This paper presents a new systolic array implementation of the Kalman filter that is not excessive in either hardware or computation steps. For a dynamic system with N states and M observation components, the array us...
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This paper presents a new systolic array implementation of the Kalman filter that is not excessive in either hardware or computation steps. For a dynamic system with N states and M observation components, the array uses N(N+1) processors and about 4N+6M computation steps. In some applications, it is also required that the processing system continue to function even after some of the components of the system fail. The Kalman filter systolic array is extended to one that is tolerant of faults in the processing elements of the array by using techniques of algorithm-based fault tolerance. Overhead for fault tolerance is about 47% additional hardware and 17% additional computational steps in the example of radar tracking.
A new parallel Jacobi-like algorithm for computing the eigenvalues of a general complex matrix is presented. The asymptotic convergence rate of this algorithm is provably quadratic and this is also demonstrated in num...
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A new parallel Jacobi-like algorithm for computing the eigenvalues of a general complex matrix is presented. The asymptotic convergence rate of this algorithm is provably quadratic and this is also demonstrated in numerical experiments. The algorithm promises to be suitable for real-time signalprocessing applications. In particular, the algorithm can be implemented using n2/4 processors, taking O (n log2 n) time for random matrices.
Effective signal detection and feature extraction in noisy environments generally depend on exploiting some knowledge of the signal. When the signal is exactly known, the matched filter is the optimum signal processin...
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We develop an algorithm for adaptively estimating the noise subspace of a data matrix, as is required in signalprocessing applications employing the 'signal subspace' approach. The noise subspace is estimated...
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We develop an algorithm for adaptively estimating the noise subspace of a data matrix, as is required in signalprocessing applications employing the 'signal subspace' approach. The noise subspace is estimated using a rank-revealing QR factorization instead of the more expensive singular value or eigenvalue decompositions. Using incremental condition estimation to monitor the smallest singular values of triangular matrices, we can update the rank-revealing triangular factorization inexpensively when new rows are added and old rows are deleted. Experiments demonstrate that the new approach usually requires O(n2) work to update an n × n matrix, and accurately tracks the noise subspace.
Cumulants, and their associated Fourier transforms, known as polyspectra, are very useful in situations where one or more of the preceding phenomena - non-Gaussianity, nonminimum phase, colored Gaussian noise, and non...
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Cumulants, and their associated Fourier transforms, known as polyspectra, are very useful in situations where one or more of the preceding phenomena - non-Gaussianity, nonminimum phase, colored Gaussian noise, and nonlinearities - are present. Because second-order-based techniques have not led to very useful results in the face of these phenomena, it is no exaggeration to believe that it should be possible to reexamine every application and/or method that has ever made use of second-order statistics, using higher-order statistics, to see if better results can be obtained. The purpose of this paper is to give a brief introduction to cumulants and polyspectra and to give a brief overview of some of their applications.
We are presenting a new class of transforms which facilitates the processing of signals that are nonlinearly stretched or compressed in time. We refer to nonlinear stretching and compression as warping. While the magn...
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We are presenting a new class of transforms which facilitates the processing of signals that are nonlinearly stretched or compressed in time. We refer to nonlinear stretching and compression as warping. While the magnitude of the Fourier transform is invariant under time shift operations, and the magnitude of the scale transform is invariant under (linear) scaling operations, the new class of transforms is magnitude invariant under warping operations. The new class contains the Fourier transform and the scale transform as special cases. Important theorems, like the convolution theorem for Fourier transforms, are generalized into theorems that apply to arbitrary members of the transform class. Cohen's class of time-frequency distributions is generalized to joint representations in time and arbitrary warping variables. Special attention is payed to a modification of the new class of transforms that maps an arbitrary time-frequency contour into an impulse in the transform domain. A chirp transform is derived as an example.
This paper presents the application of the Linear Sequential Array (LSA) retiming approach, developed for conventional digit-recurrence algorithms, to on-line multiplication. The result is a modular and fast pipelined...
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This paper presents the application of the Linear Sequential Array (LSA) retiming approach, developed for conventional digit-recurrence algorithms, to on-line multiplication. The result is a modular and fast pipelined structure which due to a small constant fan-out and cycle time independent of precision is suitable for FPGA implementation. First we present the basics of on-line multiplication, and determine data dependencies according to the LSA design methodology. Based on these dependencies we redesign the traditional on-line multiplier to obtain the LSA structure. Since in DSP applications one of the multiplier operands is fixed for a long sequence of operations, we briefly present a parallel-serial multiplication unit that receives one of the operands in parallel and the other operand in Most-Significant-Digit-First format. Performance and area results are provided for the LSA on-line multiplier design and then compared with the conventional on-line design, using Xilinx FPGAs as the target technology.
Linear Algebra (i. e. , the algebra of vector spaces) provides widely used mathematical tools and concepts which are today considered for implementation in special computer architectures. It seems that so many signal ...
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ISBN:
(纸本)0892524669
Linear Algebra (i. e. , the algebra of vector spaces) provides widely used mathematical tools and concepts which are today considered for implementation in special computer architectures. It seems that so many signalprocessing problems can be expressed and, more importantly, implemented efficiently as a sequence of vector and matrix operations, that a signalprocessing system with a capability for high speed linear algebra is necessary if the more advanced signal processing algorithms are to be implemented to operate in real time. This paper supports the notion that linear algebra is a sound basis for important signalprocessing system implementations and suggests that multilinear algebra (i. e. , the algebra of vector, bivector, trivector, etc. spaces) offers an even broader set of signalprocessing tools. Examples and ideas from direction finding and time series analysis are discussed.
This paper describes an efficient implementation of auxiliary constraints for a concurrent block least squares adaptive sidelobe canceller when a single array of sensors is used to form one or more main beams. The app...
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ISBN:
(纸本)0819406945
This paper describes an efficient implementation of auxiliary constraints for a concurrent block least squares adaptive sidelobe canceller when a single array of sensors is used to form one or more main beams. The approach is to compute QR decomposition of the auxiliary data matrix and then send this information to main beam processors, where the constraints are applied using a blocking matrix and the individual residuals are computed. The blocking matrix can be chosen with special structure which is used to derive a new fast algorithm and architecture for constrained main beam processing that reduces the operation count from order n3 to order n2, where n is the number of auxiliary sensors.
We introduce the use of multidimensional logarithmic number system (MDLNS) as a generalization of the classical 1-D logarithmic number system (LNS) and analyze its use in DSP applications. The major drawback of the LN...
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We introduce the use of multidimensional logarithmic number system (MDLNS) as a generalization of the classical 1-D logarithmic number system (LNS) and analyze its use in DSP applications. The major drawback of the LNS is the requirement to use very large ROM arrays in implementing the additions and subtraction and it limits its use to low-precision applications. MDLNS allows exponential reduction of the size of the ROMs used without affecting the speed of the computational process: moreover, the calculations over different bases and digits are completely independent, which makes this particular representation perfectly suitable for massively parallel DSP architectures. The use of more than one base has at least two extra advantages. Firstly, the proposed architecture allows us to obtain the final result straightforwardly in binary form, thus, there is no need of the exponential amplifier, used in the known LNS architectures. Secondly, the second base can be optimized in accordance to the specific digital filter characteristics. This leads to dramatic reduction of the exponents used and, consequently, to large area savings. We offer many examples showing the computational advantages of the proposed approach.
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