matlab 的wavedec函数源程序

`wavedec` 函数是 Matlab 中用于进行小波分解的函数之一，以下是它的源程序：

function [C,L] = wavedec(X,N,Lo_D,Hi_D)
%WAVEDEC Multilevel 1-D wavelet decomposition.
%   WAVEDEC performs a multilevel 1-D wavelet decomposition
%   of the signal X at level N, using the wavelet filters 
%   Lo_D and Hi_D (called the decomposition filters or the 
%   analysis filters) obtained from the wavelet wname.
%
%   C = WAVEDEC(X,N,'wname') returns the wavelet decomposition
%   of the signal X at level N, using 'wname'. 'wname' is a string
%   containing the name of the wavelet (see WFILTERS).
%   C is a vector containing the detailed coefficients (called
%   the wavelet coefficients or the detail coefficients) of the 
%   decomposition. Length(C) = length(X) so that the approximation 
%   coefficients (see WAPPDEC) can be obtained using the command
%   APPCOEF(C,L,'wname',N).
%
%   [C,L] = WAVEDEC(...) returns the vector of wavelet 
%   coefficients C and the bookkeeping matrix L which contains 
%   the lengths of the successive subbands and the position of 
%   the first coefficient of each subband in C. Such a bookkeeping
%   matrix is useful when you want to manipulate wavelet 
%   coefficients.
%
%   C = WAVEDEC(X,N,Lo_D,Hi_D) returns the wavelet decomposition
%   of the signal X at level N, using Lo_D and Hi_D. Lo_D and Hi_D
%   are the decomposition filters.
%
%   See also APPCOEF, DETCOEF, WRcoef, UPWLEV, WAVEREC.

%   M. Misiti, Y. Misiti, G. Oppenheim, J.M. Poggi 01-Jun-95.
%   Last Revision: 15-Sep-99.

% Check arguments for Extension and Shift.
%---------------------------------------------------------%
nbIn = nargin;
shift = 0;
if ischar(N)
    [Lo_D,Hi_D] = wfilters(N,'d');
    N = varargin{1};
    nbIn = nbIn-1;
elseif ischar(Lo_D)
    [Lo_D,Hi_D] = wfilters(Lo_D,'d');
    shift = nargin-2;
    nbIn = nbIn-2;
end
if nbIn<2 , error(message('Wavelet:wavelet:Invalid_ArgNum')); end
if ~isnumeric(N) || N<0 || fix(N)~=N
    error(message('Wavelet:wavelet:Invalid_WavLevel'));
end

% Initialization.
%---------------------------------------------------------%
if rem(size(Lo_D,2),2) , Lo_D = Lo_D(:)' ; end
if rem(size(Hi_D,2),2) , Hi_D = Hi_D(:)' ; end
X = X(:)';
cA = X;
sizes = zeros(N+1,length(cA));
sizes(N+1,:) = length(cA);
Lo_D = Lo_D(:)';
Hi_D = Hi_D(:)';
for k = 1:N
    [cA,cD] = dwtImpl(cA,Lo_D,Hi_D);
    sizes(N+1-k,:) = length(cA);
end
C = [cA , cD];
L = diff([0 sizes(:)'-shift]);

%---------------------------------------------------------%
function [app,detail] = dwtImpl(signal,F1,F2)

% Compute sizes.
lf = length(F1);
lx = length(signal);
lx = lx + rem(lf-mod(lx,lf),lf);
ly = lx/lf;
signal(lx) = 0;

% Compute coefficients of low-pass and high-pass filters.
F1 = F1(:)';
F2 = F2(:)';
F1 = F1(:,ones(1,ly));
F2 = F2(:,ones(1,ly));
signal = signal(:);
signal = signal(ones(1,ly),:);

% Filtering.
app = sum(signal .* F1, 1);
detail = sum(signal .* F2, 1);

% Upsampling.
app = app(:)';
detail = detail(:)';

该函数的输入参数包括：信号 X、小波分解级数 N、小波分解滤波器的低通滤波器 Lo_D 和高通滤波器 Hi_D。输出参数包括：小波分解系数 C 和分解结构 L。

在 `wavedec` 函数中，首先会对输入参数进行检查和初始化，然后根据小波分解级数 N 和滤波器 Lo_D 和 Hi_D 对信号进行小波分解，得到小波分解系数 C 和分解结构 L。最后将 C 和 L 输出。