An analysis of Daubechies discrete wavelet transform based on algebraic integer encoding scheme

A new and novel encoding scheme of Daubechies wavelet coefficients for implementing discrete wavelet transform based on algebraic integer is proposed. This encoding technique eliminates the requirements to approximate the transformation matrix elements. Instead of approximating the matrix coefficients, we are able to obtain the exact representations for them. As a result, we achieve error-free calculations up to the final reconstruction step where we can choose an approximate substitution precision based on hardware/accuracy trade-off. A comparison between Daubechies 4 and 6 coefficients is also performed. The last part demonstrates that the new encoding technique offers better performance compared to the classical binary (fixed-point binary) design and it is also very well suited for high-speed VLSI implementation.