A multiprocessor architecture is presented using a number of Motorola DSP96002 digital signal processors in parallel with no required glue logic. It is shown how this configuration can be used efficiently to implement a parallel Jacobi algorithm. Processor overhead is practically negligible because of the DSP96002 dual bus structure, its independent DMA channels, and its host interfaces. The example discussed (eigenvalues decomposition) is only one of many applications that can benefit from the architecture. It is shown how the multiprocessing features of the DSP96002 can naturally lead to relatively inexpensive implementations of high-speed number crunchers, offering literally hundreds or even thousands of megaFLOPS in one low-power, compact system.>

The authors describe the implementation of real and complex FFT (fast Fourier transform) algorithms on the Motorola DSP96002. The DSP96002 is a general-purpose, dual-bus IEEE standard floating-point digital signal processor (DSP). At a 74-ns instruction cycle, the DSP96002 implements a 1024-point real FFT in 0.905 ms and a 1024-point complex FFT in 1.55 ms. This performance is achieved by calculating up to three floating-point results in a single instruction cycle, or 40.5 MFLOPS peak. A radix-2 FFT butterfly is executed every four cycles, an average of 33.75 IEEE MFLOPS. The instruction set and architecture of the DSP96002 provide the basis for efficient implementation of FFTs and other fast transforms, such as the discrete Walsh-Hadamard transform, discrete cosine transform, and discrete Hartley transform.>

It is shown that simple orthogonal representations exist for signals which are of a decaying, rather than purely sinusoidal nature. This orthogonality is expressed in terms of a weighting function. It is shown that alternate, nonuniform sampling techniques for representation and processing of these signals are appropriate. Using this nonuniform sampling scheme, a simple discrete representation, very much like the discrete Fourier transform, can be derived. Hence, it is pointed out that traditional, frequency-spectrum-based techniques for signal analysis may be replaced by methods that are better suited for the specific decaying signal type.>

Expressions are derived for the misadjustment in Infinite Impulse Response Adaptive filters. The decomposition method [1] for solving difference equations with randomly time-varying coefficients is thereby employed. Specifically, it is shown how higher order terms in the decomposition of the output correspond to the excess error caused by measurement noise in the coefficients. A simple example of an all-pole adaptive filter is included. It is shown that the misadjustment is largely dependent on the pole locations of the optimal filter.

The problem of estimating the time constants of real, decaying exponentials in noise is investigated. Specifically, algebraic characterization using singular value decomposition of the correlation matrix of the data is employed. An alternate, weighted minimum-norm solution, based on a Z-plane mapping, is introduced. Improvement of performance over the traditional minimum-norm solution is illustrated.

A generalized form of the matrix inversion lemma is shown which allows particular forms of this lemma to be derived simply. The relationships between this direct method for solving linear matrix equations, lower-diagonal-upper decomposition, and iterative methods such as point-Jacobi and Hotelling's method are established. The generalized form is used to derive a new factorization scheme and a new matrix inversion algorithm with a high degree of parallelism.

This paper suggests that adaptive filters can be the direct results of optimization problems, if a suitable optimization criterion is used, together with a practical set of constraints. That idea is different from traditional concepts, where adaptive algorithms are used as "real-time" approximations to an "optimal" processor. By allowing the optimal processor to be a stochastic operator, adaptive systems are introduced into the optimization process.

A stochastic fixed-point theorem is used as a basis for the study of stochastic convergence properties (in mean-squares sense) of the adaptive gradient lattice filter. Such properties include conditions on the stepsize in the adaptive algorithm and analytic expressions for the misadjustment and convergence rate.

The structure for the adaptive multichannel space-time processor which implements a likelihood ratio processor for detection of multiple slowly fluctuating scatterers in a nonstationary, anisotropic, Gaussian interference is derived. The adaptive part of the processor can be realized by multi-input, multi-output unconstrained lattice filters. This structure has the advantage that the adaptive part of the processor is determined by the spatial and temporal properties of the noise field and it is common to all of the beam-steering directions. The adaptive processor is followed by a beamsteering operator, consisting of a matrix of delay operators, which simultaneously forms a set of beams in all the desired look directions. This structure is computationally more efficient than structures based on the constrained adaptive algorithms.