adding a new wavelet algorithms Coifman-Wickerhauser decomposition discrete wavelet transform (DWT) fast wavelet transform (FWT) filters for biorthogonal lifting wavelet transform (LWT) Mallat polyphase rationale reconstruction stationary wavelet transform (SWT) analysis biorthogonal case study continuous coefficients features procedure continuous complex continuous or discrete continuous real discrete coefficients procedure illustrated examples local local and global multiscale one-dimensional discrete wavelet one-dimensional wavelet packet orthogonal algorithm and wavelet families basis dbN wavelets filters redundant time-scale compared to other views using redundant representation instead translation invariant two-dimensional discrete wavelet two-dimensional wavelet packet wavelet wavelet packet See also transforms approximations coefficients discrete wavelet transform extracting one-dimensional extracting two-dimensional definition description notation reconstruction example code filters wavelet decomposition axes view bases See analysis,wavelet packets besttree function binning density estimation processed data regression estimation biorthogonal quadruplets biorthogonal wavelets definition presentation See also analysis border distortion boundary value replication periodic extension periodic padding periodized wavelet transform smooth padding symmetric extension symmetrization zero-padding breakdowns frequency peak proximal slopes rupture second derivative signal's derivative variance calculating a default global threshold centfrq function chirp signal example analysis coefficients approximation extracting one-dimensional fast wavelet transform coloration complex continuous wavelet continuous wavelet detail fast wavelet transform one-dimensional two-dimensional discrete wavelet Wavelet 1-D tool Wavelet 2-D tool line load See importing to the GUI save See exporting from the GUI coiflets definition presentation Coloration Mode color coding controlling controlling the colormap Coloration Mode menu colored AR(3) noise example complex frequency B-spline wavelets complex Gaussian wavelets complex Morlet wavelets complex Shannon wavelets compressing images fingerprint example using graphical interface compression ddencmp function difference with de-noising energy ratio methods norm recovery number of zeros predefined strategies procedure wavelet packets wavelets retained energy thresholding strategies using wavelet packets continuous wavelet transform (CWT) creating definition difference from discrete wavelet transform See also analysis, transforms CWT See continuous wavelet transform (CWT) Daubechies wavelets definition presentation ddencmp command decimation See downsampling decomposition best-level choosing optimal displaying results of multilevel entropy-based criteria hierarchical organization load See importing to the GUI multistep optical comparison performing multilevel using command line using graphical interface save See exporting from the GUI single-level structure one-dimensional two-dimensional wavelet decomposition tree de-noising basic model one-dimensional two-dimensional default values fixed form threshold graphical interface tools option methods minimax performance noise size estimate nonwhite noise predefined strategies procedure wavelet packets wavelets SURE estimate thresholding using SWT 1-D using command line 1-D using graphical interface 2-D analysis example 2-D using graphical interface using thresholding variance adaptive white noise de-noising images 2-D wavelet analysis and 2-D stationary wavelet analysis stationary wavelet transform two-dimensional procedure de-noising signals process wavelet analysis density estimation definition one-dimensional wavelet details coefficients extracting one-dimensional extracting two-dimensional decomposition definition mathematical definition notation orientation reconstruction from command line procedure wavelet decomposition dilation equation twin-scale relation discontinuities detecting See also breakdowns discrete Meyer wavelet discrete wavelet transform (DWT) definition See also analysis, transforms display mode 2-D square tree downsampling one-dimensional two-dimensional DWT See discrete wavelet transform, transforms dyadic scale edge effects See border distortion elementary lifting steps (ELS) ELS See lifting entropy criterion to select the best decomposition definitions estimation default values See also function estimation examples colored AR(3) noise frequency breakdown polynomial + white noise ramp + colored noise ramp + white noise real electricity consumption signal second-derivative discontinuity sine + white noise step signal sum of sines triangle + a sine triangle + a sine + noise two proximal discontinuities uniform white noise exporting from the GUI complex continuous wavelet continuous wavelet discrete stationary wavelet 1-D discrete stationary wavelet 2-D discrete wavelet 2-D image extension signal extension variance adaptive thresholding wavelet 1-D wavelet density estimation 1-D wavelet packets wavelet regression estimation 1-D extension mode See border distortion fast multiplication of large matrices fast wavelet transform (FWT) See transforms filters FIR biorthogonal case M-file used for construction high-pass low-pass minimum phase quadrature mirror construction example definition reconstruction scaling See also twin-scale relations fixed design See regression Fourier analysis basic function introduction short-time analysis (STFT) windowed Fourier coefficients Fourier transform fractal properties of signals and images redundant methods fractional Brownian motion frequencies identifying pure parameter related to scale wavelets interpretation frequency breakdown example frequency B-spline wavelets Full Decomposition Mode function estimation fusion of images See image fusion FWT See transforms Gaussian wavelets GUI complex continuous wavelet continuous wavelet density estimation full window resolution image de-noising using SWT image extension / truncation local variance adaptive thresholding regression estimation signal de-noising using SWT signal extension / truncation using menus using the mouse wavelet coefficients selection 1-D wavelet coefficients selection 2-D wavelet display wavelet one-dimensional wavelet packet wavelet packet display wavelet two-dimensional Haar wavelet definition presentation Heisenberg uncertainty principle IDWT See inverse discrete wavelet transform, transforms ILWT See inverse lifting wavelet transform image fusion images indexed importing to the GUI complex continuous wavelet continuous wavelet discrete stationary wavelet 1-D discrete stationary wavelet 2-D discrete wavelet 2-D variance adaptive