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Time-varying higher order spectra

Time-varying higher order spectra

引用

advanced signal processing algorithms, architectures, and implementations ii

作者： Boashash, Boualem O'Shea, Peter Queensland Univ. of Technology Brisbane Queensland Australia

ISBN: (纸本)0819406945

A general solution for the problem of time-frequency signal representation of nonlinear FM signals is provided, based on a generalization of the Wigner-Ville distribution. The Wigner-Ville distribution (WVD) is a second order time-frequency representation. That is, it is able to give ideal energy concentration for quadratic phase signals and its ensemble average is a second order time-varying spectrum. The same holds for Cohen's class of time-frequency distributions, which are smoothed versions of the WVD. The WVD may be extended so as to achieve ideal energy concentration for higher order phase laws, and such that the expectation is a time-varying higher order spectrum. The usefulness of these generalized Wigner-Ville distributions (GWVD) is twofold. Firstly, because they achieve ideal energy concentration for polynomial phase signals, they may be used for optimal instantaneous frequency estimation. Second, they are useful for discriminating between nonstationary processes of differing higher order moments. In the same way that the WVD is generalized, we generalize Cohen's class of TFDs by defining a class of generalized time-frequency distributions (GTFDs) obtained by a two dimensional smoothing of the GWVD. Another results derived from this approach is a method based on higher order spectra which allows the separation of cross-terms and auto- terms in the WVD.

关键词： signal Theory

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Comparison of time-frequency-based techniques for estimating instantaneous frequency parameters of nonstationary processes

Comparison of time-frequency-based techniques for estimating...

引用

Proceedings of the 1999 advanced signal processing algorithms, architectures, and implementations IX

作者： Bonato, Paolo Erim, Zeynep Roy, Serge H. De Luca, Carlo J. Boston Univ Boston United States

The aim of this work is to contrast techniques used to estimate two instantaneous frequency parameters of the surface electromyographic (EMG) signal, the instantaneous median frequency and the instantaneous mean frequency, based on their estimation error. Three methods are compared: Cohen class and Cohen-Posch class time-frequency representations are used to compute both the above-mentioned instantaneous frequency parameters, and a cross-time-frequency based technique is adopted to derive the instantaneous mean frequency. The results demonstrate that the algorithm based on Cohen-Posch class transformations leads to a standard deviation of the instantaneous frequency parameters that is smaller than that obtained using Cohen class representations. However, the cross-time-frequency estimation procedure for instantaneous mean frequency produced the smallest standard deviation compared to the other techniques. The algorithms based on Cohen class and Cohen-Posch class transformations often provided a lower bias than the cross-time-frequency based technique. This advantage was particularly evident when the instantaneous mean frequency varied non-linearly within the epochs used to derive the cross-time-frequency representation of the surface EMG signal.

关键词： signal processing

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Blind channel estimation and deconvolution in colored noise using higher-order cumulants

Blind channel estimation and deconvolution in colored noise ...

引用

advanced signal processing: algorithms, architectures, and implementations V

作者： Tugnait, Jitendra K. Gummadavelli, Uma Auburn Univ. Auburn AL USA

ISBN: (纸本)0819416207

Existing approaches to blind channel estimation and deconvolution (equalization) focus exclusively on channel or inverse-channel impulse response estimation. It is well-known that the quality of the deconvolved output depends crucially upon the noise statistics also. Typically it is assumed that the noise is white and the signal-to-noise ratio is known. In this paper we remove these restrictions. Both the channel impulse response and the noise model are estimated from the higher-order (fourth, e.g.) cumulant function and the (second-order) correlation function of the received data via a least-squares cumulant/correlation matching criterion. It is assumed that the noise higher-order cumulant function vanishes (e.g., Gaussian noise, as is the case for digital communications). Consistency of the proposed approach is established under certain mild sufficient conditions. The approach is illustrated via simulation examples involving blind equalization of digital communications signals.

关键词： signal processing

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Wavelets, tomography, and line segment image representations

Wavelets, tomography, and line segment image representations

引用

advanced signal-processing algorithms, architectures, and implementations

作者： Altes, Richard A. Chirp Corp La Jolla United States

The scale dependent wavelet transform can be augmented by a rotation dependent version as well as other generalizations. Tomographic analysis and line segment transforms are special cases of rotation dependent wavelet analysis. Other cases suggested by biological analogy9 are a rotation dependent edge segment transform (using edge segments rather than line segments) and a binocular rotation dependent wavelet transform that introduces depth information into the reconstructed image. Applications to robot vision and synthetic aperture radar appear particularly promising.

