casade.m

小波插值与小波基构造

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % 小波构造
function casade
clear;clc;
t=3;phi=[0,1,0]; h=wfilters('db7','r');h=h*sqrt(2); h_e=h(1,[2:2:14]);h_o=h(1,[1:2:13]); 
for m=1:15;stem(phi);drawnow;pause(1);
    ee=conv(h_e,phi);oo=conv(h_o,phi);phi(1,[2:2:2*length(ee)])=ee;phi(1,[1:2:2*length(oo)-1])=oo;
end; 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
cubic_average（立方b样条）% 均值插值
% 初始化
s=[0 0 1 0 0] % 正弦波% 
f=50;% 
ts=1/200;% 
n=0:16;% 
s=sin(2*pi*f*n*ts); % 系数
se=[1/8,6/8,1/8];so=[4/8,4/8] % 循环
for p=1:10;t=length(s)-1;
    o(1:t)=s(1:t)*so(1)+s(2:t+1)*so(2);
    e(1)=s(t+1)*se(1)+s(1)*se(2)+s(2)*se(3);
    e(2:t)=s(1:t-1)*se(1)+s(2:t)*se(2)+s(3:t+1)*se(3);
    e(t+1)=s(t)*se(1)+s(t+1)*se(2)+s(1)*se(3);
    s([1:2:2*t+1])=e([1:t+1]);s([2:2:2*t])=o([1:t]);plot(s);drawnow;
end; 
% 抽取
t=length(s); % 总长度
p=128; % 需要点数 % 间隔
d=(t-1)/p; % 最终尺度函数
r=s(2:d:t-1); % 画图
figure(2);plot(r);%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %
cubic_subdivision（立方插值）% 细分插值 % %% 初始化（尺度函数）%
s=[0,0,1,0,0]; % 正弦函数
n=1:20;f=50;ts=1/200;s=sin(2*pi*f*n*ts); % 指数函数%
n=0:16;%
s=exp(n); % % 系数
a=[-1/16,9/16,9/16,-1/16]; % 循环
for p=1:4;t=length(s)-1;o(1)=s(4)*a(1)+s(1)*a(2)+s(2)*a(3)+s(3)*a(4);
    o(2:t-1)=s(1:t-2)*a(1)+s(2:t-1)*a(2)+s(3:t)*a(3)+s(4:t+1)*a(4);
    o(t)=s(t-2)*a(4)+s(t+1)*a(3)+s(t)*a(2)+s(t-1)*a(1);
    s([1:2:2*t+1])=s([1:t+1]);s([2:2:2*t])=o([1:t]);plot(s);drawnow;
end; % % 抽取% t=length(s); % 总长度%
p=128; % 需要点数%% % 间隔% 
d=(t-1)/p;%% % 最终尺度函数% 
r=s(2:d:t-1);%% % 画图% 
figure(2);% plot(r);