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.
The proceedings contain 33 papers. The topics discussed include: signalprocessing computational needs;the use of pivoting to improve the numerical performance of toeplitz solvers;stability, strong stability, and weak...
The proceedings contain 33 papers. The topics discussed include: signalprocessing computational needs;the use of pivoting to improve the numerical performance of toeplitz solvers;stability, strong stability, and weak stability of algorithms for solving linear equations;a conjugate gradient method for the solution of equality constrained least squares problems;parallel QR decomposition of toeplitz matrices;on the implementation of a fully parallel algorithm for the symmetric eigenvalue problem;systolic array computation of the SVD of complex matrices;highly parallel eigenvector update methods with applications to signalprocessing;a systolic array for linearly constrained least-squares problems;analysis of a recursive least squares signalprocessing algorithm;and a subspace approach to determining sensor gain and phase with applications to array processing.
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.
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.
This paper addresses the problem of designing signals for general group representations subject to constraints which are formulated as convex sets in the Hilbert space of the group states. In particular, the paper con...
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This paper addresses the problem of designing signals for general group representations subject to constraints which are formulated as convex sets in the Hilbert space of the group states. In particular, the paper considers irreducible representations in an infinite dimensional Hilbert space and derives an iterative procedure for proceeding from an arbitrary element of the Hilbert space to a state of the group subject to a priori imposed constraints with closed convex range. As examples, the paper focusses on narrowband and wideband radar ambiguity synthesis.
Current bilinear time-frequency representations apply a fixed kernel to smooth the Wigner distribution. However, the choice of a fixed kernel limits the class of signals that can be analyzed effectively. This paper pr...
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Current bilinear time-frequency representations apply a fixed kernel to smooth the Wigner distribution. However, the choice of a fixed kernel limits the class of signals that can be analyzed effectively. This paper presents optimality criteria for the design of signal-dependent kernels that suppress cross-components while passing as much auto-component energy as possible, irrespective of the form of the signal. A fast algorithm for the optimal kernel solution makes the procedure competitive computationally with fixed kernel methods. Examples demonstrate the superior performance of the optimal kernel for a frequency modulated signal.
Autocorrelation and spectra of linear random processes can be can be expressed in terms of cumulants and polyspectra, respectively. The insensitivity of the latter to additive Gaussian noise of unknown covariance, is ...
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Autocorrelation and spectra of linear random processes can be can be expressed in terms of cumulants and polyspectra, respectively. The insensitivity of the latter to additive Gaussian noise of unknown covariance, is exploited in this paper to develop spectral estimators of deterministic and linear non-Gaussian signals using polyspectra. In the time-domain, windowed projections of third-order cumulants are shown to yield consistent estimators of the autocorrelation sequence. Both batch and recursive algorithms are derived. In the frequency-domain, a Fourier-slice solution and a least-squares approach are described for performing spectral analysis through windowed bi-periodograms. Asymptotic variance expressions of the time- and frequency-domain estimators are also presented. Two-dimensional extensions are indicated, and potential applications are discussed. Simulations are provided to illustrate the performance of the proposed algorithms and compare them with conventional approaches.
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