Feb. 2, 2010

1 / 8

# Feb. 2, 2010 - PowerPoint PPT Presentation

Feb. 2, 2010. Introduction to Lifting Wavelet Transform (computationally efficient filterbank implementation) and Homework 3. Lazy Wavelet Transform-I. x 1 : even samples of x[n] and x 2 = x odd [n-1] x'[n] = x[n-1] It is lazy because it does not filter the input signal.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about 'Feb. 2, 2010' - dava

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Feb. 2, 2010Introduction to Lifting Wavelet Transform (computationally efficient filterbank implementation)and Homework 3
Lazy Wavelet Transform-I
• x1: even samples of x[n] and x2 = xodd[n-1]
• x'[n] = x[n-1]
• It is lazy because it does not filter the input signal
Lazy Wavelet Transform-II
• x1: even samples; x2: odd samples of x[n]
• x'[n] = x[n]
• It is lazy because it does not filter the input signal
Lifting Idea
• Use filters in the down-sampled rate:
• Perfect reconstruction: x'[n] = x[n-1]
• You can add more branches and filters
• You can use Noble identity
Example: Halfband filters
• H(z)+H(-z) = 1 =>
• where
Example: Both low- and highpass filters:
• Analysis filterbank:
• Synthesis filterbank:
Lifting summary:
• Computationally efficient ! (Don't compute the samples that you are going to drop during down-sampling)
• Perfect reconstruction property is trivially true
• It is used in JPEG-2000 image coding standard
• We will discuss Lifting later in more detail: Theorem (Sweldens and Daubechies): Every perfect reconstruction filterbank can be implemented using lifting stages
Homework 3
• Show that lazy wavelet transforms achieve perfect reconstruction
• a) Implement a 2-channel Perfect Reconstruction Filter Bank (PRFB) using Matlab
• b) Apply an input signal to your PRFB and show that your filter reconstructs the input. Plot the subsignals.