.TH QCCWAVWAVELETDWT1D 3 "QCCPACK" "".SH NAMEQccWAVWaveletDWT1D, QccWAVWaveletInverseDWT1D \- discrete wavelet transform and inverse transform for a 1D signal.SH SYNOPSIS.B #include "libQccPack.h".sp.BI "int QccWAVWaveletDWT1D(const QccVector " input_signal ", QccVector " output_signal ", int " signal_length ", int " signal_origin ", int " subsample_pattern ", int " num_scales ", const QccWAVWavelet *" wavelet );.br.BI "int QccWAVWaveletInverseDWT1D(const QccVector " input_signal ", QccVector " output_signal ", int " signal_length ", int " signal_origin ", int " subsample_pattern ", int " num_scales ", const QccWAVWavelet *" wavelet );.br.BI "int QccWAVWaveletDWTSubbandLength(int " original_length ", int " level ", int " highband ", int " signal_origin ", int " subsample_pattern );.SH DESCRIPTION.B QccWAVWaveletDWT1D()performs a discrete wavelet transform (DWT) of a one-dimensional signal..I num_scalesgives the number of scales, or levels, of the decomposition..BR QccWAVWaveletDWT1D()implements a dyadic decomposition of.IR input_signal ;that is, the lowpass subband is recursively decomposed into lowpass andhighpass bands for each level of decomposition.The transform is critically sampled; that is,each subband produced in each decomposition levelhas roughly half as many samples as the lowpass band of the preceding level..I output_signalcontains the subbands output from the DWT;the subbands are nested in.I output_signalstarting with the lowpass subband of the lowest (coarsest) level ofdecomposition (i.e., the baseband) with subsequent highpass subbandsof increasing resolution following..LPEssentially,.BR QccWAVWaveletDWT1D()calls.BR QccWAVWaveletAnalysis1D (3)for each level of decomposition..BR QccWAVWaveletAnalysis1D (3)in turn calls either.BR QccWAVFilterBankAnalysis (3)or.BR QccWAVLiftingAnalysis (3)depending on whether.I waveletspecifies a filter-bank orlifting implementation.In either case,.I signal_originindicates the sample index at which .I input_signalstarts..LP.B QccWAVWaveletInverseDWT1D()performs the inverse DWT of.IR input_signalwhich is assumed to have been producedby.BR QccWAVWaveletDWT1D() ..I num_scalesgives the number of levels of decomposition that exist in.IR input_signal .Essentially,.B QccWAVWaveletInverseDWT1D()calls.BR QccWAVWaveletSynthesis1D (3)for each level of synthesis;.BR QccWAVWaveletSynthesis1D (3)in turn calls either.BR QccWAVFilterBankSynthesis (3)or.BR QccWAVLiftingSynthesis (3)depending on whether.I waveletspecifies a filter-bank orlifting implementation.In either case,.I signal_originindicates the sample index at which.I input_signalstarts..LP.I subsample_patternindicates the even- or odd-phase subsampling to be used at each levelof decomposition. In most applications, even subsampling at alllevels is desired, in which case.I subsample_patternshould be set to zero.In more general settings, when some mixture of even- and odd-phase subsamplingis desired, .I subsample_patterncan be an integer between 0 and.RI "2^" num_levels " - 1."In this integer, the .IR j thbit (where.I j= 1 is the least-significant bit) indicates whether the.IR j thlevel of decomposition employseven or odd subsampling (0 = even, 1 = odd).For example, if.I subsample_patternis 5, then the first and third decompositions use odd-phasesubsampling, while all others use even subsampling..LPFor both.BR QccWAVWaveletDWT1D()and.BR QccWAVWaveletInverseDWT1D() ,sufficient space for.I output_signalmust be allocated prior to callingthe routines..LP.BR QccWAVWaveletDWTSubbandLength()gives the length of a subband produced by.BR QccWAVWaveletDWT1D() ..I original_lengthgives the original length of the undecomposed original signal..I leveland.I highpassindicates for which subband the length is to be returned..I levelgives the level of decomposition of the subband of interest,with 0 denoting the highest resolution (i.e., the level of the originalsignal) and.I num_scalesbeing the lowest resolution scale (where .I num_scalesis the number of scales used by.BR QccWAVWaveletDWT1D()in the decomposition)..I highpassindicates whether the highpass.RI ( highpass= 1)or lowpass.RI ( highpass= 0)subband at the given.I levelis of interest..I signal_originindicates the sample index at which the original signal started..SH "RETURN VALUES".BR QccWAVWaveletDWTSubbandLength()returns the subband length;the other routinesreturn 0 on success and 1 on error..SH "SEE ALSO".BR QccWAVWaveletAnalysis1D (3),.BR QccWAVWaveletSynthesis1D (3),.BR QccWAVFilterBankAnalysis (3),.BR QccWAVFilterBankSynthesis (3),.BR QccWAVLiftingAnalysis (3),.BR QccWAVLiftingSynthesis (3),.BR QccWAVWaveletRedundantDWT1D (3),.BR QccWAVWavelet (3),.BR QccPackWAV (3),.BR QccPack (3).LPM. Antonini, M. Barlaud, P. Mathieu, and I. Daubechies,"Image Coding Using Wavelet Transform,".IR "IEEE Transactions on Image Processing" ,vol. 1, pp. 205-220, April 1992..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.