Number theoretic techniques applied to algorithms and architectures for digital signal processing

Many of the techniques for the computation of a two-dimensional convolution of a small fixed window with a picture are reviewed. It is demonstrated that Winograd's cyclic convolution and Fourier Transform Algorithms, together with Nussbaumer's two-dimensional cyclic convolution algorithms, have a common general form. Many of these algorithms use the theoretical minimum number of general multiplications. A novel implementation of these algorithms is proposed which is based upon one-bit systolic arrays. These systolic arrays are networks of identical cells with each cell sharing a common control and timing function. Each cell is only connected to its nearest neighbours. These are all attractive features for implementation using Very Large Scale Integration (VLSI). The throughput rate is only limited by the time to perform a one-bit full addition. In order to assess the usefulness to these systolic arrays a 'cost function' is developed to compare them with more conventional techniques, such as the Cooley-Tukey radix-2 Fast Fourier Transform (FFT). The cost function shows that these systolic arrays offer a good way of implementing the Discrete Fourier Transform for transforms up to about 30 points in length. The cost function is a general tool and allows comparisons to be made between different implementations of the same algorithm and between dissimilar algorithms. Finally a technique is developed for the derivation of Discrete Cosine Transform (DCT) algorithms from the Winograd Fourier Transform Algorithm. These DCT algorithms may be implemented by modified versions of the systolic arrays proposed earlier, but requiring half the number of cells

The Deep Space Network

Tracking and data acquisition research and technology for the DSN is discussed

The deep space network

Deep Space Network progress in flight support, tracking and data acquisition research and technology, network engineering, hardware and software implementation, and operations are reported

Extending Winograd's Small Convolution Algorithm to Longer Lengths

Conference PaperFor short data sequences, Winograd's convolution algorithms attaining the minimum number of multiplications also attain a low number of additions, making them very efficient. However, for longer lengths they require a larger number of additions. Winograd's approach is usually extended to longer lengths by using a nesting approach such as the Agarwal-Cooley or Split-Nesting algorithms. Although these nesting algorithms are organizationally quite simple, they do not make the greatest use of the factorability of the data sequence length. The algorithm proposed it this paper adheres to Winograd's original approach more closely than do the nesting algorithms. By evaluating polynomials over simple matrices we retain, in algorithms for longer lengths, the basic structure and strategy of Winograd's approach

The Deep Space Network, volume 39

The functions, facilities, and capabilities of the Deep Space Network and its support of the Pioneer, Helios, and Viking missions are described. Progress in tracking and data acquisition research and technology, network engineering and modifications, as well as hardware and software implementation and operations are reported

The Deep Space Network

Progress in flight project support, tracking and data acquisition (TDA) research and technology, network engineering, hardware and software implementation, and operations are reported

Portable high-performance programs

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1999.Includes bibliographical references (p. 159-169).by Matteo Frigo.Ph.D