19.67816092 -0.19047619
19.72413793 -0.19047619
19.77011494 -0.19047619
19.81609195 -0.380952381
19.86206897 -0.380952381
19.90804598 -0.19047619
19.95402299 -0.19047619
20 -0.19047619

fzwxjtu · 发表于 2012-4-25 09:18

本帖最后由 fzwxjtu 于 2012-4-25 09:46 编辑

三次样条插值龙格现象严重

分段线性插值效果比较好，但是不光滑

ChaChing · 发表于 2012-4-25 11:54

使用7F,一种有效的包络线算法 http://forum.vibunion.com/thread-32967-1-1.html; 12F的资料

load findenv
x=D1(:,1); y=D1(:,2); plot(x,y)
[up,down] = envelope(x,y,'linear');
hold on; plot(x,[up down],'r');

复制代码

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[绘图技巧] 求助：找包络线的方法

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