User manual MATHWORKS WAVELET TOOLBOX RELEASE NOTES

[. . . ] Please see www. mathworks. com/patents for more information. Contents Summary by Version . Version 4. 6 (R2010b) Wavelet Toolbox Software Version 4. 5 (R2010a) Wavelet Toolbox Software 1 4 6 8 9 10 11 13 14 16 18 19 20 21 22 . . . . . . Version 4. 4 (R2009a) Wavelet Toolbox Software Version 4. 3 (R2008b) Wavelet Toolbox Software Version 4. 2 (R2008a) Wavelet Toolbox Software Version 4. 1 (R2007b) Wavelet Toolbox Software Version 4. 0 (R2007a) Wavelet Toolbox Software Version 3. 1 (R2006b) Wavelet Toolbox Software . . . . . . Version 3. 0. 3 (R14SP3) Wavelet Toolbox Software Version 3. 0. 2 (R14SP2) Wavelet Toolbox Software Version 3. 0. 1 (R14SP1) Wavelet Toolbox Software . . . . [. . . ] See conofinf for details. Wavelet Cross Spectrum and Coherence In R2010b, you can estimate the wavelet cross spectrum and wavelet coherence of two time series. The wavelet cross spectrum and coherence provide wavelet-based alternatives for the Fourier-based cross spectrum and 4 Version 4. 6 (R2010b) Wavelet ToolboxTM Software coherence. Using a complex-valued analyzing wavelet, you can also examine intervals in the time-scale plane where the two time series exhibit common phase behavior. See wcoher and the new demo Wavelet Coherence for details. Wavelet Packet Spectrum In R2010b, you can compute the wavelet packet spectrum with wpspectrum. The wavelet packet spectrum provides a time-frequency analysis of a time series. The wavelet packet spectrum is useful as wavelet-based counterpart of the short-time Fourier transform. Natural and Frequency Ordering of Wavelet Packet Terminal Nodes In R2010b, you can order the wavelet packet transform terminal nodes by natural (Payley) or frequency (sequency) order. See otnodes for details. Image and Signal Approximation Quality Metrics In R2010b, you can measure the quality of your signal or image approximation using a number of widely-used quality metrics. These metrics include: the peak signal-to-noise ratio (PSNR), the mean square error (MSE), the maximum absolute error, and the energy ratio of the approximation to the original. See measerr for details. 5 Wavelet ToolboxTM Release Notes Version 4. 5 (R2010a) Wavelet Toolbox Software This table summarizes what is new in Version 4. 5 (R2010a): New Features and Changes Yes Version Compatibility Considerations No Fixed Bugs and Known Problems Bug Reports Includes fixes Related Documentation at Web Site Printable Release Notes: PDF Current product documentation New features and changes introduced in this version are · "3-D Discrete Wavelet Transform" on page 6 · "Nondecimated Wavelet Transform" on page 6 · "New Denoising Function" on page 7 3-D Discrete Wavelet Transform This release adds new functions and a GUI to support the 3-D discrete wavelet transform. This new functionality lets you decompose, analyze, and display a 3-D object using a different wavelet for each dimension. A demo (wavelet3ddemo) is also included. Nondecimated Wavelet Transform New nondecimated wavelet transform functions support signals of arbitrary size and different extension modes. Previous functionality had two limitations: signal length had to equal a power of 2 and the only allowable extension mode was periodized. A demo (ndwtdemo) is also included. 6 Version 4. 5 (R2010a) Wavelet ToolboxTM Software New Denoising Function The new cmddenoise function uses interval-dependent denoising to compute the denoised signal and coefficients. This allows you to apply different denoising thresholds to different portions of the signal, which is typically nonuniform. You can also export thresholds from the GUI and use them in the cmddenoise function. The toolbox includes a denoising demo (cmddenoise). 7 Wavelet ToolboxTM Release Notes Version 4. 4. 1 (R2009b) Wavelet Toolbox Software This table summarizes what is new in Version 4. 4. 1 (R2009b): New Features and Changes No Version Compatibility Considerations No Fixed Bugs and Known Problems Bug Reports Includes fixes Related Documentation at Web Site Printable Release Notes: PDF Current product documentation 8 Version 4. 4 (R2009a) Wavelet ToolboxTM Software Version 4. 4 (R2009a) Wavelet Toolbox Software This table summarizes what is new in Version 4. 4 (R2009a): New Features and Changes Yes Details below Version Compatibility Considerations No Fixed Bugs and Known Problems Bug Reports Includes fixes Related Documentation at Web Site Printable Release Notes: PDF New features introduced in this version are three new demos. New Demos The toolbox now includes three new demos: Adding a New Wavelet Wavelet Interval-dependant Denoising Wavelet Scalograms 9 Wavelet ToolboxTM Release Notes Version 4. 3 (R2008b) Wavelet Toolbox Software This table summarizes what is new in Version 4. 