An algebraic integer based encoding scheme for implementing Daubechies discrete wavelet transforms

Abstract

A novel approach for implementing a discrete wavelet transform (DWT), based on algebraic integer encoding of Daubechies wavelet coefficients is proposed. These encoding techniques eliminate the requirement to approximate the matrix element; rather they use algebraic 'placeholders' for them. Using these mapping techniques, we were able to obtain error-free calculations up to the final reconstruction step, where we can choose an appropriate approximate substitution precision based on hardware/accuracy trade-offs. This paper also demonstrate the new encoding technique offers better performance compared to classical fixed-point binary designs and that it is well suited for high-speed VLSI implementation.