   
   
   
Contents Files in WaveLab version v802
   
   
 
 
%%%%%%%%%%%%%%%%%%%%%%%%   WaveLab:Contents.m   %%%%%%%%%%%%%%%%%%%%%%%%%
 WaveLab Main Directory, Version 802

 This is the main directory of the WaveLab package; the full package
 contains over 1300 files, consisting of .m files, .mex files and datasets.

              .m files in this directory

   Contents.m          -    This file
   startup.m           -    Sample Startup file
   WavePath.m          -    Sets up global variables and pathnames
   InstallMEX.m        -    Install MEX files

              Subdirectories

   Biorthogonal/       -    Bi-Orthogonal Wavelet Transform tools
   Books               -    figures for books
     /WaveTour         -    Figures of the book "A Wavelet Tour of Signal Processing"
   Browsers/           -    WaveLab Browsers
     /One-D            -    One-D Signal Browser
     /WaveTour         -    Figures of the book "A Wavelet Tour of Signal Processing"
   Continuous/         -    Continuous Wavelet Transform tools
   Datasets/           -    Data for use with WaveLab
   DeNoising/          -    Wavelet Shrinkage tools
   Documentation/      -    System-Wide Documentation
   FastAlgorithms/     -    Tools for Fast Algorithms
   Fractals/           -    Fractal Analysis
   Interpolating/      -    Refinement schemes & Bi-Orthogonal Wavelet Transforms
   Invariant/          -    Invariant Wavelet Transform tools
   Median/             -    Median Interpolating Pyramid Transform Tools
   MEXSource/          -    c reservoir for mex files.
   Meyer/              -    Periodic Meyer Wavelet Transform tools
   Orthogonal/         -    Standard Orthogonal Wavelet Transforms
   Packets/            -    Wavelet Packets, Cosine Packets, Best Basis Algorithm
     /One-D            -    1-d Wavelet Packets, Cosine Packets, Best Basis
     /Two-D            -    2-d Wavelet Packets, Cosine Packets, Best Basis
   Pursuit/            -    Matching Pursuit in Wavelet Packet/Cosine Packet Dict.
   Stationary/         -    Stationary Wavelet Transform tools
   TimeFrequency/      -    Time-Frequency Distribution Tools
   Utilities/          -    System-Wide scripting utilities

   Papers/             -    Scripts recreating figures in published articles:

     /Adapt            -    figures for ``Adapting to Unknown Smoothness via 
                                          Wavelet Shrinkage''
     /Asymp            -    figures for ``Wavelet Shrinkage: Asymptopia?'' 
     /Blocky           -    figures for ``Smooth Wavelet Decompositions with 
                                          Blocky Coefficient Kernels''
     /Correl           -    figures for ``Wavelet Threshold Estimators for 
                                          Data with Correlated Noise''
     /Ideal            -    figures for ``Ideal Spatial Adaptation via
                                          Wavelet Shrinkage''
     /MinEntSeg        -    figures for ``On Minimum Entropy Segmentation''
     /MIPT             -    figures for ``Nonlinear Wavelet Transforms
                                          based on Median-Interpolation'' 
     /RiskAnalysis     -    figures for ``Exact Risk Analysis of Wavelet Regression''
     /ShortCourse      -    figures for ``Nonlinear Wavelet Methods for Recovery  
                                          of Signals, Densities, Spectra and
                                          Images from Incomplete and Noisy Data''
     /SpinCycle        -    figures for ``Translation-Invariant De-Noising''
     /Tour             -    figures for ``Wavelet Shrinkage and W.V.D. 
                                          -- a Ten-Minute Tour''
     /VillardDeLans    -    figures for ``WaveLab and Reproducible Research''

   Workouts/           -    Scripts giving WaveLab features a workout

     /BestOrthoBasis   -    Best Basis workout
     /MatchingPursuit  -    Matching Pursuit workout
     /MultiFractal     -    Continuous Wavelet Transform workout
     /Toons            -    Cartoon Guide to Wavelets

 Other

   README              -    General information blurb

 
 
 
 
 
 
%%%%%%%%%%%%%%%%%%%%%%%%   Biorthogonal:Contents.m   %%%%%%%%%%%%%%%%%%%%%%%%%
 Biorthogonal:Contents v802 -- Bi-Orthogonal Wavelet Transform tools

 The routines in this directory perform periodic- biorthogonal wavelet
 analysis of 1-d and 2-d signals.
 
 The main idea of the algorithms, and the reason for naming the directory
 Symmetric, is that the underlying filtering operations, rather than
 being one-sided as in the directory Wavelab/Orthogonal, are two-sided
 and extend an equal distance into the past and future. Filters are not
 actually required to be symmetric, but they must be of length 2k+1, the
 middle sample being taken as the filter coefficient attached to zero lag.
 
 The main tools for all-purpose use are FWT_PBS and IWT_PBS.

          Wavelet Transforms

 FWT_PBS           -  Forward Wavelet Transform, Periodized,
                           Bi-Orthogonal, Symmetric
 FWT_PB            -  new name of FWT_PBS

 IWT_PBS           -  Inverse Wavelet Transform, Periodized,
                           Bi-Orthogonal, Symmetric
 IWT_PB            -  new name of IWT_PBS

 FWT_SBS           -  Forward Wavelet Transform, Symmetric Extended,
                           Bi-Orthogonal, Symmetric
 IWT_SBS           -  Inverse Wavelet Transform, Symmetric Extended
                           Bi-Orthogonal, Symmetric

 FWT2_PBS          -  Forward Wavelet Transform, 2-d, Periodized,
                           Bi-Orthogonal, Symmetric
 FWT2_PB           -  new name of FWT2_PBS

 IWT2_PBS          -  Inverse Wavelet Transform, 2-d, Periodized,
                           Bi-Orthogonal, Symmetric
 IWT2_PB           -  new name of IWT2_PBS

 FWT2_SBS          -  Forward Wavelet Transform, 2-d, Symmetric Extended,
                           Bi-Orthogonal, Symmetric
 IWT2_SBS          -  Inverse Wavelet Transform, 2-d, Symmetric Extended,
                           Bi-Orthogonal, Symmetric

          Wavelet Transform Displays

 PlotPBSMultiRes   -  Display Mallat-style Multiresolution Decomposition

          Filter and Wavelet Generators

 MakeBSFilter      -  Generate Symmetric Filters for FWT_PBS and FWT_SBS
 MakeWavelet       -  Make periodized orthogonal wavelet

          Two-Scale Operators
 
 UpDyadHi_PBS      -  Upsampling Hi Pass operator   (used in IWT_PBS)
 UpDyadLo_PBS      -  Upsampling Lo Pass operator   (used in IWT_PBS)
 DownDyadHi_PBS    -  Downsampling Hi Pass operator (used in FWT_PBS)
 DownDyadLo_PBS    -  Downsampling Lo Pass operator (used in FWT_PBS)
 UpDyad_SBS      -  Upsampling operator   (used in IWT_SBS)
 DownDyad_SBS    -  Downsampling operator (used in FWT_SBS)

          Utilities

 symm_aconv        -  Periodic convolution of x with reverse of symmetric f
 symm_iconv        -  Periodic convolution of x with symmetric f
 MirrorSymmFilt    -  Conjugate Symmetric Filter
 extend            -  Perform various finds of symmetric extension
 dyadpartition     -  determine dyadic partition in wavelet transform of 
                      nondyadic signals

 
 
 
 
 
 
%%%%%%%%%%%%%%%%%%%%%%%%   Continuous:Contents.m   %%%%%%%%%%%%%%%%%%%%%%%%%
 Continuous:Contents  v802 -- Continuous Wavelet Transform tools

 The routines in this directory perform periodic Continuous Wavelet
 Transforms of 1-d signals, and tasks associated with CWT -- ridge and
 skeleton extraction. The underlying computations are completely
 different than in the usual orthogonal wavelet transforms -- they are
 all based on convolution with gaussian-type windows, using frequency
 domain implementations. Reconstruction is of little interest. Instead,
 the aim is to calculate local scaling exponents at various points in
 the signal, and to calculate generalized fractal dimensions.

