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% LTFAT - Wavelets
%
% Zdenek Prusa, 2013 - 2018.
%
% If you use the wavelets module for a scientific work, please cite:
%
% Z. Průša, P. L. Soendergaard, and P. Rajmic. “Discrete Wavelet Transforms in the Large
% Time-Frequency Analysis Toolbox for MATLAB/GNU Octave.” ACM Trans. Math. Softw. 42, 4,
% Article 32, 2016. DOI: 10.1145/2839298
%
% Basic analysis/synthesis
% FWT - Fast Wavelet Transform
% IFWT - Inverse Fast Wavelet Transform
% FWT2 - 2D Fast Wavelet Transform
% IFWT2 - 2D Inverse Fast Wavelet Transform
% UFWT - Undecimated Fast Wavelet Transform
% IUFWT - Inverse Undecimated Fast Wavelet Transform
% FWTLENGTH - Length of Wavelet system to expand a signal
% FWTCLENGTH - Lengths of the wavelet coefficient subbands
%
% Advanced analysis/synthesis
% WFBT - Transform using general Wavelet Filter Bank Tree
% IWFBT - Inverse transform using general Wavelet Filter Bank Tree
% UWFBT - Undecimated transform using general Wavelet Filter Bank Tree
% IUWFBT - Inverse Undecimated transform using general Wavelet Filter Bank Tree
% WPFBT - Wavelet Packet Transform using general Wavelet Filter Bank Tree
% IWPFBT - Inverse Wavelet Packet Transform using general Wavelet Filter Bank Tree
% UWPFBT - Undecimated Wavelet Packet Transform using general Wavelet Filter Bank Tree
% IUWPFBT - Inverse Undecimated Wavelet Packet Transform using general Wavelet Filter Bank Tree
% WPBEST - Best Tree selection
% WFBTLENGTH - Length of Wavelet filter bank system to expand a signal
% WFBTCLENGTH - Lengths of Wavelet filter bank coefficient subbands
% WPFBTCLENGTH - Lengths of Wavelet Packet transform coefficient subbands
%
% Dual-tree complex wavelet transform
% DTWFB - Dual-Tree Wavelet Filter Bank
% IDTWFB - Inverse Dual-Tree Wavelet Filter Bank
% DTWFBREAL - Dual-Tree Wavelet Filter Bank for real-valued signals
% IDTWFBREAL - Inverse Dual-Tree Wavelet Filter Bank for real-valued signals
%
% Wavelet Filterbank trees manipulation
% WFBTINIT - Wavelet Filter Bank tree structure initialization
% DTWFBINIT - Dual-Tree wavelet filter bank structure initialization
% WFBTPUT - Puts node (basic filter bank) to the specific tree coordinates
% WFBTREMOVE - Removes node (basic filter bank) from the specific tree coordinates
% WFBT2FILTERBANK - WFBT or FWT non-iterated filter bank using the multi-rate identity
% WPFBT2FILTERBANK - WPFBT non-iterated filter bank using the multi-rate identity
% DTWFB2FILTERBANK - DTWFB or DTWFBREAL non-iterated filter bank
% FWTINIT - Basic Wavelet Filters structure initialization
%
% Frame properties of wavelet filter banks:
% WFBTBOUNDS - Frame bounds of WFBT and FWT (or UWFBT and UFWT)
% WPFBTBOUNDS - Frame bounds of WPFBT or UWPFBT
% DTWFBBOUNDS - Frame bounds of DTWFB
%
% Plots
% PLOTWAVELETS - Plot wavelet coefficients
% WFILTINFO - Plot wavelet filters impulse and frequency responses and approximation of scaling and wavelet functions
% WFILTDTINFO - Plot the same as WFILTINFO but for dual-tree wavelet transform
%
% Auxilary
% WAVFUN - Approximate of the continuous scaling and wavelet functions
% WAVCELL2PACK - Changes wavelet coefficient storing format
% WAVPACK2CELL - Changes wavelet coefficient storing format back
%
% Wavelet Filters defined in the time-domain
% WFILT_ALGMBAND - An ALGebraic construction of orthonormal M-BAND wavelets with perfect reconstruction
% WFILT_CMBAND - M-Band cosine modulated wavelet filters
% WFILT_COIF - Coiflets
% WFILT_DB - DauBechies orthogonal filters (ortonormal base)
% WFILT_DDEN - Double-DENsity dwt filters (tight frame)
% WFILT_DGRID - Dense GRID framelets (tight frame, symmetric)
% WFILT_HDEN - Higher DENsity dwt filters (tight frame, frame)
% WFILT_LEMARIE - Battle and Lemarie quadrature filters
% WFILT_MATLABWRAPPER - Wrapper of the wfilters function from the Matlab Wavelet Toolbox
% WFILT_MBAND - M-band filters
% WFILT_REMEZ - Wavelet orthonogal filters based on the Remez Exchange algorithm
% WFILT_SYMDS - SYMmetric wavelet Dyadic Siblings (frames)
% WFILT_SPLINE - Biorthogonal spline wavelet filters
% WFILT_SYM - Least asymmetric Daubechies wavelet filters
% WFILT_SYMDDEN - Symmetric Double-DENsity dwt filters (tight frame)
% WFILT_SYMORTH - Symmetric nearly-orthogonal and orthogonal nearly-symmetric wav. filters
% WFILT_SYMTIGHT - Symmetric nearly shift-invariant tight frame wavelets
% WFILT_QSHIFTA - First tree filters from WFILTDT_QSHIFT
% WFILT_QSHIFTB - Second tree filters from WFILTDT_QSHIFT
% WFILT_ODDEVENA - First tree filters from WFILTDT_ODDEVEN
% WFILT_ODDEVENB - Second tree filters from WFILTDT_ODDEVEN
% WFILT_OPTSYMA - First tree filters from WFILTDT_OPTSYM
% WFILT_OPTSYMB - Second tree filters from WFILTDT_OPTSYM
% WFILT_DDENA - First tree filters from WFILTDT_DDEN
% WFILT_DDENB - Second tree filters from WFILTDT_DDEN
%
% Dual-Tree Filters
% WFILTDT_QSHIFT - Kingsbury's quarter-shift filters
% WFILTDT_OPTSYM - Optimizatized Symmetric Self-Hilbertian Filters
% WFILTDT_ODDEVEN - Kingsbury's symmetric odd and even biorthogonal filters
% WFILTDT_DDEN - Double-density dual-tree filters
%
% For help, bug reports, suggestions etc. please visit
% http://github.com/ltfat/ltfat/issues
%
% Url: http://ltfat.github.io/doc/wavelets/Contents.html
% Copyright (C) 2005-2016 Peter L. Soendergaard <peter@sonderport.dk>.
% This file is part of LTFAT version 2.3.1
%
% This program is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
%
% This program is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with this program. If not, see <http://www.gnu.org/licenses/>.
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