M. Aziz

Radix-2 /spl times/ 2 /spl times/ 2 algorithm for the 3-D discrete Hartley transform

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 /spl times/ 2 /spl times/ 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.

Fast algorithm for the 2-D new Mersenne number transform

Abstract This paper introduces the development and derivations of the 2-D vector-radix algorithm for the calculation of the 2-D new Mersenne number transform. The algorithm is implemented, its arithmetic complexity is analysed and compared to the row–column approach. The vector-radix algorithm is found to be more efficient and involves fewer arithmetic operations than the row–column approach. Using random data, an example is given showing the validity of the developed algorithm and the exact nature of the transform.

Radix-4 algorithm for the new Mersenne number transform

The one-dimensional new Mersenne number transform (NMNT) was proposed for the calculation of error free convolutions and correlations for signal processing purposes. The aim of this paper is to develop the radix-4 decimation-in-time algorithm for fast calculation of the NMNT with a sequence length equal to a power of four. The arithmetic complexity of this algorithm is analysed and the number of multiplications and additions is calculated. An example is given to prove the validity of the algorithm and the exact nature of this transform.

A hybrid parallel algorithm for digital image filtering applications

The need for processing speed in digital imaging and multidimensional signal processing seems to grow ever faster as more and more power hungry applications find their way into scientific and engineering applications. In this paper we evaluate the performance of a high-speed parallel system aiming at real time applications. The parallel system utilises a 2-D hybrid decomposition algorithm that eliminates the problem of overlapping segments in the block convolution and the boundary conditions when paralleling a 2-D filter algorithm. Finally the implementation on parallel SHARC DSPs is investigated and some examples are given.

Parallelisation of the 1-D block filter algorithm to run on multiple DSPs

Parallel processing is a vital tool for many scientific and industrial applications where real time constraints apply; in many applications the use of parallel processing and multiprocessor platforms seems to be the favourable solution for achieving acceptable throughput. Hence parallel processing algorithms are vital tools to achieve a good trade off between hardware cost, system efficiency and power. In this paper, the one-dimensional generalised parallel block filter algorithm based on the overlap-add approach is implemented on multi-DSPs platform. The mathematical concept of the input stage, output stage and the generalised direct filter equation are given. Also the 1-D parallel algorithm is shown and a suitable parallel architecture is presented.

High performance 2D parallel block-filtering system for real-time imaging applications using the Sharc ADSP21060

A simple and efficient design and implementation of the two-dimensional (2D) parallel block-filtering algorithm by fast number theoretic transforms is presented. The algorithm is generalized to accommodate any filter size for optimum segmentation of the input data in order to achieve efficient filtering and optimal parallelization. The 2D algorithm is found to improve the performance of digital filtering systems by segmenting the 2D input into smaller block sizes, which are shown to be efficient and lead to highly parallel implementation. In this paper the parallel architecture of the 2D block-filtering method is presented and the implementation of fast 2D block filtering using the 2D new Mersenne number transform (2D NMNT) for digital filtering is demonstrated on a multiprocessor platform. The mathematical derivations of the input stage, output stage and the direct 2D FIR filtering equation are also given. The algorithms efficiency is tested, and new results are given showing an improved performance, as evidenced by the highly parallel algorithm structure and the use of smaller transform sizes.

A high performance 3-D parallel filtering algorithm using the vector radix fast Hartley transform

We present an efficient method for 3-D parallel digital filtering using a new parallel filtering algorithm based on the 3-D vector radix fast Hartley transform (3-D VRFHT). This method is suitable for high resolution/high speed image/video processing. The 3-D parallel algorithm is highly parallel and efficient as it overcomes the overhead and performance limitations of the block filtering method by eliminating the overlapping segments and boundary conditions in parallel filtering applications. It also lifts the restrictions on the input size for high performance in the block-filtering algorithm, as both the 3-D input data and impulse response of the system are segmented into smaller subsections. These subsections are independent and can be simultaneously processed. The algorithms structure and mathematical derivation are given and the performance of the algorithm is tested and presented using a parallel processing system with 4-DSP processors.

Three-dimensional digital filtering algorithm for parallel DSP implementation

In this paper we present a 3-D parallel filtering algorithm. This algorithm is highly parallel and efficient as it eliminates the overhead associated with the overlapping segments in the block-filtering approach. It also lifts the restrictions on the input size for high efficiency in the block-filtering algorithm, as both the 3-D input data and impulse response of the system are decimated into eight subsections each. These subsections can be simultaneously and independently processed. The results of the implementation of the 3-D parallel filtering algorithm on multiDSP platform is presented and discussed showing a high performance reflected by the highly parallel architecture and good memory distribution of the 3-D parallel algorithm.

A high performance hybrid parallel algorithm for fast calculation of 3-D convolution/correlation using the 3-D VR FHT for multi-dimensional signal processing applications

In this paper, a fast and efficient 3-D digital filtering method based on the combination of a 3-D hybrid parallel filtering algorithm and the 3-D vector radix fast Hartley transform (3-D VR FHT) is presented. This algorithm is suitable for high resolution/high speed multi-dimensional signal and image processing. The 3-D hybrid parallel algorithm is highly parallel and efficient, as it overcomes the computations overhead and performance limitations associated with the block filtering method by eliminating the overlapping blocks and boundary conditions in parallel filtering applications. It also lifts the restrictions on the input size for high performance, as both the 3-D input data and impulse response of the system are segmented into smaller sub-sections. These sub-sections are independent and can be simultaneously processed. The algorithms structure and mathematical derivation are given and the performance of the algorithm is tested and presented using a real multi-processor parallel system with 4-DSPs.

Split-radix algorithm for the new Mersenne number transform

The one-dimensional new Mersenne number transform (NMNT) was proposed for the calculation of error free convolutions and correlations for signal processing purposes. The aim of this paper is to develop the split-radix decimation-in-time algorithm for fast calculation of the one-dimensional NMNT with a sequence length equal to a power of two. The arithmetic complexity of this algorithm is analysed and the number of multiplications and additions is calculated. An example is given to prove the validity of the algorithm and the exact nature of this transform.