.TH QCCWAVWAVELETLWT 3 "QCCPACK" "".SH NAMEQccWAVWaveletLWT, QccWAVWaveletInverseLWT \-forward and inverse lazy wavelet transform.SH SYNOPSIS.B #include "libQccPack.h".sp.BI "int QccWAVWaveletLWT(const QccVector " input_signal ", QccVector " output_signal ", int " signal_length ", int " signal_origin ", int " subsample_pattern );.br.BI "int QccWAVWaveletInverseLWT(const QccVector " input_signal ", QccVector " output_signal ", int " signal_length ", int " signal_origin ", int " subsample_pattern );.SH DESCRIPTION.B QccWAVWaveletLWT()implements a lazy wavelet transform (LWT).Essentially, the.I input_signalis partitioned into two sets: the even-indexed samples andthe odd-indexed samples.Depending on.I subsample_patternand.IR signal_origin ,one of these sets will be considered to be the"lowpass" subband, while the other will be considered to be the"highpass" subband..LP.I signal_origingives the index number of the first sample of.IR input_signal ..I signal_originis used, in conjunction with.IR subsample_pattern ,to determine the phases of subsampling in eachlevel of the signal decomposition.In most cases,the signal starts with index 0, so.I signal_originis 0..LP.I subsample_patternmay be either.B QCCWAVWAVELET_PHASE_EVENor.BR QCCWAVWAVELET_PHASE_ODD ,indicating whether even- or odd-phase subsampling is desired.In the usual case, even subsampling is normally used..LPIn the case that.I signal_lengthis even, both the odd and even "subbands" of the LWToutput are the same length.  On the other hand, if.I signal_lengthis odd, one of the two subbands will be one sample longerthan the other. Which subband will be longer will depend onwhether .IR signal_origin is odd or even, and also on which phase of subsampling isspecified by.IR subsample_pattern ..LPIf.I signal_lengthis less than 2,.BR QccWAVWaveletLWT()merely copies.I input_signalto .IR output_signal ..LP.BR QccWAVWaveletInverseLWT()performs the opposite operation as.BR QccWAVWaveletLWT() .That is, even-index samples are extracted fromthe start of.I input_signaland "interleaved" with odd-indexed samples extracted fromthe end of.IR input_signal ..I signal_originand.I subsample_patternare used to determine whether.I output_signalis to start with a odd- or even-indexed sample.If.I signal_lengthis less than 2,.I input_signalis merely copied to.IR output_signal ..LPFor both of these routines,.I output_signalmust be allocated to sufficient length before calling the routine..SH "RETURN VALUES"Both.BR QccWAVWaveletLWT()and.BR QccWAVWaveletInverseLWT()return 0 on success and 1 on error..SH "SEE ALSO".BR QccPackWAV (3),.BR QccPack (3).LPI. Daubechies and W. Sweldens,"Factoring Wavelet Transforms Into Lifting Steps,".IR "J. Fourier Anal. Appl." ,vol. 4, no. 3, pp. 245-267, 1998..SH AUTHORCopyright (C) 1997-2005  James E. Fowler.\"  The programs herein are free software; you can redistribute them an.or.\"  modify them under the terms of the GNU General Public License.\"  as published by the Free Software Foundation; either version 2.\"  of the License, or (at your option) any later version..\"  .\"  These programs are distributed in the hope that they will be useful,.\"  but WITHOUT ANY WARRANTY; without even the implied warranty of.\"  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the.\"  GNU General Public License for more details..\"  .\"  You should have received a copy of the GNU General Public License.\"  along with these programs; if not, write to the Free Software.\"  Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.