A construction of wavelets

Abstract

In this note, given a multiresolution analysis, we construct a class of four-coefficient scaling filters using only elementary algebraic operations. The method of construction also reveals that the sum conditions ∑a _even=∑a _odd=1 can also be verified without referring to the vanishing moment property.

Keywords:

• A construction of wavelets
• Daubechies wavelet
• an algebraic construction

Keywords:

• AMS Subject Classifications: 42C40
• 65C40