Optimal wordlength assignment for the discrete wavelet transform in VLSI

Dedicated VLSI implementation of DSP functions allows unequal wordlengths to be assigned to different intermediate variables in order to trade precision for area, power and speed. The authors present a method for determining the optimal wordlengths for the filter bank tree of the Discrete Wavelet Transform (DWT). In several applications such as image or speech coding, only the lower half subband is iteratively decomposed in the filter bank tree structure until a desired frequency resolution is achieved. As a result, the roundoff noise contribution (due to finite wordlength assignment) to the highest subband can be substantially different from that of the other subbands. The fixed point roundoff error expressions for DWT are derived from a statistical model. The optimal wordlength assignment problem is then formulated as balancing the roundoff noise power for each subband, while satisfying a desired total output noise constraint. It is shown to be a Quadratic Programming (QP) problem in general. For the particular case under consideration, it is then simplified and shown to be reducible to a Constrained Least Squares (CLS) problem. A solution to this CLS problem determines the optimal wordlengths. The results illustrate that it is possible to achieve a significant reduction in the wordlength assigned to the output of the high-pass filter(s) in the analysis filter bank. A reduced wordlength in turn implies a more efficient data compression. Thus, the incorporation of precision constraints can yield additional bit-savings in applications like subband coding