WT Discrete Wavelet Transform.
WT(X,H,G,SCALES) calculates the wavelet transform of vector X. If X
is a matrix (2D), WT will calculate the one dimensional wavelet
transform of each row vector. The second argument H is the lowpass
filter and the third argument G the highpass filter.
The output vector contains the coefficients of the DWT ordered from
the low pass residue at scale SCALES to the coefficients at the
lowest scale, as the following example ilustrates:
Output vector (k=3):
[------|------|------------|------------------------]
| | | |
| | | `-> 1st scale coefficients
| | `-----------> 2nd scale coefficients
| `--------------------> 3rd scale coefficients
`----------------> Low pass residue at 3rd scale
If X is a matrix, the result will be another matrix with
the same number of rows, holding each one its respective
transformation.
WT (X,H,G,SCALES,DEL1,DEL2) calculates the wavelet transform of
vector X, but also allows the user to change the alignment of the
outputs with respect to the input signal. This effect is achieved by
setting to DEL1 and DEL2 the delays of H and G respectively. The
default values of DEL1 and DEL2 are calculated using the function
WTCENTER.
This function is a wrapper for wtnd, for compatibility with UviWave. See
below for UviWave copyright.
See also: WTND, IWT, IWTND, WTCENTER, ISPLIT.
$Id: wt.m,v 1.1 2004/09/26 04:00:24 matthewbrett Exp $0001 function y=wt(x,h,g,scales,del1,del2) 0002 % WT Discrete Wavelet Transform. 0003 % 0004 % WT(X,H,G,SCALES) calculates the wavelet transform of vector X. If X 0005 % is a matrix (2D), WT will calculate the one dimensional wavelet 0006 % transform of each row vector. The second argument H is the lowpass 0007 % filter and the third argument G the highpass filter. 0008 % 0009 % The output vector contains the coefficients of the DWT ordered from 0010 % the low pass residue at scale SCALES to the coefficients at the 0011 % lowest scale, as the following example ilustrates: 0012 % 0013 % Output vector (k=3): 0014 % 0015 % [------|------|------------|------------------------] 0016 % | | | | 0017 % | | | `-> 1st scale coefficients 0018 % | | `-----------> 2nd scale coefficients 0019 % | `--------------------> 3rd scale coefficients 0020 % `----------------> Low pass residue at 3rd scale 0021 % 0022 % 0023 % If X is a matrix, the result will be another matrix with 0024 % the same number of rows, holding each one its respective 0025 % transformation. 0026 % 0027 % WT (X,H,G,SCALES,DEL1,DEL2) calculates the wavelet transform of 0028 % vector X, but also allows the user to change the alignment of the 0029 % outputs with respect to the input signal. This effect is achieved by 0030 % setting to DEL1 and DEL2 the delays of H and G respectively. The 0031 % default values of DEL1 and DEL2 are calculated using the function 0032 % WTCENTER. 0033 % 0034 % This function is a wrapper for wtnd, for compatibility with UviWave. See 0035 % below for UviWave copyright. 0036 % 0037 % See also: WTND, IWT, IWTND, WTCENTER, ISPLIT. 0038 % 0039 % $Id: wt.m,v 1.1 2004/09/26 04:00:24 matthewbrett Exp $ 0040 0041 %-------------------------------------------------------- 0042 % Copyright (C) 1994, 1995, 1996, by Universidad de Vigo 0043 % 0044 % 0045 % Uvi_Wave is free software; you can redistribute it and/or modify it 0046 % under the terms of the GNU General Public License as published by the 0047 % Free Software Foundation; either version 2, or (at your option) any 0048 % later version. 0049 % 0050 % Uvi_Wave is distributed in the hope that it will be useful, but WITHOUT 0051 % ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or 0052 % FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License 0053 % for more details. 0054 % 0055 % You should have received a copy of the GNU General Public License 0056 % along with Uvi_Wave; see the file COPYING. If not, write to the Free 0057 % Software Foundation, 675 Mass Ave, Cambridge, MA 02139, USA. 0058 % 0059 % Authors: Sergio J. Garcia Galan 0060 % Cristina Sanchez Cabanelas 0061 % e-mail: Uvi_Wave@tsc.uvigo.es 0062 %-------------------------------------------------------- 0063 0064 if nargin < 3 0065 error('Need data to transform and two filters'); 0066 end 0067 if nargin < 4 0068 scales = []; 0069 end 0070 if nargin < 5 0071 del1 = []; 0072 end 0073 if nargin < 6 0074 del2 = []; 0075 end 0076 0077 sz = size(x); 0078 n_dims = length(sz); 0079 p_dims = zeros(1, n_dims); 0080 if sz(2) > 1 0081 p_dims(2) = 1; 0082 else 0083 p_dims(1) = 1; 0084 end 0085 0086 if n_dims > 2 0087 warning('wt does a 1D transform; use wtnd for N-D transforms'); 0088 end 0089 y = wtnd(x, h, g, scales, del1, del2, p_dims);