                                           
%           ******   Biorthogonal/   ********         
% Biorthogonal:Contents v850 -- 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
%
    
    
                                           
%           ******   Books/   ********         
% Books:Contents v$VERSION$ -- Books using Wavelab
%
% This directory contains code to reproduce books using WaveLab
%
% WaveTour - Figures of the book "A Wavelet Tour of Signal Processing"
%                                Stephane Mallat, Academic Press, 1998 
% 
% This book explains the applications of wavelets to signal processing.
                                           
%           ******   Books/WaveTour/   ********         
% 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/   ********         
% Browsers:Contents v850 -- WaveLab Browsers
%
% This directory contains browsers for use with WaveLab
%
% One-D		-	One-D signal browser
% WaveTour      -       Browser for Mallat's Book
%
                                           
%           ******   Browsers/WaveTour/   ********         
% 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/One-D/   ********         
% Browsers/One-D:Contents v850 -- 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.
%
% 
    
                                           
%           ******   Continuous/   ********         
% 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/   ********         
% Datasets:Contents v850 -- 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/   ********         
% DeNoising:Contents v850 -- 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.
%
    
                                           
%           ******   Documentation/   ********         
% Documentation:Contents v850 -- 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
%
    
    
                                           
%           ******   FastAlgorithms/   ********         
% FastAlgorithms:Contents v850 -- 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/   ********         
% Fractals:Contents v850 -- 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/   ********         
% Interpolating:Contents v850 -- 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
transform
%
% PlotAIMultiRes    -   Display 1-d AI MRA
%
% AIDyadDown        -   Average-Interpolating DownSampling Operator
% AIDyadUp          -   Average-Interpolating UpSampling Operator
%
%          Utilities
%
% HCoarsen2d        -   2-d Coarsening operator based on Haar Pyramid
% HRefine2d         -   2-d Refinement based on Haar Pyramid
%
    
    
                                           
%           ******   Invariant/   ********         
% Invariant:Contents v850 -- 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/   ********         
% Median:Contents  v.850 -- 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.
% 

% 
% Copyright (c) 1997. David L. Donoho and Thomas P.Y.Yu
% 
    
                                           
%           ******   Meyer/   ********         
% Meyer:Contents  v850 -- 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/   ********         
% Orthogonal:Contents  v850 -- 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
% UpSampleN         -  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/   ********         
% Packets/One-D:Contents v850 -- 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/   ********         
% Packets/Two-D:Contents v850 -- 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
%
    
    
    
                                           
%           ******   Papers/   ********         
% Papers:Contents v850 -- 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)
%
                                           
%           ******   Pursuit/   ********         
% 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/   ********         
% TimeFrequency:Contents v850 -- 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/   ********         
% Utilities:Contents v850 -- 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
%     
    
    
                                           
%           ******   Workouts/   ********         
% Workouts:Contents v850 -- 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/   ********         
% 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/   ********         
% 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/MultiFractal/   ********         
% MultiFractal:Contents -- Continuous Wavelet Transform Workouts
%
% This directory currently consists of two scripts that illustrate
% various aspects of the continuous wavelet transform on both a
% Cantor-type signal and fractional Brownian motion.
%
% We hope to add workouts to reproduce the figures in the book by
% Arneodo et al. ("Ondelettes, Multifractals, et Turbulences,"
% Diderot Edition, Paris) and the paper by Alexandrescu et al.
% ("Detection of Geomagentic Jerks using Wavelet Analysis," 
% Journal of Geophysical Research Vol. 10, pp. 12,557-12,572).
%
% 
% MFWork01 -- CWT Analysis of Cantor Signal
% MFWork02 -- CWT Analysis of Brownian Signal
%

    
    
                                           
%           ******   Workouts/Toons/   ********         
% Toons:Contents v850 -- 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
% 
    
    

    
