CORDIC (COordinate Rotation DIgital Computer) is a well known algorithm using simple adders and shifters to evaluate various elementary functions. Thus, CORDIC is suitable for the design of high performance chips using VLSI technology. In this paper, a complete analysis of the computation error of both the (conventional) CORDIC algorithm and the CORDIC algorithm with expanded convergence range is derived to facilitate the design task. The resulting formulas regarding the relative and absolute approximation errors and the truncation error are summarized in the tabular form. As the numerical accuracy of CORDIC processors is determined by the word length of operands and the number of iterations, three reference tables are constructed for the optimal choice of these numbers. These tables can be used to facilitate the design of cost-effective CORDIC processors in terms of areas and performances. In addition, two design examples: singular value decomposition (SVD) and lattice filter for digital signal processing systems are given to demonstrate the goal and benefit of the derived numerical analysis of CORDIC.

In this paper, we propose an efficient method for rearranging the wavelet packet coefficients of an image to form hierarchical trees, by which the well known SPIHT algorithm can be applied. For images with textures, the high frequency wavelet coefficients are likely to become significant after several code passes of SPIHT, which degrades substantially the coding performance. As a result, the high frequency wavelet coefficients representing most of the high detail content of images need to be decomposed into wavelet packet coefficients for a further exploitation. The proposed rearrangement scheme has been applied to the highest frequency wavelet packet coefficients of images. Experimental results show that the performance of SPIHT can be improved, especially for fingerprint images.

Embedded zero-tree coding in wavelet domain has drawn a lot of attention for image compression applications. Among noteworthy zero-tree algorithms is the set partitioning in hierarchical trees (SPIHT) algorithm. For images with textures, high frequency wavelet coefficients are likely to become significant after a few scan passes of SPIHT, and therefore the coding results are often insufficient. It is desirable that the low frequency and high frequency components of an image are coded using different strategies. In this paper, we propose a hybrid algorithm using the SPIHT and EBC (embedded block coding) to code low frequency and high frequency wavelet coefficients, respectively; the intermediate coding results of low frequency coefficients are used to facilitate the coding operation of high frequency coefficients. Experimental results show that the coding performance can be significantly improved by the hybrid SPIHT-EBC algorithm.

Embedded zero-tree image coding in wavelet domain has drawn a lot of attention. Among noteworthy algorithms is the set partitioning in hierarchical trees (SPIHT). Typically, most of images' energy is concentrated in low frequency subbands. For an image with textures, however many middle-high frequency wavelet coefficients are likely to become significant in the early passes of SPIHT; thus the coding results are often insufficient. Middle and high frequency subbands of images may demand further decompositions using adaptive basis functions. As wavelet packet transform offers a great diversity of basis functions, we propose a quad-tree based adaptive wavelet packet transform to construct adaptive wavelet packet trees for zero-tree image coding. Experimental results show that coding performances can be significantly improved especially for fingerprints images.