 Attention; if signal length n=4096 and you use 12 voices per octave, you
 will need maybe 32 MB of RAM to successfully run this sequence of tools
 without an OUT-OF-MEMORY problem

           Wavelet Transforms

 RWT                   Real Wavelet Transform
 iRWT                  Inverse Real Wavelet Transform
 MM_RWT                Modulus Maxima of a Real Wavelet Transform
 ImageRWT              Image of Continuous Wavelet Transform

 AWT                   Analytical Wavelet Transform
 Ridge_AWT             Ridges of an Analytic Wavelet Transform

 CWT                   Continuous Wavelet Transform
 ImageCWT              Image Display of CWT

           Maxima

 WTMM                  Identify maxima of wavelet transform
 ImageWTMM             Display maxima of wavelet transform.

           Skeleton

 BuildSkelMap          Build Map of Skeleton of Wavelet Transform 
 BuildSkelMapFast      Build Map of Skeleton of Wavelet Transform -- Faster
 PlotSkelMap           Display Skeleton Map
 PruneSkelMap          Prune weak ridges from Skeleton Map 

           Ridges

 ExtractRidge          Extract Single Ridge from Skeleton Map
 PlotRidges            log-log plot of amplitudes along several ridges

           Thermodynamic Formalism

 CalcThermoPartition   Calculate Z(q,a) of Thermodynamic formalism
 PlotThermoPartition   Display   Z(q,a) of Thermodynamic formalism

 CalcGenFracDimen      Calculate D(q) of Thermodynamic formalism
 PlotGenFracDimen      Display   D(q) of Thermodynamic formalism

 CalcMomentGenFun      Calculate tau(q) of Theormodynamic formalism
 PlotMomentGenFun      Display   tau(q) of Theormodynamic formalism

 CalcFracSpectrum      Calculate f(alpha) of Multifractal formalism
 PlotFracSpectrum      Calculate f(alpha) of Multifractal formalism

                       Auxiliary

 CalcCWTScale          Tool for calculating scales used in CWT
 CalcCWTPars           Tool for calculating parameters used in CWT
 CalcCWTNorms          Tool for calculating norms scale-by-scale in CWT

 
 
 
 
 
 
%%%%%%%%%%%%%%%%%%%%%%%%   Datasets:Contents.m   %%%%%%%%%%%%%%%%%%%%%%%%%
 Datasets:Contents v802 -- Datasets, Documentation, and Readers

          Data Readers

   BrowseImages        -   Browser for Image Datasets
   ImageFig            -   Called by BrowseImages
   ReadImage           -   Uniform Interface to Image Datasets
   ReadSignal          -   Uniform Interface to Signal Datasets


          Data Fabricators

   MakeBrownian        -   Make Fractional Brownian Motions
   MakeCantor          -   Recursively generates a Cantor distribution.
   MakeFractal         -   Make fractal signals
   MakeImage           -   Make artificial 2d signal (enhanced of Make2dSignal)
   MakeProcess         -   Make locally stationary process
   MakeSignal          -   Make artificial signal
   Make2dSignal        -   Make artificial 2d signal
   makediag            -   Make diagonal pattern (used by Make2dSignal)


          1-d Signals

   caruso.asc          -   old recording by Enrico Caruso
   esca.asc            -   ESCA spectrum supplied by J.P. Bib\'erian
   greasy.asc          -   recording of the word ``greasy'' from
                             Mallat and Zhang
   HochNMR.asc         -   NMR Spectrum supplied by Jeff Hoch
   lady.asc            -   See in Books/WaveTour/WTCh06/wt06fig07.m,
                             wt06fig08.m, wt07fig03.m, wt07fig07.m
   laser.asc           -   Time Series competition Laser series
   msignal.asc         -   Artificial signal in the article of Mallat & Zhong
   RaphNMR.asc         -   NMR Spectrum supplied by Adrian Maudsley
   seismic.asc         -   standard PROMAX test seismic signal
   SonRemy.asc         -   Vocalises
   sunspots.asc        -   sunspot numbers
   transients.asc      -   artificial signal of Mallat and Zhang
   tweet.asc           -   recording of a bird singing


          2-d Images 

   barb.raw            -   ???
   barton.raw          -   painting of seashore compressed by
                             Jan-Olov Stromberg
   canaletto.raw       -   painting of Venice processed by
                             P. Perona and J. Malik
   coifman.raw         -   photo of R.R. Coifman
   daubechies.raw      -   photo of Ingrid Daubechies
   fingerprint.raw     -   someone's fingerprint
   lenna.raw           -   Lenna
   lincoln.raw         -   Honest Abe
   mriscan.raw         -   someone's brain
   peppers256.raw      -   See in Books/WaveTour/WTCh10/wt10fig05.m
   phone.raw           -   someone's phone
   

          Utilities
   makediag            -   Make a diagonal pattern
   mat2raw             -   MAT2RAW(filename,x) writes matrix 'x' into file 'filename' in
                           'raw' form.
   raw2mat             -   mat = RAW2MAT(filename,lines,columns) loads a '.raw' file into
                           matrix 'mat' of size 'lines' * 'columns'.

 
 
 
 
 
 
%%%%%%%%%%%%%%%%%%%%%%%%   DeNoising:Contents.m   %%%%%%%%%%%%%%%%%%%%%%%%%
 DeNoising:Contents v802 -- Tools for DeNoising Signals with White Gaussian Noise

  The tools in this directory implement the de-noising procedures
  described in the articles of Donoho and Johnstone and collaborators.

         Noise Suppression Tools

 WaveShrink     -  Soft Threshold Shrinkage of Wavelet Coefficients
 WPDeNoise      -  De-Noising in Best WP basis
 CPDeNoise      -  De-Noising in Best CP basis

 ThreshCP       -  Cosine packet decomposition of a noisy signal,
                   Best Basis analysis, Thresholding in Best Basis
 ThreshWP       -  Wavepacket decomposition of a noisy signal,
                   Best Basis analysis, Thresholding in Best Basis
 ThreshWave     -  Denoising of 1-d signal with wavelet thresholding.
 ThreshWave2    -  Denoising of 2-d image with wavelet thresholding.

 CohWave        -  Denoising of signal contaminated with another signal using coherent
                   structures algorithm.

 IdealWavDenoise - Simulation of an Ideal Thresholding Applied to
                   Wavelet Coefficients.
 TIDenoiseHard2  - Translation-Invariant Hard Wavelet Thresholding of Images.
 TIDenoiseSoft2  - Translation-Invariant Soft Wavelet Thresholding of Images.

         Applying Thresholding to Many Scales 

 MultiHybrid    -  Apply Shrinkage with level-dependent thresholding via SURE
 MultiMAD       -  Apply Shrinkage with level-dependent Noise level estimation
 MultiSURE      -  Apply Shrinkage with level-dependent thresholding via SURE
 MultiVisu      -  Apply sqrt(2log(n)) Thresholding to Wavelet Coefficients
 InvShrink      -  Apply Shrinkage with Exponentially Growing Threshold

         Setting Thresholds at a Single Scale

 HybridThresh   -  Modified SURE Threshold Selection
 MinMaxThresh   -  Minimax-selected Threshold
 SUREThresh     -  SURE Threshold Selection
 ValSUREThresh  -  Value of SURE-selected Threshold 
 VisuThresh     -  Visually Best Threshold Selection

         Threshold Devices

 SoftThresh     -  Apply Soft Threshold
 HardThresh     -  Apply Hard Threshold 

         Pre-Conditioner

 NormNoise      -  Normalize signal to noise level 1

         Utilities

 GWN            -  Generation of Gaussian White Noise
 GWN2           -  Generation of 2-D Gaussian White NNoise
 GWNoisy        -  Addition of a Gaussian White Noise
 GWNoisy2       -  Addition of a 2D Gaussian White Noise
 HT             -  Hard Threshold Applied to Wavelet Coefficients.
 HT2            -  Hard Threshold Applied to Image Wavelet Coefficients.
 ST             -  Soft Threshold Applied to Wavelet Coefficients.
 ST2            -  Soft Threshold Applied to Wavelet Coefficients.
 Wiener         -  Wiener filter.
 Wiener         -  Wiener filter for images.

