IWT Discrete Inverse Wavelet Transform.
IWT (WX,RH,RG,SCALES) calculates the 1D inverse wavelet transform
of vector WX, which should be a SCALES-scales direct wavelet
transform. If WX is a matrix, then it's supposed to hold a wavelet
transform vector in each of its rows, and every one of them will be
inverse transformed. The second argument RH is the synthesis
lowpass filter and the third argument RG the synthesis highpass
filter.
IWT will calculate the size of the reconstructed vector(s) the
largest as possible (maybe 1 point larger than the original) unless
it is provided using IWT(WX,RH,RG,SCALES,SIZ). A value of 0 for SIZ
is the same as ommiting it.
IWT can be used to perform a single process of multiresolution
analysis. The way to do it is by selecting the scales whose
highpass bands (detail signals) should be ignored for
reconstruction.
Using IWT(WX,RH,RG,SCALES,SIZ,SC_LEVELS) where SC_LEVELS is a
SCALES-sized vector, 1's or 0's. An i-th coefficient of 0 means
that the i-th scale detail (starting from the deepest) should be
ignored. SC_LEVELS vector can be replaced by a single number for
selecting just only the SC_LEVELS deepest scales.
An all-ones vector, or a single number equal to SCALES, is the same
as the normal inverse transform.
IWT (WX,RH,RG,SCALES,SIZ,SC_LEVELS,DEL1,DEL2) calculates the
inverse transform or performs the multiresolution analysis, but
allowing the users to change the alignment of the outputs with
respect to the input signal. This effect is achieved by setting to
DEL1 and DEL2 the analysis delays of H and G respectively, and
calculating the complementary delays for synthesis filters RH and
RG. The default values of DEL1 and DEL2 are calculated using the
function WTCENTER.
This function is a wrapper for iwtnd, for compatibility with UviWave. See
below for UviWave copyright.
See also: WTND, WT, IWT, WTCENTER, ISPLIT.
$Id: iwt.m,v 1.1 2004/09/26 04:00:24 matthewbrett Exp $0001 function y=iwt(wx,rh,rg,scales,tam,sc_levels,del1,del2) 0002 % IWT Discrete Inverse Wavelet Transform. 0003 % 0004 % IWT (WX,RH,RG,SCALES) calculates the 1D inverse wavelet transform 0005 % of vector WX, which should be a SCALES-scales direct wavelet 0006 % transform. If WX is a matrix, then it's supposed to hold a wavelet 0007 % transform vector in each of its rows, and every one of them will be 0008 % inverse transformed. The second argument RH is the synthesis 0009 % lowpass filter and the third argument RG the synthesis highpass 0010 % filter. 0011 % 0012 % IWT will calculate the size of the reconstructed vector(s) the 0013 % largest as possible (maybe 1 point larger than the original) unless 0014 % it is provided using IWT(WX,RH,RG,SCALES,SIZ). A value of 0 for SIZ 0015 % is the same as ommiting it. 0016 % 0017 % 0018 % IWT can be used to perform a single process of multiresolution 0019 % analysis. The way to do it is by selecting the scales whose 0020 % highpass bands (detail signals) should be ignored for 0021 % reconstruction. 0022 % 0023 % Using IWT(WX,RH,RG,SCALES,SIZ,SC_LEVELS) where SC_LEVELS is a 0024 % SCALES-sized vector, 1's or 0's. An i-th coefficient of 0 means 0025 % that the i-th scale detail (starting from the deepest) should be 0026 % ignored. SC_LEVELS vector can be replaced by a single number for 0027 % selecting just only the SC_LEVELS deepest scales. 0028 % 0029 % An all-ones vector, or a single number equal to SCALES, is the same 0030 % as the normal inverse transform. 0031 % 0032 % IWT (WX,RH,RG,SCALES,SIZ,SC_LEVELS,DEL1,DEL2) calculates the 0033 % inverse transform or performs the multiresolution analysis, but 0034 % allowing the users to change the alignment of the outputs with 0035 % respect to the input signal. This effect is achieved by setting to 0036 % DEL1 and DEL2 the analysis delays of H and G respectively, and 0037 % calculating the complementary delays for synthesis filters RH and 0038 % RG. The default values of DEL1 and DEL2 are calculated using the 0039 % function WTCENTER. 0040 % 0041 % This function is a wrapper for iwtnd, for compatibility with UviWave. See 0042 % below for UviWave copyright. 0043 % 0044 % See also: WTND, WT, IWT, WTCENTER, ISPLIT. 0045 % 0046 % $Id: iwt.m,v 1.1 2004/09/26 04:00:24 matthewbrett Exp $ 0047 0048 %-------------------------------------------------------- 0049 % Copyright (C) 1994, 1995, 1996, by Universidad de Vigo 0050 % 0051 % 0052 % Uvi_Wave is free software; you can redistribute it and/or modify it 0053 % under the terms of the GNU General Public License as published by the 0054 % Free Software Foundation; either version 2, or (at your option) any 0055 % later version. 0056 % 0057 % Uvi_Wave is distributed in the hope that it will be useful, but WITHOUT 0058 % ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or 0059 % FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License 0060 % for more details. 0061 % 0062 % You should have received a copy of the GNU General Public License 0063 % along with Uvi_Wave; see the file COPYING. If not, write to the Free 0064 % Software Foundation, 675 Mass Ave, Cambridge, MA 02139, USA. 0065 % 0066 % Author: Sergio J. Garcia Galan 0067 % e-mail: Uvi_Wave@tsc.uvigo.es 0068 %-------------------------------------------------------- 0069 0070 if nargin < 4 0071 error('Need data to iwt, two filters and number of scales'); 0072 end 0073 if nargin < 5 0074 tam = []; 0075 end 0076 if nargin < 6 0077 sc_levels = []; 0078 end 0079 if nargin < 7 0080 del1 = []; 0081 end 0082 if nargin < 8 0083 del2 = []; 0084 end 0085 0086 sz = size(wx); 0087 n_dims = length(sz); 0088 p_dims = zeros(1, n_dims); 0089 if sz(2) > 1 0090 p_dims(2) = 1; 0091 else 0092 p_dims(1) = 1; 0093 end 0094 0095 if n_dims > 2 0096 warning('iwt does a 1D transform; use iwtnd for N-D transforms'); 0097 end 0098 y = iwtnd(wx, rh, rg, scales, tam, sc_levels, del1, del2, p_dims);