thresholding wavelet 1-D wavelet density estimation 1-D wavelet packets wavelet regression estimation 1-D indexed images image matrix matrix indices shifting up inverse discrete wavelet transform (IDWT) inverse lifting wavelet transform (ILWT) inverse stationary wavelet transform (ISWT) ISWT See inverse stationary wavelet, transforms iswt command iswt2 command Laurent polynomial lazy wavelet level decomposition See also wavelet packet best level lifting dual elementary step (ELS) primal scheme (LS) lifting wavelet transform (LWT) load See importing in the GUI Load data for Density Estimate dialog box Load data for Stochastic Design Regression dialog box Load Signal dialog box wavelet packets wavelets local analysis See analysis local maxima lines long-term evolution detecting LS See lifting scheme LWT See lifting wavelet transform Mallat algorithm merge See wavelet packets Mexican hat wavelet definition presentation Meyer wavelet definition presentation M-files for wavelet families minimax missing data More Display Options button More on Residuals for Wavelet 1-D Compression window Morlet wavelet definition presentation multiresolution multistep node action noise ARMA colored Gaussian processing removing using GUI option suppressing See also de-noising unscaled white nondecimated DWT See transforms (stationary wavelet) objects orthogonal wavelets outliers suppressing packets See wavelet packets padding See border distortion pattern adapted wavelet detection perfect reconstruction periodic-padding signal extension periodized wavelet transform See border distortion polynomial + white noise example polyphase matrix positions predefined wavelet families type 1 type 2 type 3 type 4 type 5 quadrature mirror filters (QMF) and scaling function creating the waveform orthfilt function system ramp + colored noise example ramp + white noise example random design See regression estimation real electricity consumption signal example reconstruction approximation definition detail filters M-files multistep one step one-dimensional IDWT two-dimensional IDWT redundancy regression estimation goal one-dimensional wavelet regularity definition wavelet families resemblance index residuals display 1-D discrete wavelet compression 1-D stationary wavelet decomposition 2-D discrete wavelet compression 2-D stationary wavelet decomposition reverse biorthogonal wavelets RGB images colormap matrix converting from save See exporting from the GUI scal2frq function scale and frequency choosing using command line choosing using graphical interface definition dyadic definition for DWT to frequency display relationship scal2frq function scale factor scale mode scaling filters definition notation scaling functions definition notation shapes second-derivative discontinuity example self-similarity detecting Separate Mode Shannon wavelets shift See also translation Show and Scroll Mode Show and Scroll Mode (Stem Cfs) shrink See thresholding signal extensions border distortion signal-end effects See border distortion sine + white noise example smooth padding signal extension splines biorthogonal family filter lengths split See wavelet packets Square Mode stationary wavelet transform (SWT) step signal example STFT See Fourier analysis sum of sines example Superimpose Mode support See wavelet families SWT See stationary wavelet transform (SWT) symlets definition presentation symmetrization signal extension symmetry See wavelet families synthesis inverse transform wavelet reconstruction thresholding for optimal de-noising hard interval dependent rules tptr options soft strategies See also de-noising, compression thselect M-file time-scale See analysis transforms continuous versus discrete continuous wavelet (CWT) discrete wavelet (DWT) fast wavelet (FWT) integer to integer inverse (IDWT) reconstruction synthesis inverse lifting wavelet transform (ILWT) inverse stationary wavelet (ISWT) lifting wavelet (LWT) stationary wavelet (SWT) translation invariant transient See also breakdowns translation using the mouse See also shift translation invariance Tree Mode definition features trees best best-level decomposition mode using objects Tree Mode wavelet two-dimensional wavelet decomposition wavelet packet notation subtrees wavelet packet decomposition trend See also long-term evolution triangle + a sine + noise example triangle + a sine example twin-scale relations definition two proximal discontinuities example uniform white noise example upsampling two-dimensional IDWT wavelet reconstruction process Using Wavelet Coefficients vanishing moments suppression of signals wavelet families variance adaptive thresholding view axes Wavelet 1-D De-Noising window Wavelet 2-D Compression window Wavelet 2-D tool fingerprint example wavelet analysis advantage over Fourier as Fourier-type function de-noising signals revealing signal trends wavelet coefficients wavelet families adding new criteria full name notation properties (Part 1) properties (Part 2) regularity advantage definition short name support symmetry vanishing moments wavelet filters notation wavelet notation associated family Wavelet Packet 1-D Compression window Wavelet Packet 1-D menu item Wavelet Packet 1-D tool starting Wavelet Packet 2-D Compression window wavelet packets analysis definition and wavelet analysis differences atoms bases best level decomposition best level feature best tree best tree feature besttree function building compression computing the best tree decomposition decomposition tree complete binary tree subtrees definition de-noising ideas using SURE finding best level frequency order from wavelets to merge natural order objects organization selecting threshold for compression split tree notation wavelets adapted to a pattern adding new applications associated family Battle-Lemarie biorthogonal definition presentation candidates coiflets definition presentation complex frequency B-spline complex Gaussian complex Morlet complex Shannon Daubechies definition presentation decomposition tree defining order determining type discrete Meyer families Gaussian Haar definition presentation history "lazy" lifted Mexican hat definition presentation Meyer definition presentation Morlet definition presentation notation one-dimensional analysis one-dimensional capabilities objects table organization relationship of filters to reverse biorthogonal shapes shifted symlets definition presentation translation See also shift tree one-dimensional two-dimensional two-dimensional two-dimensional analysis two-dimensional capabilities objects table vanishing moments number of suppression of signals wavelets.asc file wavelets.inf file wavelets.prv file wavemngr command wthresh command zero-padding signal extension zoom