## Introduction

I am going to do something a little risky. I’m going to show you how to approximate a particular function – the Daubechies D4 scaling function – even though I am a little shaky on the justification.

If you have ever looked at wavelets, you have probably seen this picture. It is a quintessential “father wavelet” – more commonly, I think, called a “scaling function”.

I want to compute it; this is not relevant to computing wavelet coefficients, because just as this is computed from its definition, so wavelet coefficients which depend on it and its associated wavelets are computed from its definition rather than from its values.

Talking about this is much like talking about one of one’s favorite movies: what makes something one of my favorite movies is deeply personal, and it doesn’t usually affect my friends that way. To them, at best, it’s just another movie; at worst, they think it is a dud. Read the rest of this entry »