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Chrestenson generalized Walsh transform factorizations for parallel processing imbedded implementations on field programmable gate arrays are presented. This general base transform, sometimes referred to as the Discrete Chrestenson transform, has received special attention in recent years. In fact, the Discrete Fourier transform and Walsh-Hadamard transform are but special cases of the Chrestenson generalized Walsh transform. Rotations of a base- p hypercube, where p is an arbitrary integer, are shown to produce dynamic contention-free memory allocation, in processor architecture. The approach is illustrated by factorizations involving the processing of matrices of the transform which are function of four variables. Parallel operations are implemented matrix multiplications. Each matrix, of dimension N × N, where N = p , n integer, has a structure that depends on a variable parameter k that denotes the iteration number in the factorization process. The level of parallelism, in the form of M = p processors can be chosen arbitrarily by varying m between zero to its maximum value of n − 1. The result is an equation describing the generalised parallelism factorization as a function of the four variables n, p, k and m. Applications of the approach are shown in relation to configuring field programmable gate arrays for digital signal processing applications. [ABSTRACT FROM AUTHOR]

Recent advances in computer, robotics and Internet technologies have enhanced the importance of digital signal processing tools, parallel processing and multi-processing research. The recent developments in microelectronics and fiber optics technologies have called for faster digital signal processors for data compression, coding, secure communication, and multimedia applications. Man-machine interaction, the adaptive control of fast moving objects, spaceships and increasingly intelligent and complex robotics have motivated research in faster computers and massively parallel processors. Adaptive on-line system identification of fast time varying systems is a problem that has received greater attention in recent years. Generalized spectral analysis transforms and factorizations thereof lead to highly efficient tools for parameter identification in the presence of noise and highly efficient coding techniques. This chapter presents novel spectral analysis definitions and general base parallel processors for the implementation of DSP algorithms, and modern generalized spectral analysis transforms destined for such high-speed applications. The Weighted Laplace and z -transform generalized spectra are shown to unmask the poles and zeros of finite duration continuous time and discrete time systems. The Generalized Chrestenson-Walsh transform is shown to be a generalization of the Fourier Transform and as such provides a wider range of coding and multimedia compression possibilities. Massive parallelism is implemented using general base hypercube transformations. [ABSTRACT FROM AUTHOR]

Introduces a series of articles on digital signal processing and control including the spectral analysis definitions and general base parallel processors for the implementation of digital signal processing algorithms.