Proposed prime number Hartley transform implementation usingtransversal filter type structures

It is shown that the discrete Hartley transform can be mapped to a special hardware structure suitable for implementation, using transversal filter type structures, when the number of the input data samples is prime. This transform appears to be simpler and faster than the prime number Fourier transform calculated by the same approach     

Fast algorithm for the 3-D DCT-II

Recently, many applications for three-dimensional (3-D) image and video compression have been proposed using 3-D discrete cosine transforms (3-D DCTs). Among different types of DCTs, the type-II DCT (DCT-II) is the most used. In order to use the 3-D DCTs in practical applications, fast 3-D algorithms are essential. Therefore, in this paper, the 3-D vector-radix decimation-in-frequency (3-D VR DIF) algorithm that calculates the 3-D DCT-II directly is introduced. The mathematical analysis and the implementation of the developed algorithm are presented, showing that this algorithm possesses a regular structure, can be implemented in-place for efficient use of memory, and is faster than the conventional row-column-frame (RCF) approach. Furthermore, an application of 3-D video compression-based 3-D DCT-II is implemented using the 3-D new algorithm. This has led to a substantial speed improvement for 3-D DCT-II-based compression systems and proved the validity of the developed algorithm.     

Power-delay-area efficient modulo 2/sup n/+1 adder architecture for RNS

A new modulo 2/sup n/+1 adder architecture based on the ELM addition algorithm is introduced. A simplification to an existing modulo 2/sup n/+1 addition algorithm is also presented. VLSI implementations using 130 nm CMOS technology demonstrate the superiority of the proposed adder over existing designs in the literature.     

New transform using the Mersenne numbers

Number theoretic transforms (NTTs) find applications in the calculation of convolutions and correlations. They can perform these calculations without introducing additional noise in the processing due to rounding or truncation. Among all NTTs, Fermat and Mersenne number transforms have been given particular attention. However, the main drawback of these transforms is the inconvenient word length for the Fermat number transforms, and lack of fast algorithms for the Mersenne number transforms. The authors aim to introduce a new real transform defined modulo Mersenne numbers with long transform length equal to a power of two. This is achieved by dropping the condition that α_ should be ±2 and using a new definition for NTTs that departs from the usual Fourier-like definition. The new transform is suitable for fast algorithms. It has the cyclic convolution property and hence can be applied to the calculation of convolutions and correlations. The transform is extended to the two-dimensional case and then generalised to the multidimensional case. Examples are given for the one-dimensional and two-dimensional cases     

Novel Power-Delay-Area-Efficient Approach to Generic Modular Addition

Modular adders are fundamental arithmetic components typically employed in residue number system (RNS)-based digital signal processing (DSP) systems. They are widely used in modular multipliers and residue-to-binary converters and in implementing other residue arithmetic operations such as scaling. In this paper, a methodology for designing power-delay-area-efficient modular adders based on carry propagate addition is presented. The binary representational characteristics of the modulus are exploited to allow the sharing of hardware in a fast modular adder topology. VLSI implementation results using 0.13- standard-cell technology, together with a theoretical analysis, show that this approach produces adders that offer efficient tradeoffs when compared with the fastest through to the smallest generic modular adders in the literature.     

Radix-2 × 2 × 2 algorithm for the 3-D discrete Hartleytransform

The discrete Hartley transform (DHT) has proved to be a valuable tool in digital signal/image processing and communications and has also attracted research interests in many multidimensional applications. Although many fast algorithms have been developed for the calculation of one- and two-dimensional (1-D and 2-D) DHT, the development of multidimensional algorithms in three and more dimensions is still unexplored and has not been given similar attention; hence, the multidimensional Hartley transform is usually calculated through the row-column approach. However, proper multidimensional algorithms can be more efficient than the row-column method and need to be developed. Therefore, it is the aim of this paper to introduce the concept and derivation of the three-dimensional (3-D) radix-2 × 2 × 2 algorithm for fast calculation of the 3-D discrete Hartley transform. The proposed algorithm is based on the principles of the divide-and-conquer approach applied directly in 3-D. It has a simple butterfly structure and has been found to offer significant savings in arithmetic operations compared with the row-column approach based on similar algorithms     

New two dimensional transform

A new two dimensional transform is introduced which uses the Mersenne primes. It is symmetric, has a fast algorithm and has the convolution property. Thus, it is very suitable for the calculation of two dimensional, error free convolutions and correlations.<>     

Channel prediction for precoded spatial multiplexing multiple-input multiple-output systems in time-varying fading channels

Conventional precoded spatial multiplexing multiple-input multiple-output (MIMO) systems using limited feedback are mainly based on the notion of time invariant channels throughout transmission. Consequently, the precoding matrix can be found during the training symbols and used over the subsequent data symbols. In this study, the authors consider a more practical system where the channel varies from one block of symbols to another. In such a scenario, the precoding matrix designed at the receiver based on the previous training symbols becomes outdated, which results in significant system performance degradation. In order to avoid this problem and reduce performance degradation, the authors propose the use of a Kalman filter linear predictor at the receiver to provide the transmitter with the precoding matrix for the next block of symbols. The performance of this method is assessed using computer simulation, and the obtained results for the proposed channel prediction demonstrate improved bit error rate performance for time-varying Rayleigh fading channels.     

Video compression employing algorithm using temporal blockingstructures

A new video compression algorithm based on a temporal blocking structure, rather than the more conventional spatial blocking structure, is described. This blocking structure forms the basis of an adaptive vector quantisation (VQ) algorithm, the performance of which is then compared with a similar adaptive VQ scheme based on a spatial blocking structure