3 (R2008b): New Features and Changes Yes Details below Version Compatibility Considerations No Fixed Bugs and Known Problems Bug Reports Includes fixes Related Documentation at Web Site Printable Release Notes: PDF New features and changes introduced in this version are · "True Image Compression Support" on page 10 · "New Demo" on page 10 True Image Compression Support The new wcompress functions lets you compress 2-D image data. You can also pass the structure produced by cwt directly to the new wscalogram function. Scalograms show the percentage of energy in each wavelet coefficient. Constructing Clusters from Hierarchical Cluster Trees You can now construct clusters from hierarchical cluster trees in multisignal analysis using the new mdwtcluster function. 13 Wavelet ToolboxTM Release Notes Version 4. 0 (R2007a) Wavelet Toolbox Software This table summarizes what's new in Version 4. 0 (R2007a): New Features and Changes Yes Details below Version Compatibility Considerations No Fixed Bugs and Known Problems Bug Reports Includes fixes Related Documentation at Web Site Printable Release Notes: PDF New features and changes introduced in this version are · "1-D Multisignal Analysis, Compression, and Denoising Added" on page 14 · "1-D Multisignal Wavelet and Clustering Added" on page 15 · "Wavelet 1-D Multisignal Analysis GUI Added" on page 15 1-D Multisignal Analysis, Compression, and Denoising Added The following command-line functions for 1-D multisignal analysis, compression, and denoising have been added to the toolbox: mswcmp mswcmpscr mswcmptp mswden mswthresh Multisignal 1-D compression using wavelets. Performs Multisignal 1-D thresholding. 14 Version 4. 0 (R2007a) Wavelet ToolboxTM Software 1-D Multisignal Wavelet and Clustering Added The following command-line functions for 1-D multisignal wavelets and clustering have been added to the toolbox: chgwdeccfs mdwtdec mdwtrec wdcenergy Change Multisignal 1-D decomposition coeffs Multisignal 1-D wavelet decomposition Multisignal 1-D wavelet reconstruction. Multisignal 1-D decomposition energy repartition Note Clustering analyses require that Statistics Toolbox is installed. Wavelet 1-D Multisignal Analysis GUI Added A graphical user interface for 1-D multisignal analysis has been added. [. . . ] From the command line, use the wfusimg and wfusmat functions to fuse two images and fuse two matrices or arrays, respectively. Fractional Brownian Generation 1-D Tool Added The Fractional Brownian Generation 1-D tool performs the random generation of fractional Brownian motion, which is a useful model for Internet traffic and financial series. From the command line, use the wfbm 22 Version 3. 0 (R14) Wavelet ToolboxTM Software and wfbmesti functions to synthesize and perform parameter estimation of fractional Brownian motion, respectively. Lifting Methods Added You can use lifting methods to design new wavelets. The new lifting methods also allow integer-to-integer wavelet transforms and transforms using different length decomposition high-pass and low-pass filters. Five groups of new lifting functions are included in Wavelet Toolbox, Version 3. 0: · Key lifting scheme structures - addlift--Add primal or dual elementary lifting steps to a lifting scheme displs--Display a lifting scheme lsinfo--Information about lifting schemes · Biorthogonal quadruplets of filters bswfun--Compute and plot biorthogonal "scaling and wavelet" functions filt2ls--Transform a quadruplet of filters to a lifting scheme liftfilt--Apply elementary lifting steps on quadruplet of filters ls2filt--Transform a lifting scheme to a quadruplet of filters · Orthogonal or biorthogonal ("true") wavelets and "lazy" wavelets. liftwave--Provides lifting scheme associated to a wavelet wave2lp--Provides Laurent polynomials associated to a wavelet wavenames--Provides wavelet names available for LWT · Direct and inverse Lifting Wavelet Transform (LWT) lwt--1-D Lifting Wavelet Transform lwt2--2-D Lifting Wavelet Transform lwtcoef--Extract or reconstruct 1-D LWT wavelet coefficients lwtcoef2--Extract or reconstruct 2-D LWT wavelet coefficients ilwt--Inverse 1-D Lifting Wavelet Transform ilwt2--Inverse 2-D Lifting Wavelet Transform 23 Wavelet ToolboxTM Release Notes · Laurent polynomials and matrices (see Note below) - laurmat--Constructor for the class LM of Laurent Matrices laurpoly--Constructor for the class LP of Laurent Polynomials Compatibility Consideration If you saved laurmat or laurpoly objects using the names lm or lp, respectively, in the Beta release, you must rename them to laurmat or laurpoly, respectively, in this release of Wavelet Toolbox 3. 0. Speed Enhancements Many functions, including those involving decomposition and reconstruction, have been enhanced so they run more efficiently. New Extension Modes for DWT Four new extension modes are available for dwt, which allows specifying half- or whole-point symmetry, or half- or whole-point anti-symmetry. [. . . ]