matlab小波变换程序是关于信号处理中的小波变换分析，用matlab命令实现的

MATLAB2维小波变换经典程序

% FWT_DB.M;

% 此示意程序用DWT实现二维小波变换

% 编程时间2004-4-10，编程人沙威

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clear;clc;

T=256; % 图像维数

SUB_T=T/2; % 子图维数

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% 1.调原始图像矩阵

load wbarb; % 下载图像

f=X; % 原始图像

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% 2.进行二维小波分解

l=wfilters('db10','l'); % db10(消失矩为10)低通分解滤波器冲击响应(长度为20)

L=T-length(l);

l_zeros=[l,zeros(1,L)]; % 矩阵行数与输入图像一致，为2的整数幂

h=wfilters('db10','h'); % db10(消失矩为10)高通分解滤波器冲击响应(长度为20)

h_zeros=[h,zeros(1,L)]; % 矩阵行数与输入图像一致，为2的整数幂

for i=1:T; % 列变换

row(1:SUB_T,i)=dyaddown( ifft( fft(l_zeros).*fft(f(:,i)') ) ).'; % 圆周卷积FFT

row(SUB_T+1:T,i)=dyaddown( ifft( fft(h_zeros).*fft(f(:,i)') ) ).'; % 圆周卷积FFT

end;

for j=1:T; % 行变换

line(j,1:SUB_T)=dyaddown( ifft( fft(l_zeros).*fft(row(j,:)) ) ); % 圆周卷积FFT

line(j,SUB_T+1:T)=dyaddown( ifft( fft(h_zeros).*fft(row(j,:)) ) ); % 圆周卷积FFT

end;

decompose_pic=line; % 分解矩阵

% 图像分为四块

lt_pic=decompose_pic(1:SUB_T,1:SUB_T); % 在矩阵左上方为低频分量--fi(x)*fi(y)

rt_pic=decompose_pic(1:SUB_T,SUB_T+1:T); % 矩阵右上为--fi(x)*psi(y)

lb_pic=decompose_pic(SUB_T+1:T,1:SUB_T); % 矩阵左下为--psi(x)*fi(y)

rb_pic=decompose_pic(SUB_T+1:T,SUB_T+1:T); % 右下方为高频分量--psi(x)*psi(y)

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% 3.分解结果显示

figure(1);

colormap(map);

subplot(2,1,1);

image(f); % 原始图像

title('original pic');

subplot(2,1,2);

image(abs(decompose_pic)); % 分解后图像

title('decomposed pic');

figure(2);

colormap(map);

subplot(2,2,1);

image(abs(lt_pic)); % 左上方为低频分量--fi(x)*fi(y)

title('Phi(x)*Phi(y)');

subplot(2,2,2);

image(abs(rt_pic)); % 矩阵右上为--fi(x)*psi(y)

title('Phi(x)*Psi(y)');

subplot(2,2,3);

image(abs(lb_pic)); % 矩阵左下为--psi(x)*fi(y)

title('Psi(x)*Phi(y)');

subplot(2,2,4);

image(abs(rb_pic)); % 右下方为高频分量--psi(x)*psi(y)

title('Psi(x)*Psi(y)');

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% 5.重构源图像及结果显示

% construct_pic=decompose_matrix'*decompose_pic*decompose_matrix;

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l_re=l_zeros(end:-1:1); % 重构低通滤波

l_r=circshift(l_re',1)'; % 位置调整

h_re=h_zeros(end:-1:1); % 重构高通滤波

h_r=circshift(h_re',1)'; % 位置调整

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

top_pic=[lt_pic,rt_pic]; % 图像上半部分

t=0;

for i=1:T; % 行插值低频

if (mod(i,2)==0)

topll(i,:)=top_pic(t,:); % 偶数行保持

else

t=t+1;

topll(i,:)=zeros(1,T); % 奇数行为零

end

end;

for i=1:T; % 列变换

topcl_re(:,i)=ifft( fft(l_r).*fft(topll(:,i)') )'; % 圆周卷积FFT

end;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

bottom_pic=[lb_pic,rb_pic]; % 图像下半部分

t=0;

for i=1:T; % 行插值高频

if (mod(i,2)==0)

bottomlh(i,:)=bottom_pic(t,:); % 偶数行保持

else

bottomlh(i,:)=zeros(1,T); % 奇数行为零

t=t+1;

end

end;

for i=1:T; % 列变换

bottomch_re(:,i)=ifft( fft(h_r).*fft(bottomlh(:,i)') )'; % 圆周卷积FFT

end;

construct1=bottomch_re+topcl_re; % 列变换重构完毕

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

left_pic=construct1(:,1:SUB_T); % 图像左半部分

t=0;

for i=1:T; % 列插值低频

if (mod(i,2)==0)

