Merged arithmetic for computing wavelet transforms

A variation of merged arithmetic is applied to the implementation of the wavelet transform. This approach offers a simple design trade-off between the computational accuracy and the complexity. Our analysis shows that the trade-off is a function of the input data resolution, the number of filter taps, the arithmetic precision, and the level of the wavelet transform. The design parameter can be also fixed for a given number of taps and used to determine the minimum word size for the wavelet coefficients of the transform. The key element of this approach is to introduce a “truncation” within the merged arithmetic reduction process which provides equivalent throughput with substantially less complexity. An experiment has been conducted to verify the analysis, which suggests that 24-bit merged arithmetic is required for the EZW algorithm to handle up to a level 6-wavelet transform