On the Error-Free Computation of Fast Cosine Transform

We extend our previous work into error-free representations of transform basis functions by presenting a novel error-free encoding scheme for the fast implementation of a Linzer-Feig Fast Cosine Transform (FCT) and its inverse. We discuss an 8x8 L-F scaled Discrete Cosine Transform where the architecture uses a new algebraic integer quantization of the 1-D radix-8 DCT that allows the separable computation of a 2-D DCT without any intermediate number representation conversions. The resulting architecture is very regular and reduces latency by 50% compared to a previous error-free design, with virtually the same hardware cost.

Multiplierless DCT Algorithm for Image Compression Applications

This paper presents a novel error-free (infinite-precision) architecture for the fast implementation of 8x8 2-D Discrete Cosine Transform. The architecture uses a new algebraic integer encoding of a 1-D radix-8 DCT that allows the separable computation of a 2-D 8x8 DCT without any intermediate number representation conversions. This is a considerable improvement on previously introduced algebraic integer encoding techniques to compute both DCT and IDCT which eliminates the requirements to approximate the transformation matrix ele- ments by obtaining their exact representations and hence mapping the transcendental functions without any errors. Apart from the multiplication-free nature, this new mapping scheme fits to this algorithm, eliminating any computational or quantization errors and resulting short-word-length and high-speed-design.

An Algorithm for Fresnel Diffraction Computing Based on Fractional Fourier Transform

The fractional Fourier transform (FrFT) is used for the solution of the diffraction integral in optics. A scanning approach is proposed for finding the optimal FrFT order. In this way, the process of diffraction computing is speeded up. The basic algorithm and the intermediate results at each stage are demonstrated.