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
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%
clear;clc;
T=256; % 图像维数
SUB_T=T/2; % 子图维数
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.调原始图像矩阵
load wbarb; % 下载图像
f=X; % 原始图像
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 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)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 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)');


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 5.重构源图像及结果显示
% construct_pic=decompose_matrix'*decompose_pic*decompose_matrix;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 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