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

Performance analysis of Discrete Cosine Transform in Multibeamforming

Aperture arrays are widely used in beamforming applications where element signals are steered to a particular direction of interest and a single beam is formed. Multibeamforming is an extension of single beamforming, which is desired in the fields where sources located in multiple directions are of interest. Discrete Fourier Transform (DFT) is usually used in these scenarios to segregate the received signals based on their direction of arrivals. In case of broadband signals, DFT of the data at each sensor of an array decomposes the signal into multiple narrowband signals. However, if hardware cost and implementation complexity are of concern while maintaining the desired performance, Discrete Cosine Transform (DCT) outperforms DFT. In this work, instead of DFT, the Discrete Cosine Transform (DCT) is used to decompose the received signal into multiple beams into multiple directions. DCT offers simple and efficient hardware implementation. Also, while low frequency signals are of interest, DCT can process correlated data and perform close to the ideal Karhunen-Loeve Transform (KLT). To further improve the accuracy and reduce the implementation cost, an efficient technique using Algebraic Integer Quantization (AIQ) of the DCT is presented. Both 8-point and 16-point versions of DCT using AIQ mapping have been presented and their performance is analyzed in terms of accuracy and hardware complexity. It has been shown that the proposed AIQ DCT offers considerable savings in hardware compared to DFT and classical DCT while maintaining the same accuracy of beam steering in multibeamforming application