 
 
 
 
 
 
%%%%%%%%%%%%%%%%%%%%%%%%   FastAlgorithms:Contents.m   %%%%%%%%%%%%%%%%%%%%%%%%%
 FastAlgorithms:Contents v802 -- Tools for Fast Matrix Multiplication in Wavelet Basis

 FNWT_PO                -  Nonstandard Wavelet Transform,
                             Periodized, Orthogonal
 FSFT_PO               -   Convert Matrix to Standard Form,
                             Periodized, Orthogonal
 INWT_PO               -   Invert Nonstandard Wavelet Transform,
                             Periodized, Orthogonal
 ISFT_PO               -   Convert Standard Form to Matrix Form,
                             Periodized, Orthogonal
 Mat2SparseNSForm      -   Put Matrix into Sparse Nonstandard Form
 Mat2SparseStdForm     -   Put Matrix into Sparse Standard Form
 ndyad                 -   Index dyad of nonstandard wavelet transform
 NonStdWaveMult        -   Nonstandard Wavelet Matrix Multiplication
 StdWaveMult           -   Standard Wavelet Matrix Multiplication
 StretchMatrix         -   Stretch Matrix into BCR Nonstandard Form

 
 
 
 
 
 
%%%%%%%%%%%%%%%%%%%%%%%%   Fractals:Contents.m   %%%%%%%%%%%%%%%%%%%%%%%%%
 Fractals:Contents v802 -- Fractal Analysis

 The routines in this directory perform periodic- biorthogonal wavelet
 analysis of 1-d and 2-d signals.
 
 FracPartition -- Fractal Partition Function based on wavelet modulus maxima
 FracScalExp   -- Calculate Moment Generating Function
 FracSingSpect -- Calculate Spectrum of Local Scaling Exponents
    
 
 
 
 
 
 
%%%%%%%%%%%%%%%%%%%%%%%%   Interpolating:Contents.m   %%%%%%%%%%%%%%%%%%%%%%%%%
 Interpolating:Contents v802 -- Interpolating Refinements and Wavelet Transforms

 This directory contains tools for Deslauriers-Dubuc (interpolating)
 refinement for average-interpolating refinement, and the associated
 Multi-Resolution analyses and associated Wavelet Transforms.

 Background Reading: D.L. Donoho, Interpolating Wavelet Transforms;
     Smooth Wavelet Decompositions with Blocky Coefficient Kernels

          Deslauriers-Dubuc Refinement & Associated Tools

 DDRefine          -   Deslauriers-Dubuc Refinement Scheme
 MakeDDFilter      -   Filters for Deslauriers-Dubuc Refinement
 MakeDDBdryFilter  -   Edge Filters for Deslauriers-Dubuc Refinement

 FWT_DD            -   Fast interpolating wavelet transform
 IWT_DD            -   Fast interpolating inverse wavelet transform

 PlotDDMultiRes  - Display 1-d DD MRA

 DDDyadDown        -   Interpolating DownSampling Operator
 DDDyadUp          -   Interpolating UpSampling Operator

          Average-Interpolating Refinement & Associated Tools

 AIRefine          -   Average-Interpolating Refinement Scheme
 AIRefine2d        -   Average-Interpolating Refinement Scheme (2d)
 MakeAIFilter      -   Filters for Average-Interpolating Refinement
 MakeAIBdryFilter  -   Edge Filters for Average-Interpolating Refinement

 FWT_AI            -   Fast average-interpolating wavelet transform
 IWT_AI            -   Fast average-interpolating inverse wavelet
 
 
 
 
 
 
%%%%%%%%%%%%%%%%%%%%%%%%   Invariant:Contents.m   %%%%%%%%%%%%%%%%%%%%%%%%%
 Invariant:Contents v802 -- Invariant Wavelet Transform tools
 
 The routines in this directory perform periodic, "stationary" wavelet
 analysis of 1-d.  By Stationary we mean that the results are in some
 sense invariant under circulant shift of the signal.
 
 The main tools for all-purpose use are FWT_Stat and IWT_Stat.
 
 Another set of tools has to do with finding the best circulant shift of
 the signal, in the sense of minimizing the entropy of the transform
 coefficients.
 
 The underlying computations are carried out by FWT_TI. This looks
 completely different than in the usual orthogonal wavelet transforms --
 it resembles closely the wavelet packet calculations.  It is based on
 applying the usual operators to all shifts of a signal, and results in
 a special data structure, called TI Table.
 
 The Stationary wavelet transform unscrambles the TI table, producing a
 Stat Table, which can be displayed and analyzed.
 
 The TI table is that natural structure for use with the adaptive ''best
 shift'' algorithm
 

            Wavelet Transforms

 FWT_ATrou         -  Fast Dyadic Wavelet Transform (periodized, orthogonal)
 IWT_ATrou         -  Inverse Dyadic Wavelet Transform

 FWT_Stat          -  Stationary Wavelet Transform, Periodized
 IWT_Stat          -  Stationary Wavelet Transform, Periodized

 FWT_TI            -  Translation-Invariant Wavelet Transform
 IWT_TI            -  Translation-Invariant Wavelet Transform
 
 FWT2_TI           -  Translation-Invariant Wavelet Transform
 IWT2_TI              Inverse Translation-Invariant Wavelet Transform, 
                      based on mean.

 FWT2_Atrou        -  2-D Fast Dyadic Wavelet Transform (not available yet)

            Adaptive Best Circulant Shift algorithm

 BestShift          -  Best-Shift of all circulant shifts
 CalcShiftTree      -  Fill Stat Tree with entropy numbers       
 UnpackShiftCoeffs  -  Unpack basis coeffs from TI Table
 PackShiftCoeffs    -  Pack basis coeffs into TI Table

            Modulus Maxima

 MM_DWT             -  Modulus Maxima of a Dyadic Wavelet Transform
 IMM_DWT            -  Inverse Reconstruction of signals from Modulus
                       Maxima of a Dyadic Wavelet Transform

 MM2_DWT            -  2-D Modulus Maxima of a Dyadic Wavelet Transform
 IMM2_DWT           -  Inverse of MM2_DWT

            Display

 PlotStatTable      -  Plot Stationary Wavelet Transform Coefficients

            Utilities

 MakeDyadFilter     -  Generate Biorthonormal Quadratic Spline Filter Pair
 MakeATrouFilter    -  Generate Biorthonormal Quadratic Spline Filter Pair
 ModulusMaxima      -  Maximum of modulus
 TI_2_Stat          -  Convert TI-transform to Stationary-transform
 Stat_2_TI          -  Convert Stationary-transform to TI-transform

 
 
 
 
 
 
%%%%%%%%%%%%%%%%%%%%%%%%   Median:Contents.m   %%%%%%%%%%%%%%%%%%%%%%%%%
 Median:Contents  v.802 -- Median Interpolating Pyramid Transform Tools
 
   The routines in this directory perform a new kind of multiresolution
 decomposition of 1-d signals which is nonlinear and possesses robust
 properties when applied to highly nongaussian data.
 The main tools are FMIPT and IMIPT.

 Background Reading: D.L. Donoho and T. P.Y. Yu, Robust Nonlinear Wavelet
     Transform based on Median Interpolation

          MIPT Transform

 FMIPT             -  Forward Median Interpolating Pyramid Transform
 IMIPT             -  Inverse Median Interpolating Pyramid Transform

          Wavelet Transform Displays

 PlotMRA_MT        -  Display MIPT Multiresolution Decomposition
 PlotMTCoeff       -  Spike Plot of MIPT Coefficients
 
          Two-Scale Operators
 
 MedITriadDown      -  Median Interpolating DownSampling Operator (used in FMIPT)
 MedITriadUp        -  Median Interpolating UpSampling Operator   (used in IMIPT)
 QuadMedRef         -  Quadratic Median Interpolating Refinement
 
          Utilities

 TriMergeSort       -  Triadic Merge Sort
 quadmedian         -  Computation of block median of quad. poly.
 