leftll(:,i)=left_pic(:,t); % 偶数列保持

else

t=t+1;

leftll(:,i)=zeros(T,1); % 奇数列为零

end

end;

for i=1:T; % 行变换

leftcl_re(i,:)=ifft( fft(l_r).*fft(leftll(i,:)) ); % 圆周卷积FFT

end;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

right_pic=construct1(:,SUB_T+1:T); % 图像右半部分

t=0;

for i=1:T; % 列插值高频

if (mod(i,2)==0)

rightlh(:,i)=right_pic(:,t); % 偶数列保持

else

rightlh(:,i)=zeros(T,1); % 奇数列为零

t=t+1;

end

end;

for i=1:T; % 行变换

rightch_re(i,:)=ifft( fft(h_r).*fft(rightlh(i,:)) ); % 圆周卷积FFT

end;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

construct_pic=rightch_re+leftcl_re; % 重建全部图像

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% 结果显示

figure(3);

colormap(map);

subplot(2,1,1);

image(f); % 源图像显示

title('original pic');

subplot(2,1,2);

image(abs(construct_pic)); % 重构源图像显示

title('reconstructed pic');

error=abs(construct_pic-f); % 重构图形与原始图像误值

figure(4);

mesh(error); % 误差三维图像

title('absolute error display');

clear

clc

%在噪声环境下语音信号的增强

%语音信号为读入的声音文件

%噪声为正态随机噪声

sound=wavread('c12345.wav');

count1=length(sound);

noise=0.05*randn(1,count1);

for i=1:count1

signal(i)=sound(i);

end

for i=1:count1

y(i)=signal(i)+noise(i);

end

%在小波基'db3'下进行一维离散小波变换

[coefs1,coefs2]=dwt(y,'db3'); %[低频 高频]

count2=length(coefs1);

count3=length(coefs2);

energy1=sum((abs(coefs1)).^2);

energy2=sum((abs(coefs2)).^2);

energy3=energy1+energy2;

for i=1:count2

recoefs1(i)=coefs1(i)/energy3;

end

for i=1:count3

recoefs2(i)=coefs2(i)/energy3;

end

%低频系数进行语音信号清浊音的判别

zhen=160;

count4=fix(count2/zhen);

for i=1:count4

n=160*(i-1)+1:160+160*(i-1);

s=sound(n);

w=hamming(160);

sw=s.*w;

a=aryule(sw,10);

sw=filter(a,1,sw);

sw=sw/sum(sw);

r=xcorr(sw,'biased');

corr=max(r);

%为清音(unvoice)时，输出为1；为浊音(voice)时，输出为0

if corr>=0.8

output1(i)=0;

elseif corr<=0.1

output1(i)=1;

end

end

for i=1:count4

n=160*(i-1)+1:160+160*(i-1);

if output1(i)==1

switch abs(recoefs1(i))

case abs(recoefs1(i))<=0.002

recoefs1(i)=0;

case abs(recoefs1(i))>0.002 & abs(recoefs1(i))<=0.003

recoefs1(i)=sgn(recoefs1(i))*(0.003*abs(recoefs1(i))-0.000003)/0.002;

otherwise recoefs1(i)=recoefs1(i);

end

elseif output1(i)==0

recoefs1(i)=recoefs1(i);

end

end

%对高频系数进行语音信号清浊音的判别

count5=fix(count3/zhen);

for i=1:count5

n=160*(i-1)+1:160+160*(i-1);

s=sound(n);

w=hamming(160);

sw=s.*w;

a=aryule(sw,10);

sw=filter(a,1,sw);

sw=sw/sum(sw);

r=xcorr(sw,'biased');

corr=max(r);

%为清音(unvoice)时，输出为1；为浊音(voice)时，输出为0

if corr>=0.8

output2(i)=0;

elseif corr<=0.1

output2(i)=1;

end

end

for i=1:count5

n=160*(i-1)+1:160+160*(i-1);

if output2(i)==1

switch abs(recoefs2(i))

case abs(recoefs2(i))<=0.002

recoefs2(i)=0;

case abs(recoefs2(i))>0.002 & abs(recoefs2(i))<=0.003

recoefs2(i)=sgn(recoefs2(i))*(0.003*abs(recoefs2(i))-0.000003)/0.002;

otherwise recoefs2(i)=recoefs2(i);

end

elseif output2(i)==0

recoefs2(i)=recoefs2(i);

end

end

%在小波基'db3'下进行一维离散小波反变换

output3=idwt(recoefs1, recoefs2,'db3');

%对输出信号抽样点值进行归一化处理

maxdata=max(output3);

output4=output3/maxdata;

%读出带噪语音信号，存为'101.wav'

wavwrite(y,5500,16,'c101');

