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[[Wavelet]]s are often used to analyse piece-wise smooth signals.<ref>{{cite book|last1=Mallat|first1=Stéphane|title=A Wavelet Tour of Signal Processing|date=2008|publisher=Academic Press}}</ref> Wavelet coefficients can efficiently represent a signal which has led to data compression algorithms using wavelets.<ref>{{cite book |doi=10.1109/DCC.1991.213386|isbn=978-0-8186-9202-4|chapter=Data compression using wavelets: Error, smoothness and quantization|title=[1991] Proceedings. Data Compression Conference|pages=186–195|year=1991|last1=Devore|first1=R.A.|last2=Jawerth|first2=B.|last3=Lucier|first3=B.J.|s2cid=11964668
▲[[Wavelet]]s are often used to analyse piece-wise smooth signals.<ref>{{cite book|last1=Mallat|first1=Stéphane|title=A Wavelet Tour of Signal Processing|date=2008|publisher=Academic Press}}</ref> Wavelet coefficients can efficiently represent a signal which has led to data compression algorithms using wavelets.<ref>{{cite book |doi=10.1109/DCC.1991.213386|isbn=978-0-8186-9202-4|chapter=Data compression using wavelets: Error, smoothness and quantization|title=[1991] Proceedings. Data Compression Conference|pages=186–195|year=1991|last1=Devore|first1=R.A.|last2=Jawerth|first2=B.|last3=Lucier|first3=B.J.|s2cid=11964668 |chapter-url=https://www.semanticscholar.org/paper/8b93bc5d02cc102b82c17d3db9c98909275d8132}}</ref> Wavelet analysis is extended for [[multidimensional signal processing]] as well. This article introduces a few methods for wavelet synthesis and analysis for multidimensional signals. There also occur challenges such as directivity in multidimensional case.
== Multidimensional separable discrete wavelet transform (DWT) ==
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{{math| H<sub>x</sub> H<sub>y</sub> {ψ(x)<sub>h</sub>ψ(y)<sub>h</sub>} {{=}} ψ(x)<sub>g</sub>ψ(y)<sub>g</sub> }}
For the 2-D case, this is named dual tree '''[[quaternion]] wavelet transform (QWT)'''.<ref>{{cite journal|last1=Lam Chan|first1=Wai|last2=Choi|first2=Hyeokho|last3=Baraniuk|first3=Richard|title=Coherent Multiscale Image Processing Using Dual-Tree Quaternion Wavelets|journal=IEEE Transactions on Image Processing|volume=17|issue=7|pages=1069–1082|date=2008|doi=10.1109/TIP.2008.924282|pmid=18586616|bibcode=2008ITIP...17.1069C|s2cid=16789586
The total redundancy in M-D is {{math|2<sup>m</sup>}} tight frame.
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