matlab 小波的分解与重构

痛定思痛。 2023-06-20 06:37 5阅读 0赞

小波的分解和重构在很多领域都有运用。

# 第一： matlab中相关小波函数 #

##    1、 wavedec:  Multilevel 1-D wavelet decomposition    小波分解 ##

\[C,L\] = wavedec(X,N,*`'wname'`*)      
                  \[C,L\] = wavedec(X,N,Lo\_D,Hi\_D)

*  `Lo_D`, the decomposition low-pass filter
 *  `Hi_D`, the decomposition high-pass filter
 *  X is signal，N is layer，C 是小波系数 ,L是小波.

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjUyODA4OQ_size_16_color_FFFFFF_t_70][]

##      2、 detcoef:  Multilevel 1-D wavelet detail  coefficients    小波细节系数，目的是获取上图种的cDx ##

D = detcoef(C,L,N)  
                  D = detcoef(C,L)

##      3、appcoef ：1-D approximation coefficients     小波近似系数， 目的是获取cA ##

A = appcoef(C,L,'*`wname`*',N)  
                  A = appcoef(C,L,*`'wname'`*)  
                  A = appcoef(C,L,Lo\_R,Hi\_R)  
                  A = appcoef(C,L,Lo\_R,Hi\_R,N)

##    4、 waverec :   Multilevel 1-D wavelet reconstruction  小波重构 ##

X = waverec(C,L,Lo\_R,Hi\_R)  
                    X = waverec(C,L,*`'wname'`*)  
                    X = appcoef(C,L,*`'wname'`*,0)

第二： 案例

用小波分解重构函数后，用MSE 来进行比较分析

eg1：  小波信号分解到a1 ,和b1 然后重构信号。

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjUyODA4OQ_size_16_color_FFFFFF_t_70 1][]    eg2： 小波分解到第三层重构信号

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjUyODA4OQ_size_16_color_FFFFFF_t_70 2][]

eg3: 小波分解到第三层，但是通过第二层的a2,d2,d1,最后重构部分要加上length(ecg)

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjUyODA4OQ_size_16_color_FFFFFF_t_70 3][]

eg4: idwt 重构函数：

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjUyODA4OQ_size_16_color_FFFFFF_t_70 4][]

完整代码：

clc,clear all;close all;
    fs=180;
    N=2000;
    t=(1:N-1)/fs;
    s=1.2*sin(2*pi*t*20)+0.5*cos(2*pi*t*60);%%% 滤掉60Hz的信号
    % level=8; wavename='bior2.6';
    figure;
    subplot(211); plot(t,s); title('原始信号') ;  grid on
    [f, spectrum ] = gan_fft(s,fs,N);
    subplot(212);plot(f,spectrum); title('原始信号pinpu');   grid on
    [C,L]=wavedec(s,2,'db6');
    X = waverec(C,L,'db6');
    
    figure;
    subplot(211);plot(t,X); title('原始信号分解后又重构的信号') ; grid on
    [f, spectrum ] = gan_fft(X,fs,N);
    subplot(212);plot(f,spectrum); title('原始信号分解后又重构pinpu');  grid on
    %%%% 均方误差
    MSE=sum((X-s).^2)/length(s);

function [f, spectrum ] = gan_fft(s,Fs,L)
    %GAN_FFT 此处显示有关此函数的摘要
    %   此处显示详细说明
    y=fft(s);
    p2=abs(y/L);
    p1=p2(1:L/2+1);
    p1(2:end-1)=2*p1(2:end-1);
    f = Fs*(0:(L/2))/L;
    spectrum=p1;
     
    end

例子2：

clc,clear all;close all;
    fs=180;
    N=2000;
    t=(1:N-1)/fs;
    s=1.2*sin(2*pi*t*20)+0.5*cos(2*pi*t*60);%%% 滤掉60Hz的信号
    % level=8; wavename='bior2.6';
    figure;
    subplot(211); plot(t,s); title('原始信号') ;  grid on
    [f, spectrum ] = gan_fft(s,fs,N);
    subplot(212);plot(f,spectrum); title('原始信号pinpu');   grid on
    [C,L]=wavedec(s,3,'db6');
    X = waverec(C,L,'db6');
    [A1]=appcoef(C,L,'db6',1);
    [A2]=appcoef(C,L,'db6',2);
    [A3]=appcoef(C,L,'db6',3);
    [D1,D2,D3]=detcoef(C,L,[1 2 3]);
    C1=[A3,D3,D2,D1];%%% z注意此处是逗号还是分号
    %[length(A3);length(D3);length(D2);length(D1);length(s)]
    x2=waverec(C1,L,'db6');
    MSE=sum((x2-s).^2)/length(s)

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