%读出处理后语音信号，存为'102.wav'

wavwrite(output4,5500,16,'c102');

function [I_W , S] = func_DWT(I, level, Lo_D, Hi_D);

%通过这个函数将I进行小波分解，并将分解后的一维向量转换为矩阵形式

% Matlab implementation of SPIHT (without Arithmatic coding stage)

% Wavelet decomposition

% input: I : input image

% level : wavelet decomposition level

% Lo_D : low-pass decomposition filter

% Hi_D : high-pass decomposition filter

% output: I_W : decomposed image vector

% S : corresponding bookkeeping matrix

% please refer wavedec2 function to see more

[C,S] = func_Mywavedec2(I,level,Lo_D,Hi_D);

S(:,3) = S(:,1).*S(:,2); % dim of detail coef nmatrices 求低频和每个尺度中高频的元素个数

%st=S(1,3)+S(2,3)*3+S(3,3)*3;%%%%对前两层加密

%C(1:st)=0;

L = length(S); %a求S的列数

I_W = zeros(S(L,1),S(L,2));%设一个与原图像大小相同的全零矩阵

% approx part

I_W( 1:S(1,1) , 1:S(1,2) ) = reshape(C(1:S(1,3)),S(1,1:2)); %将LL层从C中还原为S(1,1)*S(1,2)的矩阵

for k = 2 : L-1 %将C向量中还原出HL,HH,LH 矩阵

rows = [sum(S(1:k-1,1))+1:sum(S(1:k,1))];

columns = [sum(S(1:k-1,2))+1:sum(S(1:k,2))];

% horizontal part

c_start = S(1,3) + 3*sum(S(2:k-1,3)) + 1;

c_stop = S(1,3) + 3*sum(S(2:k-1,3)) + S(k,3);

I_W( 1:S(k,1) , columns ) = reshape( C(c_start:c_stop) , S(k,1:2) );

% vertical part

c_start = S(1,3) + 3*sum(S(2:k-1,3)) + S(k,3) + 1;

c_stop = S(1,3) + 3*sum(S(2:k-1,3)) + 2*S(k,3);

I_W( rows , 1:S(k,2) ) = reshape( C(c_start:c_stop) , S(k,1:2) );

% diagonal part

c_start = S(1,3) + 3*sum(S(2:k-1,3)) + 2*S(k,3) + 1;

c_stop = S(1,3) + 3*sum(S(2:k,3));

I_W( rows , columns ) = reshape( C(c_start:c_stop) , S(k,1:2) );

end

%%%%%%%mallat algorithm%%%%% clc; clear;tic; %%%%original signal%%%% f=100;%%frequence ts=1/800;%%抽样间隔 N=1:100;%%点数 s=sin(2*ts*pi*f.*N);%%源信号 figure(1) plot(s);%%%源信号s title('原信号'); grid on; %%%%小波滤波器%%%% ld=wfilters('db1','l');%%低通 hd=wfilters('db1','h');%%高通 figure(2) stem(ld,'r');%%%低通 grid on; figure(3) stem(hd,'b')%%%高通 grid on; %%%%% tem=conv(s,ld);%%低通和原信号卷积 ca1=dyaddown(tem);%%抽样 figure(4) plot(ca1); grid on; tem=conv(s,hd);%%高通和原信号卷积 cb1=dyaddown(tem);%%抽样 figure(5) plot(cb1); grid on; %%%%%%%% %[ca3,cb3]=dwt(s,'db1');%%小波变换 %%%%%%%% [lr,hr]=wfilters('db1','r');%%重构滤波器 figure(6) stem(lr); figure(7) stem(hr); tem=dyadup(cb1);%%插值 tem=conv(tem,hr);%%卷积 d1=wkeep(tem,100);%%去掉两头的分量 %%%%%%%%% tem=dyadup(ca1);%%插值 tem=conv(tem,lr);%%卷积 a1=wkeep(tem,100);%%去掉两头的分量 a=a1+d1;%%%重构原信号 %%%%%%%%% %a3=idwt(ca3,cb3,'db1',100);%%%小波逆变换 %%%%%%%%% figure(8) plot(a,'.b'); hold on; plot(s,'r'); grid on; title('重构信号和原信号的比较');toc; %figure(9) %plot(a3,'.b'); %hold on; %plot(s,'r'); %grid on; %title('重构信号和原信号的比较');