 
 
 
 
 
 
%%%%%%%%%%%%%%%%%%%%%%%%   Median:HigherDegree:Contents.m   %%%%%%%%%%%%%%%%%%%%%%%%%
 Median:Contents  v.802 -- Median Interpolating Pyramid Transform Tools
 
   The routines in this directory implements an iterative algorithm
 for median-interpolation for D > 2. At the moment, the convergence
 property of this algorithm is still missing a step in the proof. 
 However, experiments (and the not yet completed theory) suggest 
 an exponential rate of convergence.

 Background Reading: D.L. Donoho and T. P.Y. Yu, Robust Nonlinear Wavelet
     Transform based on Median Interpolation

 
 
 
 
 
 
%%%%%%%%%%%%%%%%%%%%%%%%   Meyer:Contents.m   %%%%%%%%%%%%%%%%%%%%%%%%%
 Meyer:Contents  v802 -- Periodic Meyer Wavelet Transform Tools

 The routines in this directory perform periodic, orthogonal Meyer
 wavelet analysis of 1-d and 2-d signals. The main tools for all-purpose
 use are FWT_YM and IWT_YM.   The underlying computations are completely
 different than in the usual orthogonal wavelet transforms -- they are
 all based on windowing, folding, extension, and projection in the
 frequency domain -- rather than filtering and decimation in the time
 domain.

 These routines have been developed by Eric Kolaczyk as part of his
 Stanford Ph.D. Thesis, 1994.  Dave Donoho helped out.  The best
 documentation for the algorithm is currently Eric's Thesis.

           Wavelet Transforms

 FWT_YM            -  Forward Wavelet Transform, Periodized, Meyer Wavelet
 IWT_YM            -  Inverse Wavelet Transform, Periodized, Meyer Wavelet

 FWT2_YM           -  Forward Wavelet Transform, 2-d, Periodized, Meyer Wavelet
 FTWT2_YM			-  Forward Tensor Wavelet Transform, 2-d, Periodized, Meyer Wavelet
 IWT2_YM           -  Inverse Wavelet Transform, 2-d, Periodized, Meyer Wavelet
 ITWT2_YM			-  Inverse Tensor Wavelet Transform, 2-d, Periodized, Meyer Wavelet

           Display

 PlotYMMultiRes    -  Plot MRA, Meyer Wavelet

           Single-Level Operators

 CoarseMeyerCoeff  -  Resume coefficients, coarse level C
 DetailMeyerCoeff  -  Detail coefficients, level j, 3 <= j <= J-2
 FineMeyerCoeff    -  Meyer Coefficients, finest level J-1

 DetailMeyerProj   -  Invert Meyer Transform, level j, 3 <= j <= J-2
 CoarseMeyerProj   -  Invert Meyer Transform, coarse level C
 FineMeyerProj     -  Invert Meyer Transform, finest level J-1

           Extension, Folding, Windowing Operators
 
 CombineCoeff      -  Combine local trig. coeff. into wavelet coeff.
 SeparateCoeff     -  Separate wavelet coeff. into local trig. coeff.

 FoldMeyer         -  Fold a vector onto itself using a specified window
 UnfoldMeyer       -  Unfold a vector using a specified window
 ExtendProj        -  Extend a projection to all of the integers -n/2+1 -> n/2

 WindowMeyer       -  auxiliary window function for Meyer wavelets.

           Local Trigonometric Transforms

 QuasiDCT           -  Nearly the "Discrete Cosine Transform of Type I"
 dct_ii             -  Discrete Cosine Transform of Type II
 dct_iii            -  Discrete Cosine Transform of Type III
 QuasiDST           -  Nearly the "Discrete Sine Transform of Type I"
 dst_ii             -  Discrete Sine Transform of Type II
 dst_iii            -  Discrete Sine Transform of Type III

 
 
 
 
 
 
%%%%%%%%%%%%%%%%%%%%%%%%   Orthogonal:Contents.m   %%%%%%%%%%%%%%%%%%%%%%%%%
 Orthogonal:Contents  v802 -- Orthogonal Wavelet Transform Tools

   The routines in this directory perform periodic- and boundary-corrected
 wavelet analysis of 1-d and 2-d signals. The main tools for all-purpose
 use are FWT_PO and IWT_PO.

          Wavelet Transforms

 FWT_PO            -  Forward Wavelet Transform, Periodized, Orthogonal
 IWT_PO            -  Inverse Wavelet Transform, Periodized, Orthogonal

 FWT_CDJV          -  Forward Wavelet Transform, Boundary-Corrected
 IWT_CDJV          -  Inverse Wavelet Transform, Boundary-Corrected

 FWT_IO            -  Forward Wavelet Transform (boundary-corrected)
 IWT_IO            -  Inverse Wavelet Transform  (boundary corrected)

 FWT2_PO           -  Forward Wavelet Transform, 2-d MRA, Periodized,
                         Orthogonal
 IWT2_PO           -  Inverse Wavelet Transform, 2-d MRA, Periodized, 
                         Orthogonal

 FTWT2_PO          -  Forward Wavelet Transform, 2-d Tensor, Periodized, 
                         Orthogonal
 ITWT2_PO          -  Inverse Wavelet Transform, 2-d Tensor, Periodized, 
                         Orthogonal

          Wavelet Transform Displays

 ContourMultiRes   -  Multi-Resolution Mesh Display of 1-d Wavelet Transform
 DisplayMutltiRes  -  Mesh, Contour or Image Plot of Multi-Resolution
 DisplayWaveCoeff  -  Mesh, Contour or Image Plot of Wavelet Coefficients
 PlotMultiRes      -  Display Mallat-style Multiresolution Decomposition
 PlotWaveCoeff     -  Spike Plot of Wavelet Coefficients

          Filter and Wavelet Generators

 MakeCDJVFilter    -  Generate Filters for CDJV Boundary-Corrected Transform
 MakeONFilter      -  Generate Filters for Daubechies, Coiflets, Symmlets, Haarlets
 MakeOBFilter      -  Makes Orthogonal Boundary conjugate mirror filters 
                      of Cohen-Daubechies-Jawerth-Vial
 MakeWavelet       -  Make periodized orthogonal wavelet
 Make2dWavelet     -  Make 2-d wavelet

          Two-Scale Operators
 
 UpDyadHi          -  Upsampling Hi Pass operator   (used in IWT_PO)
 UpDyadLo          -  Upsampling Lo Pass operator   (used in IWT_PO)
 DownDyadHi        -  Downsampling Hi Pass operator (used in FWT_PO)
 DownDyadLo        -  Downsampling Lo Pass operator (used in FWT_PO)
 CDJVDyadDown      -  Downsampling operator         (used in FWT_CDJV)
 CDJVDyadUp        -  Upsampling operator           (used in IWT_CDJV)

          Utilities

 aconv             -  Filtering by periodic convolution of x with
                        time reverse of f
 iconv             -  Filtering by periodic convolution of x with f
 dyad              -  Access entire j-th dyad of 1-d transform
 dyad2ix           -  Convert (j,k) index to linear index
 dyadlength        -  Length and Dyadic Length of 1-d array
 quad2ix           -  Convert (j,k) index to linear index
 quadlength        -  Length and Dyadic Length of 2-d array
 rshift            -  Circulant right shift
 lshift            -  Circulant left shift
 MirrorFilt        -  Apply (-1)^t modulation
 reverse           -  Reverse order of samples
 UpSample          -  Interpolate zeros between samples
 PlotSpikes        -  Plot an array as as spikes on baseline
 UpDyadHi          -  Hi-Pass Upsampling operator; periodized
 UpDyadLo          -  Lo-Pass Upsampling operator; periodized

 
 
 
 
 
 
%%%%%%%%%%%%%%%%%%%%%%%%   Packets:One-D:Contents.m   %%%%%%%%%%%%%%%%%%%%%%%%%
 Packets/One-D:Contents v802 -- One-d Wavelet- and Cosine- Packet Tools

   The routines in this directory perform wavelet packet analysis and
 cosine packet analysis of 1-d signals. The main tools for all-purpose
 use are WPTour and CPTour.  The other tools are all invoked by these.


