LTFAT - Wavelets

Zdenek Prusa, 2013 - 2023.

If you use the wavelets module for a scientific work, please cite:

Z. Průša, P. L. Søndergaard, 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