How to reconstruct a signal using the Discrete Haar Wavelet transform?

[XcKyle93]

Homework Statement

Hi, for a project for school, I need to implement the Discrete Haar Wavelet Transform to compress an audio signal. This would be fine and dandy, but I do not really understand how to use the the DHWT. Could anyone direct me towards some resources that would be very helpful in my understanding? If someone could provide a step-by-step algorithm that goes through the deconstruction and reconstruction of the signal, that would be nice. The textbook that I'm using is a math textbook, so it is more interested in proving properties of the filters & wavelets instead giving examples and exercises. This is great, until I actually need to apply it towards something.

Homework Equations

I know that there are vector spaces V and W that are orthogonal to each other; V is associated with the scaling function ∅, W is associated with the mother wavelet ψ. I think the first step in the DHWT is to pick a resolution j, but beyond that I don't understand.

The Attempt at a Solution

 

[NascentOxygen]

Hi XcKyle93. I don't know anything about the DHWT, but has a google search not turned up information to help you? There seems to be plenty, at various levels. http://www.whydomath.org/node/wavlets/hwt.html

Good luck!

 

[XcKyle93]

Sorry, I had seen that resource and it's much different from what we've done in class.