Notes

function [a,d] = dwt(x,varargin)
%DWT Single-level discrete 1-D wavelet transform.
% DWT performs a single-level 1-D wavelet decomposition
% with respect to either a particular wavelet ('wname',
% see WFILTERS for more information) or particular wavelet filters
% (Lo_D and Hi_D) that you specify.
%
% [CA,CD] = DWT(X,'wname') computes the approximation
% coefficients vector CA and detail coefficients vector CD,
% obtained by a wavelet decomposition of the vector X.
% 'wname' is a string containing the wavelet name.
%
% [CA,CD] = DWT(X,Lo_D,Hi_D) computes the wavelet decomposition
% as above given these filters as input:
% Lo_D is the decomposition low-pass filter.
% Hi_D is the decomposition high-pass filter.
% Lo_D and Hi_D must be the same length.
%
% Let LX = length(X) and LF = the length of filters; then
% length(CA) = length(CD) = LA where LA = CEIL(LX/2),
% if the DWT extension mode is set to periodization.
% LA = FLOOR((LX+LF-1)/2) for the other extension modes.
% For the different signal extension modes, see DWTMODE.
%
% [CA,CD] = DWT(...,'mode',MODE) computes the wavelet
% decomposition with the extension mode MODE you specify.
% MODE is a string containing the extension mode.
%
% Example:
% x = 1:8;
% [ca,cd] = dwt(x,'db1','mode','sym')
%
% See also DWTMODE, IDWT, WAVEDEC, WAVEINFO.

% M. Misiti, Y. Misiti, G. Oppenheim, J.M. Poggi 12-Mar-96.
% Last Revision: 06-Feb-2011.
% Copyright 1995-2011 The MathWorks, Inc.
% $Revision: 1.15.4.5 $

% Check arguments.
nbIn = nargin;
error(nargchk(2,7,nbIn,'struct'))
if ischar(varargin{1})
[Lo_D,Hi_D] = wfilters(varargin{1},'d'); next = 2;
else
Lo_D = varargin{1}; Hi_D = varargin{2}; next = 3;
end

% Check arguments for Extension and Shift.
DWT_Attribute = getappdata(0,'DWT_Attribute');
if isempty(DWT_Attribute) , DWT_Attribute = dwtmode('get'); end
dwtEXTM = DWT_Attribute.extMode; % Default: Extension.
shift = DWT_Attribute.shift1D; % Default: Shift.
for k = next:2:nbIn-1
switch varargin{k}
case 'mode' , dwtEXTM = varargin{k+1};
case 'shift' , shift = mod(varargin{k+1},2);
end
end

% Compute sizes and shape.
lf = length(Lo_D);
lx = length(x);

% Extend, Decompose & Extract coefficients.
first = 2-shift;
flagPer = isequal(dwtEXTM,'per');
if ~flagPer
lenEXT = lf-1; last = lx+lf-1;
else
lenEXT = lf/2; last = 2*ceil(lx/2);
end
y = wextend('1D',dwtEXTM,x,lenEXT);

% Compute coefficients of approximation.
z = wconv1(y,Lo_D,'valid');
a = z(first:2:last);

% Compute coefficients of detail.
z = wconv1(y,Hi_D,'valid');
d = z(first:2:last);