In this paper we introduce a new definition for the instantaneous frequency of a discrete-time analytic signal. Unlike the existing definition which uses only two data samples around a particular time this method util...
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ISBN:
(纸本)0819404098
In this paper we introduce a new definition for the instantaneous frequency of a discrete-time analytic signal. Unlike the existing definition which uses only two data samples around a particular time this method utilizes all the data samples for estimating the instantaneous frequency. We prove that this quantity is identical to the average frequency evaluated at the particular time in the discrete-time TFD. This property is consistent with the analogous continuous-time property. We also derive requirements on the discrete-time kernel needed to satisfy this property. Using computer-generated signals and real data performance comparisons are made between the proposed approach and the existing one.
The proceedings contains 49 papers. The papers are grouped under following session headings: signalprocessing techniques;nonlinear signalprocessing and neural networks;time-frequency distribution and nostationary si...
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The proceedings contains 49 papers. The papers are grouped under following session headings: signalprocessing techniques;nonlinear signalprocessing and neural networks;time-frequency distribution and nostationary signals;wavelets and wideband ambiguity functions;matrix computations;and real-time implementations. Some of the specific topics discussed are;wavelets and related time-scale transforms;adaptive lattice bilinear filters;optimal kernels for time-frequency analysis;applications of fast wavelet transform;and updating signal subspaces.
This paper presents the development of a pair of recursive least squares (ItLS) algorithms for online training of multilayer perceptrons which are a class of feedforward artificial neural networks. These algorithms in...
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ISBN:
(纸本)0819404098
This paper presents the development of a pair of recursive least squares (ItLS) algorithms for online training of multilayer perceptrons which are a class of feedforward artificial neural networks. These algorithms incorporate second order information about the training error surface in order to achieve faster learning rates than are possible using first order gradient descent algorithms such as the generalized delta rule. A least squares formulation is derived from a linearization of the training error function. Individual training pattern errors are linearized about the network parameters that were in effect when the pattern was presented. This permits the recursive solution of the least squares approximation either via conventional RLS recursions or by recursive QR decomposition-based techniques. The computational complexity of the update is 0(N2) where N is the number of network parameters. This is due to the estimation of the N x N inverse Hessian matrix. Less computationally intensive approximations of the ilLS algorithms can be easily derived by using only block diagonal elements of this matrix thereby partitioning the learning into independent sets. A simulation example is presented in which a neural network is trained to approximate a two dimensional Gaussian bump. In this example RLS training required an order of magnitude fewer iterations on average (527) than did training with the generalized delta rule (6 1 BACKGROUND Artificial neural networks (ANNs) offer an interesting and potentially useful paradigm for signalprocessing and pattern recognition. The majority of ANN applications employ the feed-forward multilayer perceptron (MLP) network architecture in which network parameters are " trained" by a supervised learning algorithm employing the generalized delta rule (GDIt) [1 2]. The GDR algorithm approximates a fixed step steepest descent algorithm using derivatives computed by error backpropagatiori. The GDII algorithm is sometimes referred to as the
Conventional scale dependent wavelet analysis represents a signal or iniage as a superposition of translated differently scaled versions of the same basis function. When the basis function for time series analysis is ...
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ISBN:
(纸本)0819404098
Conventional scale dependent wavelet analysis represents a signal or iniage as a superposition of translated differently scaled versions of the same basis function. When the basis function for time series analysis is a chirp with linear frequency modulation a scale dependent wavelet representation is equivalent to a sequence of projections of the signal timefrequency distribution along differently rotated lines and reconstruction of the signal from its chirped wavelet representation is analogous to tomographic reconstruction from time frequency projections. The same analogy applies in two dimensions if scaled basis functions are replaced by rotated ones such that an image is represented by a superposition of translated differently rotated versions of the same basis function. For rotation dependent wavelet analysis basis functions consisting of very long line segments yield a tomographic representation while shorter line segments yield a line segment image representation as in the primate visual cortex. Applications include binocular robot vision and synthetic aperture radar.
The proceedings contain 49 papers. The topic discussed include: wavelets and related time-scale transforms;tomographic techniques in image and signalprocessing;higher-order statistics (spectra) and their application ...
The proceedings contain 49 papers. The topic discussed include: wavelets and related time-scale transforms;tomographic techniques in image and signalprocessing;higher-order statistics (spectra) and their application in signalprocessing;real-time SAR change-detection using neural networks;nonlinear signalprocessing using radial basis functions;nonlinear classification and adaptive structures;global search of adaptive IIR filter error surfaces using stochastic learning automata;direction finding using a modified minimum-eigenvector technique;and translation, rotation, and scaling invariant object and texture classification using polyspectra.
The Fourier-Mellin transform (FMT) of an input function is defined as and is the magnitude squared of the Mellin transform of the magnitude squared of the Fourier transform of the input function [1]. As such the FMT i...
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ISBN:
(纸本)0819404098
The Fourier-Mellin transform (FMT) of an input function is defined as and is the magnitude squared of the Mellin transform of the magnitude squared of the Fourier transform of the input function [1]. As such the FMT is unchanged by translations and dilations of the input function. While the FMT has found applications in optical pattern recognition [3] [5] ship classification by sonar and radar [15] and image processing [10] only cursory attention has been paid to the truncation error incurred by using a finite number of samples of the input function. This paper establishes truncation bounds for computing the FMT for band-limited functions from a finite number of samples of the input function. These bounds naturally suggest an implementation of the FMT by the method of direct expansions [4] [14]. This approach readily generalizes to a direct expansion for the Wigner-Ville distribution [13] and the Q distribution [2]. 1 Principal Notation u(x) fff00 e_2tu(t)dt Fourier transform of u M(u s) fD x_i2r8() Mellin transform of u . FM(u s) M(lI(x)I2 s)________ Fourier-Mellin transform of u Q(U V f002rt U(wft)_V(w/fr) Q distribution of U and V W(U V t w) fe_i2ntY U(w + y/2) V(w y/2) dy Wigner-Ville distribution of U and V
A multiresolution model of a discrete fractional Brownian motion is developed. The model leads to a multiscale algorithm for constructing the optimal filter that must be used in detection problems involving a fraction...
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CORDIC algorithms offer an attractive alternative to multiply-and-add based algorithms for the implementation of two-dimensional rotations, preserving either norm: (x2 + y2) 1/2 or (x2 - y2) 1/2 . Indeed these nor who...
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CORDIC algorithms offer an attractive alternative to multiply-and-add based algorithms for the implementation of two-dimensional rotations, preserving either norm: (x2 + y2) 1/2 or (x2 - y2) 1/2 . Indeed these nor whose computation is a significant part of the evaluation of the two-dimensional rotations, are computed much more easily by the CORDIC algorithms. However the part played by norm computations in the evaluation of rotations becomes quickly small as the dimension of the space increases. Thus, in spaces of dimension 5 or more, there is no practical alternative to multiply-and-add based algorithms. In the intermediate region, dimensions 3 and 4, extensions of the CORDIC algorithms are an interesting option. The four-dimensional extensions are particularly elegant and are the main object of this paper.
In this paper, we propose a new algorithm for computing a singular value decomposition of a matrix product. We show that our algorithm is numerically desirable in that all relevant residual elements will be numericall...
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In this paper, we propose a new algorithm for computing a singular value decomposition of a matrix product. We show that our algorithm is numerically desirable in that all relevant residual elements will be numerically small. Our algorithm can be extended to a product of a larger number of upper triangular matrices.
This paper addresses the problem of designing signals for general group representations subject to constraints which are formulated as convex sets in the Hubert space of the group states. In particular, the paper cons...
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