          Wavelet Packet Analysis/Synthesis

 WPAnalysis           -   Dyadic table of all Wavelet Packet coefficients
 WPSynthesis          -   Synthesize signal from Wavelet Packet coefficients
 WPTour               -   Wavelet Packet decomposition & Best Basis analysis


          Cosine Packet Analysis/Synthesis

 CPAnalysis           -   Dyadic table of all Cosine Packet coefficients
 CPSynthesis          -   Synthesize signal from Cosine Packet coefficients
 CPTour               -   Cosine Packet decomposition & Best Basis analysis


          Search for Best Basis

 BestBasis            -   Coifman-Wickerhauser Best-Basis Algorithm
 CalcStatTree         -   Build tree with entropy numbers
 PlotBasisTree        -   Display basis tree with decorated branch lengths


          Packet Table Displays

 PlotPacketTable      -   Display entries in wavelet, cosine packet tables


          Phase Plane Displays

 ImagePhasePlane      -   Time-Frequency Display using ``image'' graphics
 PlotPhasePlane       -   Time-Frequency Display using ``plot'' graphics


          Comparison of Different Bases

 CompareStdBases      -   calculate entropy of some standard bases
 ImageGaborPhase      -   Time-Frequency image with congruent rectangles
 ImagePhaseVarious    -   compare 4 phase plane displays
 PlotCoeffComparison  -   compare coefficients in various bases
 PlotCompressNumbers  -   plot compression numbers for a signal
 PlotGaborPhase       -   Time-Frequency plot with congruent rectangles
 PlotPhaseVarious     -   compare 4 phase plane displays
 PlotWavePhase        -   Time-Frequency plot with wavelet tiling

 
          Working in a Single Basis

 FPT_WP               -   Fast transform into specific Wavelet Packet basis
 IPT_WP               -   Fast reconstruction from specific Wavelet Packet basis
 FPT_CP               -   Fast transform from specific Cosine Packet basis
 IPT_CP               -   Fast reconstruction from specific Cosine Packet basis


          Synthesis of Individual Basis Elements

 MakeCosinePacket     -   Make cosine packet
 MakeWaveletPacket    -   Make periodized orthogonal wavelet packet


          Cosine Packet Infrastructure

 fold                 -   folding projection with (+,-) polarity
 edgefold             -   folding projection with (+,-) polarity at edges
 unfold               -   undo folding projection with (+,-) polarity
 edgeunfold           -   undo folding projection with (+,-) polarity at edges
 MakeONBell           -   Make Bell for Orthonormal Local Cosine Analysis
 dct_iv               -   Type (IV) Discrete Cosine Xform


          Data Access Functions

 CalcWPLocation       -   calculate location of wavelet packet entry
 node                 -   tree indexing function
 packet               -   packet table indexing
 MakeBasis            -   Create a basis tree for a standard basis
 PackBasisCoeff       -   Insert basis coefficients into packet table
 UnpackBasisCoeff     -   Extract basis coefficients from packet table
 UnpackStatValue      -   Unpack the value for given basis from the stat tree


          Utilities

 CalcTreeHeight       -   Utility for PlotBasisTree
 DrawHeisenberg       -   Utility for PlotPhasePlane

 
 
 
 
 
 
%%%%%%%%%%%%%%%%%%%%%%%%   Packets:Two-D:Contents.m   %%%%%%%%%%%%%%%%%%%%%%%%%
 Packets/Two-D:Contents v802 -- 2-d Wavelet- and Cosine- Packet Tools

   The routines in this directory perform wavelet packet analysis and
 cosine packet analysis of 2-d signals. The main tools for all-purpose
 use are WP2dTour and CP2dTour.  The other tools are all invoked by these.

          Wavelet Packet Analysis/Synthesis

 WP2dTour             -   Wavelet Packet decomposition & Best Basis analysis
 WP2Tour              -   Wavelet Packet decomposition & Best Basis analysis 
 FPT2_WP              -   Analyze signal into specific 2-d Wavelet Packet basis
 IPT2_WP              -   Synthesize signal from Wavelet Packet coefficients

          Cosine Packet Analysis/Synthesis

 CP2dTour             -   Cosine Packet decomposition & Best Basis analysis
 CP2Tour              -   Cosine Packet decomposition & Best Basis analysis
 FPT2_CP              -   Analyze signal into specific 2-d Cosine Packet basis
 IPT2_CP              -   Synthesize signal from Cosine Packet coefficients
 

          Search for Best Basis

 Best2dBasis          -   Coifman-Wickerhauser Best-Basis Algorithm
 Calc2dStatTree       -   Build tree with entropy numbers from image
 Calc2dSQTree         -   Build tree with entropy numbers from packet table
 Plot2dBasisTree      -   Display basis quad tree with decorated branch lengths
 Plot2dPartition      -   Show partition of Time/Freq plane by best basis


          Packet Table Displays

 There are no Packet Tables in 2-d.  Data storage requirements would be overwhelming.


          Phase Plane Displays

 There are none in 2-d. TF ``Plane'' is a four-space. Difficult to visualize.
 

          Synthesis of Individual Basis Elements

 Make2dWaveletPacket  -   Make Individual 2-d Wavelet Packet
 Make2dCosinePacket   -   Make Individual 2-d Cosine Paket


          Wavelet Packet Infrastructure

 DownQuad             -   Split 2-d array into four subbands
 UpQuad               -   Merge four subbands into 2-d array


          Cosine Packet Infrastructure

 dct2_iv              -   Type (IV) Discrete Cosine Transform


          Data Access Functions

 qnode                -   tree indexing function
 quadbounds           -   determine bounds of 2-d packet in 2-d array
 qpkt2ix              -   convert 2-d packet indices to linear indices
 BuildFBITree         -   create basis tree used for fingerprint compression
 Calc2dPktTable       -   Put Wavelet/Cosine Packet Coefficients into 2-d Table
 Unpack2dBasisCoef    -   extract 2-d packet coeffs from table 

          Utilities

 Calc2dTreeHeight     -   Utility used by Plot2dBasisTree
 CalcEntropy          -   Utility used by Make2dBasisTree

 
 
 
 
 
 
%%%%%%%%%%%%%%%%%%%%%%%%   Pursuit:Contents.m   %%%%%%%%%%%%%%%%%%%%%%%%%
 Pursuit:Contents v802 -- Matching Pursuit with Wavelet- and Cosine- Packet Dictionaries

   The routines in this directory perform matching pursuit decomposition
 and reconstruction for 1-d signals. The main tools for all-purpose
 use are WPPursuit and CPPursuit.


