小波消噪笔记

Matlab相关函数介绍

wavedec

简介

wavedec用于一维小波分解。

语法

[C, L] = wavedec(X, N, 'wave_name')

• X：一维信号。

• N：分解层数。

• wave_name：小波名，如“db4”、“haar”等。

• [C, L]：分解后各级的系数，其结构如下图：

  

  图中\(cA_i\)是第i层分解后的低频系数，\(cD_i\)是高频系数。

例程

% The current extension mode is zero-padding (see dwtmode).

% Load original one-dimensional signal.
load sumsin;
s = sumsin;

% Perform decomposition at level 3 of s using db1.
[c,l] = wavedec(s,3,'db1');

% Using some plotting commands,
% the following figure is generated.
subplot(2, 1, 1);
plot(s);
title('Original Signal s');
subplot(2, 1, 2);
plot(c);
title('Wavelet Decomposition Structure');

wden

简介

wden用于一维信号的小波消噪。

语法

[XD, CXD, LXD] = wden(X, TPTR, SORH, SCAL, N, 'wname')

• 该函数对信号X消噪，结果返回给XD。

• [CXD, LXD]是XD的小波分解结构（见图1）。

• TPTR指定了阈值的计算方式，其取值如下：

  • rigrsure
  • heursure
  • sqtwolog
  • minimaxi

• SORH（取值为s或h）指定软阈值或硬阈值处理方式。

• SCAL指定阈值的缩放，其取值如下：

  • one
  • sln
  • mln

• N和wname指定了小波分解的层数和使用的小波。

例程

% The current extension mode is zero-padding (see dwtmode).

% Set signal to noise ratio and set rand seed.
snr = 3; init = 2055615866;

% Generate original signal and a noisy version adding
% a standard Gaussian white noise.
[xref,x] = wnoise(3,11,snr,init);

% De-noise noisy signal using soft heuristic SURE thresholding
% and scaled noise option, on detail coefficients obtained
% from the decomposition of x, at level 5 by sym8 wavelet.
lev = 5;
xd = wden(x,'heursure','s','one',lev,'sym8');

% Plot signals.
subplot(611), plot(xref), axis([1 2048 -10 10]);
title('Original signal');
subplot(612), plot(x), axis([1 2048 -10 10]);
title(['Noisy signal - Signal to noise ratio = ',...
num2str(fix(snr))]);
subplot(613), plot(xd), axis([1 2048 -10 10]);
title('De-noised signal - heuristic SURE');

% De-noise noisy signal using soft SURE thresholding
xd = wden(x,'heursure','s','one',lev,'sym8');

% Plot signal.
subplot(614), plot(xd), axis([1 2048 -10 10]);
title('De-noised signal - SURE');

% De-noise noisy signal using fixed form threshold with
% a single level estimation of noise standard deviation.
xd = wden(x,'sqtwolog','s','sln',lev,'sym8');

% Plot signal.
subplot(615), plot(xd), axis([1 2048 -10 10]);
title('De-noised signal - Fixed form threshold');

% De-noise noisy signal using minimax threshold with
% a multiple level estimation of noise standard deviation.
xd = wden(x,'minimaxi','s','sln',lev,'sym8');

% Plot signal.
subplot(616), plot(xd), axis([1 2048 -10 10]);
title('De-noised signal - Minimax');

% If many trials are necessary, it is better to perform
% decomposition once and threshold it many times:

% decomposition.
[c,l] = wavedec(x,lev,'sym8');

% threshold the decomposition structure [c,l].
xd = wden(c,l,'minimaxi','s','sln',lev,'sym8');

% Editing some graphical properties,
% the following figure is generated.