08 Wavelet Lifting Scheme Problems PDF

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Chair of Media Technology Technische Universität München

Multidimensional Digital Signal Processing Summer Semester 2020

Tutorial 8: The Wavelet Lifting Scheme

Problem 1: Decomposition of a PR Filter Bank into Lifting Steps The representation of the DWT as cascaded 2-channel filter bank can also be implemented in an equivalent lifting scheme. This brings about advantages in terms of computational efficiency, and facilitates systematic filter bank design altogether. In the following, we will determine the polyphase representation for the 5/3 LeGall filter bank with 1 (z + 2 + z −1 ), 4 1 G1 (z) = (−z −1 − 2 + 6z − 2z 2 − z 3 ). 4

1 (−z 2 + 2z + 6 + 2z −1 − z −2 ), 4 1 F1 (z) = (−z −2 + 2z −1 − 1), 4

G0 (z) =

F0 (z) =

Classical representation of 2-channel filter bank

The same filter bank in polyphase representation e a) Compute the polyphase matrix P(z) and its dual P(z), then verify that this is a PR filter bank. e b) Decompose P(z) into lifting steps and sketch the resulting lifting structure. c) Name at least three advantages of the lifting implementation over the filter-based approach!

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