An algebraic integer based encoding scheme for implementing Daubechies Discrete Wavelet Transforms

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 elements; rather they use algebraic 'placeholders' for them. Using this mapping techniques, we are 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 demonstrates that 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.