Wavelets and Filter Banks

Wavelet and short-time Fourier analysis is introduced in the context of frequency decompositions. Wavelet type frequency decompositions are associated with lter banks, and using this fact, lter bank theory is used to construct multiplicity M wavelet frames and tight frames. The way in which lter banks lead to decomposition and recomposition of arbitrary separable Hilbert spaces is also described. E cient computational structures for both lter banks and wavelets are also discussed. Contact Address: Ramesh A. Gopinath Department of EE, A235 Rice University, Houston, TX-77251 Phone (713) 527-8750 x3577 email: ramesh@rice.edu This work was supported by AFOSR under grant 90-0334 funded by DARPA Appears in Wavelets: A Tutorial in Theory and Applications, ed. C.K.Chui, Academic Press WAVELETS AND FILTER BANKS R.A.Gopinath and C.S.Burrus Department of Electrical and Computer Engineering, Rice University, Houston, TX-77251 CML TR-91-20 30th September '91

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