          Matching Pursuit in Wavelet Packets Dictionary

 WPMPursuitTour      -   Wavelet Packet atomic decomposition
 WPPursuitTour       -   Matching Pursuit Tour with Wavelet Packet Dictionary
 WPPursuit           -   Atomic Decomposition into Wavelet Packets by Matching Pursuit
 WPPursuitBF         -   Matching Pursuit using Wavelet Packet Dictionary with backfitting
 WPAtomicSynthesis   -   generate signal from list of WP-components
 FWPAtomicSynthesis  -   Fast Wavelet Packet synthesis from atom list
 FWPSynthesis        -   synthesize signal from full wavelet packet table


          Matching Pursuit in Cosine Packets Dictionary

 CPPursuit           -   Atomic Decomposition into Cosine Packets via Matching Pursuit
 CPPursuitBF         -   Matching Pursuit using Cosine Packet Dictionary with backfitting
 CPPursuitTour       -   Matching Pursuit Tour with Cosine Packet Dictionary
 CPAtomicSynthesis   -   generate signal from list of CP-components
 FCPSynthesis        -   synthesize signal from full cosine packet table
                    
                    
          Basis Pursuit and Gabor Analysis (not available yet)

 GaborPursuitTour    -   Matching pursuit algorithm in a Gabor dictionary
 WPBPursuitTour      -   Basis pursuit algorithm in a wavelet packet dictionnary
 CPBPursuitTour      -   Basis pursuit algorithm in a cosine packet dictionnary


          Displays  
                    
 PlotAtomicPhase     -   Time-Frequency display of atom list using ``plot'' graphics
 ImageAtomicPhase    -   Time-Frequency display of atom list using ``image'' graphics
 PlotSynthesisTable  -   Display entries in atomlist as wavelet/cosine packet


          Utilities

 WPImpulse           -   full WP packet table analysis of a single WP basis element
 CPImpulse           -   full CP packet table analysis of a single CP basis element
 pkt2ix              -   convert packet table index to linear index
 ix2pkt              -   convert packet table index to linear index
 MakeSynthesisTable  -   convert atom list to packet table
 MonitorPursuit      -   display intermediate Pursuit progress

 
 
 
 
 
 
%%%%%%%%%%%%%%%%%%%%%%%%   TimeFrequency:Contents.m   %%%%%%%%%%%%%%%%%%%%%%%%%
 TimeFrequency:Contents v802 -- Time-Frequency Distribution Tools

 The routines in this directory compute various time-frequency
 distributions of 1-d signals.

 WindowFT       - Window Fourier Transform
 IWindowFT      - Inverse Window Fourier Transform
 Ridge_WindowFT - Find Ridges of Window Fourier Transform
 CohenDist      - Choi William Distribution
 Spectrogram    - Time-Varying Spectrum
 WVDist         - Wigner-Ville Distribution
 WignerDist     - Alias-Free Wigner-Ville Distribution (new by Maureen)
 WVDist_AF      - Alias-Free Wigner-Ville Distribution (old by Shaobing)
 TFDist_AF      - Alias-Free Generalized Discrete Time-Frequency Distribution
    
 
 
 
 
 
 
%%%%%%%%%%%%%%%%%%%%%%%%   Utilities:Contents.m   %%%%%%%%%%%%%%%%%%%%%%%%%
 Utilities:Contents v802 -- Utilties for Writing Scripts

 AppendTitle       -   Utility to Build Title String
 AutoImage         -   Automatic Scaling for Image Display
 CutDyad           -   Truncate signal to Dyadic length
 GrayImage         -   Image display of Gray-scaled digital images
 HitAnyKey         -   Tool for pausing in scripts
 LockAxes          -   Version-independent axis command
 MakeTiledFigures  -   Tile the screen with figures
 PadDyad           -   Zero-fill signal to Dyadic length
 RegisterPlot      -   Add legend with file name, date, flag
 ShapeAsRow        -   Reshape 1d vector as row
 ShapeLike         -   Reshape first argument like second argument
 UnlockAxes        -   Version-independent axis command
 WaitUntil         -   Burn up CPU cycles until sec seconds elapse
 WhiteNoise        -   Version-independent white noise generator
 ifprint           -   Conditional printing to postscript file
 log2lin           -   Transform log-scale image to linear-scale image
 pic256            -   Show image of 256 gray scale
 rnshift           -   Circular right shift of 1-d signal
 versaplot         -   Version-independent plot routine
     
 
 
 
 
 
 
%%%%%%%%%%%%%%%%%%%%%%%%   Documentation:Contents.m   %%%%%%%%%%%%%%%%%%%%%%%%%
 Documentation:Contents v802 -- Directory of Documentation Tools

   The files in this directory provide documentation about the function-
   ality, philosophy and construction of the WaveLab software library.

 ADDINGNEWFEATURES       -  How to Add New Features to WaveLab
 BUGREPORT               -  How to report bugs about WaveLab
 COPYING                 -  WaveLab Copying Permissions
 DATASTRUCTURES          -  Basic data structures in WaveLab
 FEEDBACK                -  Give feedback about WaveLab
 GETTINGSTARTED          -  Ideas for getting started with WaveLab
 INSTALLATION            -  Installation of WaveLab
 LIMITATIONS             -  WaveLab known limitations
 PAYMENT                 -  No Charge for WaveLab Software
 READING                 -  Sources for further reading about wavelets
 REGISTRATION            -  WaveLab Registration
 SUPPORT                 -  WaveLab Support
 THANKS                  -  Thanks to contributors
 VERSION                 -  Part of WaveLab Version v802
 WARRANTY                -  No Warranty on WaveLab software

 WLAlphaHelpListing      -  all help files arranged by function name
 WLAlphaSynopsisListing  -  one-line synopses arranged by function name
 WLContentsListing       -  all Contents.m files
 WLFiles                 -  listing of all WaveLab files arranged by directory
 WLHelpHeaders           -  listing of all first lines of help headers
 WLHelpListing           -  all help files arranged by directory

 
 
 
 
 
 
%%%%%%%%%%%%%%%%%%%%%%%%   Books:WaveTour:Contents.m   %%%%%%%%%%%%%%%%%%%%%%%%%
 WaveTour - Figures of the book "A Wavelet Tour of Signal Processing"
 
 	A Wavelet Tour of Signal Processing
 		Stephane Mallat
 	 ISBN: 0-12-466605-1
 	   Academic Press, 1998 
 
 This book explains the applications of wavelets to signal processing.
 A preview of the book can be found in:
 
    http://www.cmap.polytechnique.fr/users/www.mallat
       and
    http://cs.nyu.edu/cs/faculty/mallat
 
 The subdirectories WTCh... contain files that reproduce the figures in 
 each chapter, as explained in the Appendix B of the book.

 
 
 
 
 
 
%%%%%%%%%%%%%%%%%%%%%%%%   Browsers:Contents.m   %%%%%%%%%%%%%%%%%%%%%%%%%
 Browsers:Contents v802 -- WaveLab Browsers

 This directory contains browsers for use with WaveLab

 One-D		-	One-D signal browser
 WaveTour      -       Browser for Mallat's Book

 
 
 
 
 
 
%%%%%%%%%%%%%%%%%%%%%%%%   Browsers:One-D:Contents.m   %%%%%%%%%%%%%%%%%%%%%%%%%
 Browsers/One-D:Contents v802 -- 1-d Signal Browser

 The routines in this directory implement a point-and-click browser that
 allows the user to select signals, select wavelet, wavelet packet,
 discrete cosine transforms, etc.  Some of the options, including
 WTCompress, WPCompress and CPCompress contain other possibilities for
 interaction, such as interactive wavelet thresholding -- changing a
 threshold interactively and watching the effects upon reconstruction.

 Invoke this browser via the command
 
    WLBrowser
  
 Upon initialization, four new figure windows will tile the screen and
 several menu items will appear at the top of the figure window at the
 upper left of the screen:

    File Edit Window *Data *Signal *Transform *Options *Action

 The starred items are the ones supplied by the browser.  If you click
 the mouse button while pointing at the *Data item, a pull-down menu
 will appear with the names of datasets, etc.  In this way, by point and
 click operations, you can select wavelet types, transform types, and
 immediately see the results of such operations.

 
 
 
 
 
 
 
%%%%%%%%%%%%%%%%%%%%%%%%   Papers:Contents.m   %%%%%%%%%%%%%%%%%%%%%%%%%
 Papers:Contents v802 -- Reproducing Figures from Published Articles
 
 This directory contains several subdirectories; each one of these
 contains scripts that were used to produce figures in our published
 articles.  As new articles are written by members of our group, we will
 add new subdirectories. Each subdirectory contains a ``demo'' file
 which allows one to reproduce the figures in the corresponding article.
 
 When a demo file is invoked, a menu bar will appear on the screen. 
 Clicking with the mouse on the menu item ``Show All Figures'' will
 produce, in sequence, each figure in the corresponding article.  As
 each figure appears in the Matlab figure window, the command window
 will contain narrative explaining what the figure window illustrates.
 