通用函数

Allnodes 计算树结点

appcoef 提取一维小波变换低频系数

appcoef2 提取二维小波分解低频系数

bestlevt 计算完整最佳小波包树

besttree 计算最佳(优)树

*　 biorfilt 双正交样条小波滤波器组

biorwavf 双正交样条小波滤波器

*　 centfrq 求小波中心频率

cgauwavf Complex Gaussian小波

cmorwavf coiflets小波滤波器

cwt 一维连续小波变换

dbaux Daubechies小波滤波器计算

dbwavf Daubechies小波滤波器 dbwavf(W) W='dbN' N=1,2,3,...,50

ddencmp 获取默认值阈值(软或硬)熵标准

depo2ind 将深度-位置结点形式转化成索引结点形式

detcoef 提取一维小波变换高频系数

detcoef2 提取二维小波分解高频系数

disp 显示文本或矩阵

drawtree 画小波包分解树(GUI)

dtree 构造DTREE类

dwt 单尺度一维离散小波变换

dwt2 单尺度二维离散小波变换

dwtmode 离散小波变换拓展模式

*　 dyaddown 二元取样

*　 dyadup 二元插值

entrupd 更新小波包的熵值

fbspwavf B样条小波

gauswavf Gaussian小波

get 获取对象属性值

idwt 单尺度一维离散小波逆变换

idwt2 单尺度二维离散小波逆变换

ind2depo 将索引结点形式转化成深度—位置结点形式

*　 intwave 积分小波数

isnode 判断结点是否存在

istnode 判断结点是否是终结点并返回排列值

iswt 一维逆SWT(Stationary Wavelet Transform)变换

iswt2 二维逆SWT变换

leaves 　 Determine terminal nodes

mexihat 墨西哥帽小波 meyer Meyer小波

meyeraux Meyer小波辅助函数 morlet Morlet小波

nodease 计算上溯结点

nodedesc 计算下溯结点(子结点)

nodejoin 重组结点 nodepar 寻找父结点

nodesplt 分割(分解)结点

noleaves 　 Determine nonterminal nodes

ntnode 　 Number of terminal nodes

ntree 　 Constructor for the class NTREE

*　 orthfilt 正交小波滤波器组

plot 绘制向量或矩阵的图形

*　 qmf 镜像二次滤波器

rbiowavf 　 Reverse biorthogonal spline wavelet filters

read 读取二进制数据 readtree 读取小波包分解树

*　 scal2frq 　 Scale to frequency

set

shanwavf 　 Shannon wavelets

swt 一维SWT(Stationary Wavelet Transform)变换

swt2 二维SWT变换

symaux 　 Symlet wavelet filter computation.

symwavf Symlets小波滤波器

thselect 信号消噪的阈值选择

thodes 　 References

treedpth 求树的深度

treeord 求树结构的叉数

upcoef 一维小波分解系数的直接重构 upcoef2 二维小波分解系数的直接重构

upwlev 单尺度一维小波分解的重构 upwlev2 单尺度二维小波分解的重构

wavedec 单尺度一维小波分解 wavedec2 多尺度二维小波分解

wavedemo 小波工具箱函数demo

*　wavefun 小波函数和尺度函数 *　 wavefun2 二维小波函数和尺度函数

wavemenu 小波工具箱函数menu图形界面调用函数

*　 wavemngr 小波管理函数

waverec 多尺度一维小波重构 waverec2 多尺度二维小波重构

wbmpen 　 Penalized threshold for wavelet 1-D or 2-D de-noising

wcodemat 对矩阵进行量化编码

wdcbm 　 Thresholds for wavelet 1-D using Birge-Massart strategy

wdcbm2 　Thresholds for wavelet 2-D using Birge-Massart strategy

wden 用小波进行一维信号的消噪或压缩

wdencmp 　De-noising or compression using wavelets

wentropy 计算小波包的熵

wextend 　Extend a vector or a matrix

*　 wfilters 小波滤波器

wkeep 提取向量或矩阵中的一部分

*　 wmaxlev 计算小波分解的最大尺度

wnoise 产生含噪声的测试函数数据

wnoisest 估计一维小波的系数的标准偏差

wp2wtree 从小波包树中提取小波树

wpcoef 计算小波包系数

wpcutree 剪切小波包分解树

wpdec 一维小波包的分解 wpdec2 二维小波包的分解

wpdencmp 用小波包进行信号的消噪或压缩

wpfun 小波包函数

wpjoin 　重组小波包

wprcoef 小波包分解系数的重构

wprec 一维小波包分解的重构 wprec2 二维小波包分解的重构

wpsplt 分割(分解)小波包

wpthcoef 进行小波包分解系数的阈值处理

wptree 　 显示小波包树结构

wpviewcf 　 Plot the colored wavelet packet coefficients.

wrcoef 对一维小波系数进行单支重构

wrcoef2 对二维小波系数进行单支重构

wrev 向量逆序

write 向缓冲区内存写进数据

wtbo 　 Constructor for the class WTBO

wthcoef 一维信号的小波系数阈值处理

wthcoef2 二维信号的小波系数阈值处理

wthresh 进行软阈值或硬阈值处理

wthrmngr 阈值设置管理

wtreemgr 管理树结构