## Introduction

What do I propose to show you? (Certainly not all in one post.)

My understanding is neither complete nor rigorous. But wavelets and scaling functions, and their coefficients g and h, respectively, have a lot of properties. I want to sort them out.

I’m not trying for rigor. (Heresy!) I’m laying things out on a table so I can begin to relate them to each other.

The properties which I want to show you seem to fall into 4 categories.

- Where do the dilation equation and wavelets come from?
- What can we deduce from the dilation equation?
- What can we deduce from the requirement that the scaling function and its integer translates be orthogonal?
- A few things that I really, really don’t understand yet.

There is a fair bit of repetition in here. In particular, it seemed worthwhile to repeat things within the examples. Read the rest of this entry »