 The directory name, corresponding paper name and corresponding demo name
 are listed herein:
 
 Adapt           -   ``Adapting to Unknown Smoothness via Wavelet Shrinkage''
                       (AdaptDemo)
 Asymp           -   ``Wavelet Shrinkage: Asymptopia?'' (AsympDemo)
 Blocky          -   ``Smooth Wavelet Decomposition with Blocky Coefficient
                       Kernals'' (BlockyDemo)
 Correl          -   ``Wavelet Threshold Estimators for Data with
                       Correlated Noise" (CorrelDemo)
 Ideal           -   ``Ideal Spatial Adaptation via Wavelet Shrinkage''
                       (IdealDemo)
 MinEntSeg       -   ``On Minimum Entropy Segmentation'' (MESDemo)
 MIPT            -   ``Nonlinear Wavelet Transforms based on Median-
                       Interpolation'' (MIPTDemo)
 RiskAnalysis    -   ``Exact Risk Analysis of Wavelet Regression'' (RiskDemo)
 ShortCourse     -   ``Nonlinear Wavelet Methods for Recovery of Signals,
                       Densities, Spectra and Images from Incomplete and
                       Noisy Data'' (SCDemo)
 Tour            -   ``Wavelet Shrinkage and W.V.D. -- A Ten-Minute Tour''
                       (TourDemo)
 SpinCycle       -   ``Translation-Invariant De-Noising'' (SpinDemo)
 VillardDeLans   -   ``WaveLab and Reproducible Research'' (VdLDemo)

 
 
 
 
 
 
%%%%%%%%%%%%%%%%%%%%%%%%   Workouts:Contents.m   %%%%%%%%%%%%%%%%%%%%%%%%%
 Workouts:Contents v802 -- WaveLab Workouts

 This directory contains several subdirectories, each containing
 scripts to "work out" various aspects of wavelet theory and
 applications.  They are:

 BestOrthoBasis    -   Workouts for Best Ortho Basis (Coifman-Wickerhauser)

 MatchingPursuit   -   Workouts for Matching Pursuits (Mallat-Zhang)

 MultiFractal      -   Workouts illustrating some aspects
                       of the Continuous Wavelet Transform

 Toons             -   "Cartoon Guide to Wavelets"

 
 
 
 
 
 
%%%%%%%%%%%%%%%%%%%%%%%%   Workouts:BestOrthoBasis:Contents.m   %%%%%%%%%%%%%%%%%%%%%%%%%
 BBWorkout:Contents -- BestBasis Workout

 The aim of this directory is to give the Best-Basis
 Routines a work-out in some systematic way.

 To this end, a variety of synthetic and real signals is
 analyzed using Best-Basis in both Cosine Packet and Wavelet
 Packet Dictionaries.

 We also illustrate illustrations of time-frequency tilings 
 and tree <--> basis correspondence

 BBWork01 -- Illustrate Time-Frequency Tiling  by Wavelet Packets
 BBWork02 -- Illustrate Time-Frequency Tiling by Cosine Packets
 BBWork03 -- Ilustrate Tiling <--> Tree Correspondence, WP Dict;
 BBWork04 -- Ilustrate Tiling <--> Tree Correspondence,CP Dict;
 BBWork11 -- Illustrate WP Methodology on LoSine, SlowChirp
 BBWork12 -- Illustrate CP Analysis Techniques on SlowChirp
 BBWork21 -- Wavelet Packet Tour on Four Basic Signals
 BBWork22 -- Wavelet Packet Tour on Four Complex Signals
 BBWork31 -- Cosine Packet Tour on Four Basic Signals
 BBWork32 -- Cosine Packet Tour on Four Complex Signals
 BBWork41 -- Illustrate CP/WP Analysis Techniques on Seismic
 BBWork42 -- Illustrate CP/WP Analysis Techniques on Warble
 BBWork61 -- Compression Numbers on Four Basic Signals

 PRINTING Note
   A key feature of these scripts is their ability to print copies
   of all the plots they generate.  The variable PRINTING controls this
   If PRINTING==1, postscript files will be generated for all plots
   made by running a script. if PRINTING==0, no postscript files will
   be generated.  Set this variable before you run any script.

 
 
 
 
 
 
%%%%%%%%%%%%%%%%%%%%%%%%   Workouts:MatchingPursuit:Contents.m   %%%%%%%%%%%%%%%%%%%%%%%%%
 MPWorkout:Contents -- Matching Pursuit Workout

 The aim of this directory is to give the Matching Pursuit
 Routines a work-out in some systematic way.

 To this end, a variety of synthetic and real signals is
 analyzed using Matching Pursuit in both Cosine Packet and
 Waveket Packet Dictionaries.

 For each signal analyzed, we use [CW]PPursuitTour to present a
 display that shows the synthesis table used, the residuals from
 Matching Pursuit, the Compression Numbers, and the phase plane 
 that is generated.

 We also present, in batches of four objects at a time, plots of the
 compression numbers, equivalent dimensions, and equivalent rates
 for objects:

   in MPWork21.m (WP); in MPWork31.m (CP); in MPWork61.m (Wrap-up)

       HeaviSine
       Doppler
       QuadChirp
       MishMash

   in MPWork22.m (WP); in MPWork32.m (CP); in MPWork62.m (Wrap-up)

       Sorrows
       Riemann
       Seismic
       Tweet

 MPWork00 -- Basics of Matching Pursuit -- Illustrate Step-by-Step Behavior
 MPWork21 -- Matching-Pursuit, Wavelet Packet Tour on Four Basic Signals
 MPWork22 -- Matching-Pursuit, Wavelet Packet Tour on Four Complex Signals
 MPWork31 -- Matching-Pursuit, Cosine Packet Tour on Four Basic Signals
 MPWork32 -- Matching-Pursuit, Cosine Packet Tour on Four Complex Signals
 MPWork61 -- Matching-Pursuit, Best-Basis Compression # Comparison on Four Basic Signals
 MPWork62 -- Matching-Pursuit, Best-Basis Compression # Comparison on Four Complex Signals


 PRINTING Note
   A key feature of these scripts is their ability to print copies
   of all the plots they generate.  The variable PRINTING controls this
   If PRINTING==1, postscript files will be generated for all plots
   made by running a script. if PRINTING==0, no postscript files will
   be generated.  Set this variable before you run any script.

 
 
 
 
 
 
%%%%%%%%%%%%%%%%%%%%%%%%   Workouts:Toons:Contents.m   %%%%%%%%%%%%%%%%%%%%%%%%%
 Toons:Contents v802 -- Cartoon Guide to Wavelets

 This directory contains more than 100 scripts which exercise various
 features of WaveLab.  A comprehensive outline of these scripts and
 what they do is given below.  

