clear;
clc;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%  1.原始信號

f=50;    % 信號頻率
fs=800;  % 采樣頻率
N=128;   % 采樣點 

%  信號賦值
n=1:N;
y=sin(2*pi*f*n/fs);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%  2.噪聲
noise=0.4*rand(1,128);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%  3.染噪信號
y_noise=y+noise;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%  4.硬消噪采用cycle_spinning技術(shù)

%  累加量
z5=zeros(1,N);

%  平移變換頻移法
for i=1:N;
    z=circshift(y_noise.',i-1).';  %  源信號右平移
    [z1,z2]=lwt(z,'db3');    %  小波正變換
    z2=zeros(1,N/2);         %  高頻分量全部為零（主要噪聲，硬消噪）
    z3=ilwt(z1,z2,'db3');    %  小波反變換  
    z4=circshift(z3.',-(i-1)).';  %  變換后信號左平移  
    z5=z5+z4/N;  %  平均  
end;
    
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%  5.顯示

error=norm(y-z5)/norm(y);  % 相對誤差

figure(1);
subplot(2,1,1)
plot(y,'r');
legend('源信號');
subplot(2,1,2);
plot(y_noise);
legend('染噪信號');


figure(2);
subplot(2,1,1)
plot(y,'r');
legend('源信號');
title(error);
subplot(2,1,2);
plot(z5);
legend('消噪后信號');