Orthogonal and Biorthogonal Filter Banks

Daubechies' extremal-phase, least-asymmetric, and best-localized wavelets, Fejér-Korovkin filters, coiflets, Han linear-phase filters, Morris minimum-bandwidth filters, Beylkin and Vaidyanathan filters, biorthogonal spline filters

Orthogonal wavelet filter banks generate a single scaling function and wavelet, whereas biorthogonal wavelet filters generate one scaling function and wavelet for decomposition, and another pair for reconstruction. The orthogonal and biorthogonal wavelet filter banks are all suitable for N-D discrete wavelet and wavelet packet analysis. Daubechies’ least-asymmetric filters have the most linear phase response of the orthogonal filters. If you require linear phase, use biorthogonal filters. To learn about the wavelets available in Wavelet Toolbox™ that are suitable for continuous wavelet analysis, see Choose a Wavelet.

Functions

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Orthogonal Wavelets

`blscalf`	Best-localized Daubechies scaling filter (Since R2022b)
`coifwavf`	Coiflet wavelet filter
`dbaux`	Daubechies wavelet filter computation
`dbwavf`	Daubechies wavelet filter
`fejerkorovkin`	Fejér-Korovkin wavelet filters
`hanscalf`	Han real orthogonal scaling filters with sum and linear-phase moments (Since R2022b)
`mbscalf`	Morris minimum-bandwidth discrete-time wavelets (Since R2022b)
`symaux`	Symlet wavelet filter computation
`symwavf`	Symlet wavelet filter

Biorthogonal Wavelets

`biorfilt`	Biorthogonal wavelet filter set
`biorwavf`	Biorthogonal spline wavelet filter
`rbiowavf`	Reverse biorthogonal spline wavelet filters

Filters and Filter Banks

`dwtfilterbank`	Discrete wavelet transform filter bank
`dtfilters`	Analysis and synthesis filters for oversampled wavelet filter banks
`isbiorthwfb`	Determine if filter bank is biorthogonal wavelet filter bank (Since R2022b)
`isorthwfb`	Determine if filter bank is orthogonal wavelet filter bank (Since R2022b)
`orthfilt`	Orthogonal wavelet filters
`qmf`	Scaling and wavelet filter
`wfilters`	Wavelet filters

Wavelet Management

`bswfun`	Biorthogonal scaling and wavelet functions
`wavefun`	Wavelet and scaling functions
`wavefun2`	Wavelet and scaling functions 2-D
`waveinfo`	Wavelets information
`wavemngr`	Wavelet manager

Topics

Choose a Wavelet
Learn criteria for choosing the right wavelet for your application.
Critically-Sampled Wavelet Reconstruction
Understand how to reconstruct signals from wavelet transformed data.
Add Quadrature Mirror and Biorthogonal Wavelet Filters
This example shows how to add an orthogonal quadrature mirror filter (QMF) pair and biorthogonal wavelet filter quadruple to Wavelet Toolbox™.
Construct Perfect Reconstruction Biorthogonal Filter Bank
Take an expression of a biorthogonal wavelet filter pair and create a perfect reconstruction biorthogonal wavelet filter bank.
Scaling Function and Wavelet
Show how the number of vanishing moments affects smoothness biorthogonal filter pair.