 1.0 Wavelets
     1.1 Types of Wavelets
         Haar, D4,S8, Coiflet C3                         toon0111
         Dubuc-Deslauriers Wavelets                      toon0112
         Average-Interpolating Wavelets                  toon0113
         Meyer Wavelets                                  toon0114
     1.2 Gender of Wavelets
         Father & Mother Haar                            toon0121
         Father & Mother NearSymm8                       
     1.3 Scale Families of Wavelets
         Plot 10 scales; start at V0, W0,                toon0131
         Some Symm8 at each scale, n = 1024              toon0132
     1.4 Daubechies D4 Wavelets                          toon0140
         Boundary Wavelets                               toon0141
         Periodic Wavelets                               toon0142
     1.5 Wavelet Analysis of Functions
         1.5.1 Ramp                                      toon0151
         1.5.2 Doppler Examples                          toon0152
     1.6 MRA Analysis of Functions
         Ramp and Doppler Examples                       toon0161
         Doppler Examples                                
     1.7 Smoothness of Wavelets
         Wavelet, First through Third Differences
         D4,                                             toon0171
         S8,                                             toon0172 
         S6,                                             toon0173
         Interpolating 11                                toon0174
     1.8 Frequency Content of Wavelets
         Scale Families of Waveforms
             S8                                          toon0181
             Haar                                        toon0182
         Scale Families of their Fourier Transforms
             S8                                          toon0183
             Haar                                        toon0184
 2.0 2-d Wavelets
     2.1 Mesh Plots of four wavelets
             1 page with 4 subplots                 
                 Haar                                    toon0211
                 S8                                      toon0212
     2.2 Image Plots of Four Wavelets
             1 page with 4 subplots
                 Haar                                    toon0221
                 S8                                      toon0222
     2.3 2-d Wavelet Analysis of Synthetic Objects       
         2.3.1 Stick Figure                              toon0231
         2.3.2 Box with X in it                          toon0232
         2.3.3 Ingrid                                    toon0233
 3.0 Wavelet Analysis
     3.1 Analysis of Smooth Signals
         4 Subplots: Signals, Wavelet Transform,
         Levelwise Amplitude of Ordered Coeffs
         Sinusoid, Haar                                  toon0311
         Sinusoid, S8                                    toon0312
     3.2 Analysis of Piecewise Polynomials
     3.3 Analysis of Singularities
         Signals Double Exponential Square Root          toon0331
                 Heaviside           Dirac
         Wavelet Transforms                              toon0332
         MRA's                                           toon0333
         Levelwise decay of Coefficients                 toon0334
         Ordered Coefficients                            toon0335
     3.4 Comparison of Wavelet Types
         Levelwise Amplitude, Ordered Coeffs
         Haar/S8
             (1) Doppler Levelwise                       toon0341
             (2) Doppler Ordered                         toon0342
 4.0 Wavelet Synthesis
     4.1 Partial Reconstructions
         Wavelet Reconstruction 100 First-m, Best-m
         Sinusoid/S8                                     toon0411
         Doppler/S8                                      toon0412
     4.2 Comparison of Two Wavelets
         Signal Doppler                      
         Reconstruction Haar, S8 Best 50                 toon0421
         First 64                                        toon0422
     4.3 Compression Number
         Four Objects                                    toon0431               
         Four First-m plots                              toon0432
         Four Best-m plots                               toon0433
     4.4 Comparison with other transforms
         Signal Doppler/Bumps                        
         Reconstruction DCT// S8 Best 64                 toon0441
         First 64                                        toon0442
         Four First-m plots - DCT & DWT                  toon0443
         Four Best-m plots - DCT & DWT                   toon0444
     4.5 Unconditional Basis Property
         Ramp Object                                     toon0451
         Reconstruction by Perturbing DCT                
         Reconstruction by Perturbing Haar               
         Reconstruction by Perturbing S8                 
 5.0 Applications
     5.1 Data Expansion
         Lincoln Refinement Scheme
         32*32 Lincoln                                   toon0511
         32*32 Lincoln as upper corner of 128*128 black  toon0512
         128*128 result of Inverse Transforming          toon0513
         32*32 & 128*128 side-by-side                    toon0514
     5.2 Progressive Transmission
         MRI Image                                       toon0521
         FWT of MRI Image                                toon0522
         4 subplots -- several approximations First-m    toon0523
         4 subplots -- several approximations Best-m     toon0524
     5.3 Data Compression 1-d
         1-d Seismic signal Reconstruction 100 wavelet   toon0531
         1-d Seismic signal Reconstruction 100 DCT       toon0532
         Transforms & Compression numbers                toon0533 
     5.4 Data Compression 2-d Ingrid Image
         2-d Ingrid Image                                toon0541
         FWT Imgrid Image                                toon0542
         Nonzero Patterns                                toon0543
         Co/Dec 95% FWT                                  toon0544
         Co/Dec 95% DCT                                  toon0545
         Compression Numbers                             toon0546
         Error Comparisons                               toon0547
         Side-by-Side                                    toon0548
     5.5 De-Noising
         Display spatially inhomogeneous signals         toon0551
         Display noisy versions of the above             toon0552
         Perform wavelet shrinkage                       toon0553
         Reconstruction using AutoSplines                toon0554
     5.6 Fast Algorithms         
         Depict the matrix                               toon0561
         Take the 2-d wavelet transform of the matrix    toon0562
         Show ordered coeffs of the transform            toon0563
         Compress the wavelet transform                  toon0564
         Stretch the matrix into nonstandard form        toon0565
     5.7 Construction & Analysis of Self-Similar Signals
 6.0 Messy Details
     6.1 Filtering
     6.2 Transfer Functions
 7.0 Wavelet Packets
     7.1 Some Wavelet Packets                            toon0711
     7.2 Frequency Content of WP                         toon0721
     7.3 WP As TF Atoms                                  toon0731
                                                         toon0732
     7.4 WP Decomposition of SlowChirp                   toon0741
                                                         toon0742
 8.0 Cosine Packets
     8.1 Some Cosine Packets                             toon0811
     8.2 Frequency Content of CP                         toon0821
     8.3 CP as TF atoms                                  toon0831
                                                         toon0832
     8.4 CP Decomposition of SlowChirp                   toon0841
                                                         toon0842
 9.0 Best Basis Methodology
     9.1 Wavelet Packet table                            toon0911
     9.2 Cosine Packet Table                             toon0912
     9.3 Bases as disjoint covers                        toon0913
     9.4 Bases as Trees                                  toon0914
     9.5 Bases as Partitions                             toon0915
     9.6 Trees as tilings                                toon0916
 10.0 Wavelet Packet Analysis
     10.1 LoSine                                         toon1001
     10.2 Ramp                                           toon1002
     10.3 Doppler                                        toon1003
     10.4 Dirac                                          toon1004
     10.5 HiSine                                         toon1005
     10.6 LinChirp                                       toon1006
     10.7 QuadChirp                                      toon1007
 11.0 Cosine Packet Analysis
     11.1 LoSine                                         toon1101
     11.2 Ramp                                           toon1102
     11.3 Doppler                                        toon1103
     11.4 Dirac                                          toon1104
     11.5 HiSine                                         toon1105
     11.6 LinChirp                                       toon1106
     11.7 QuadChirp                                      toon1107
 12.0 Applications of 1-d packet analysis
     12.1 Caruso De-Noising                              toon1201
     12.2 Tweet Compression                              toon1202
     12.3 TF Analysis of Tweet                           toon1203
     12.4 Speech Segmentation                            toon1204
 13.0 Comparison CP/WP
     13.1 Time-Frequency Localization
         13.1.1 Spectrogram                              toon1311
         13.1.2 TFD                                      toon1312
     13.2 Artifacts
         13.2.1 WP Tweet                                 toon1321
         13.2.2 CP Sorrows                               toon1322
         13.2.3 CP Clicks                                toon1323
 14.0 Gory Details
     14.1 WP
         14.1.1 Gray Code Indexing                       toon1411
         14.1.2 Location of Wavelet Packets              toon1412
     14.2 CP
         14.2.1 Bells                                    toon1421
 15.0 2-d Packets Analysis
     15.1 Some 2-d Wavelet Packets                       toon1501
     15.2 Some 2-d Cosine Packets                        toon1502
     15.3 2-d Wavelet Packet Decomposition               toon1503
     15.4 2-d Cosine Packet Decomposition                toon1504
 16.0 Applications of 2-d Packet Analysis
     16.1 FBI Fingerprint
         16.1.1 Display fingerprint and basis tree       toon1611
         16.1.2 First- and best-  5% reconstructions     toon1612
         16.1.3 First- and best- 10% reconstructions     toon1613
     16.2 Fast KLE                                   
     16.3 TF Analysis                                    
 17.0 Matching Pursuit
     17.1 Stepwise Behavior of Residual                  toon1701
     17.2 Behavior of Analysis Table                     toon1702
     17.3 Functions being Removed                        toon1703
     17.4 Atomic Phase Plane Plots                       toon1704
 18.0 Applications of Matching Pursuit
     18.1 Synthetic Signal; Sorrows                      toon1801
     18.2 Greasy Signal                                  toon1802
 
 
 
 
 
    
    
%   
% Part of WaveLab Version 802
% Built Sunday, October 3, 1999 8:52:27 AM
% This is Copyrighted Material
% For Copying permissions see COPYING.m
% Comments? e-mail wavelab@stat.stanford.edu
%   
    