关键词： Image processing

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Classification of vehicles using nonlinear dynamics and array processing

Classification of vehicles using nonlinear dynamics and arra...

引用

Proceedings of the 1999 advanced signal processing algorithms, architectures, and implementations IX

作者： Tung, Tai-Lai Yao, Kung Univ of California Los Angeles Los Angeles United States

The analysis of vehicle signals with methods derived from the theory of nonlinear dynamics is a potential tool to classify different vehicles. The nonlinear dynamical methodologies provide alternate system information that the linear analysis tools have ignored. In order to observe the nonlinear dynamic phenomena more clearly, and estimate system invariants more robustly, we exploit the maximum power blind beamforming algorithm as a signal enhancement and noise reduction method when locations of a source and sensors are unknown. The dynamical behavior of an acoustic vehicle signal is studied with the use of correlation dimension D2 and Lyapunov exponents. To characterize the nonlinear dynamic behavior of the acoustic vehicle signal, Taken's embedded theory is used to form an attractor in phase space based on a single observed time series. The time series is obtained from the coherently enhanced output of a blind beamforming array. Then the Grassberger-Procaccia algorithm and Sano-Sawada method are exploited to compute the correlation dimension and Lyapunov exponents. In this paper, we also propose some efficient computational methods for evaluating these system invariants. Experimental classification results show that the maximum power blind beamforming processing improves the estimation of the invariants of the nonlinear dynamic system. Preliminary results show that the nonlinear dynamics is useful for classification applications.

关键词： Acoustic signal processing

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Maximum-likelihood methods for array processing based on time-frequency distributions

Maximum-likelihood methods for array processing based on tim...

引用

Proceedings of the 1999 advanced signal processing algorithms, architectures, and implementations IX

作者： Zhang, Yimin Mu, Weifeng Amin, Moeness G. Villanova Univ Villanova United States

This paper proposes a novel time-frequency maximum likelihood (t-f ML) method for direction-of-arrival (DOA) estimation for non-stationary signals, and compares this method with conventional maximum likelihood DOA estimation techniques. Time-frequency distributions localize the signal power in the time-frequency domain, and as such enhance the effective SNR, leading to improved DOA estimation. The localization of signals with different t-f signatures permits the division of the time-frequency domain into smaller regions, each contains fewer signals than those incident on the array. The reduction of the number of signals within different time-frequency regions not only reduces the required number of sensors, but also decreases the computational load in multi-dimensional optimizations. Compared to the recently proposed time-frequency MUSIC (t-f MUSIC), the proposed t-f ML method can be applied in coherent environments, without the need to perform any type of preprocessing that is subject to both array geometry and array aperture.

关键词： signal detection

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Improved jammer localization using multiple focussing

Improved jammer localization using multiple focussing

引用

advanced signal-processing algorithms, architectures, and implementations

作者： Velez, Edgar F. Amin, Moeness G. Villanova Univ Villanova United States

Focussing techniques have proven efficient in direction-of-arrival estimation of broadband signals. However, when used alone at high frequency operation, these techniques cannot accurately locate the sources, due to the numerous spurious peaks in the spectrum. Since the spurious peaks depend on the array manifold, their location varies from one focussing frequency to another. Improved jammer localization can, therefore, be achieved by focussing at different frequencies and then averaging the corresponding MUSIC spectra. The averaging smooths out the undesired peaks while boosting the common spectral peaks, allowing correct detection and location of the waveforms impinging on the array.

关键词： signal processing

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Matrix triangularization by fixed-point redundant CORDIC with constant scale factor

Matrix triangularization by fixed-point redundant CORDIC wit...

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advanced signal-processing algorithms, architectures, and implementations

作者： Lee, Jeong-A Lang, Tomas Univ of California Los Angeles United States

We develop redundant CORDIC scheme where the scale factor is forced to be constant while computing angles for 2 × 1 plane rotations. Based on the scheme, we present a fixed-point implementation of matrix triangularization by Luk's parallel algorithm, with the following additional features: (1) the final scaling operation is done by shifting, (2) the number of iterations in CORDIC rotation unit is reduced by about 25% by expressing the direction of the rotation in radix-2 and radix-4, and (3) the conventional number representation of rotated output is obtained on-the-fly, not from a carry-propagate adder. The number of hardware modules and the speed are evaluated and compared with the previous CORDIC schemes.

关键词： signal processing

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Minimal-window time-frequency distributions

Minimal-window time-frequency distributions

引用

Proceedings of the 1999 advanced signal processing algorithms, architectures, and implementations IX

作者： Williams, William J. Aviyente, Selin Univ of Michigan Ann Arbor United States

This paper outlines means of using special sets of orthonormally related windows to realize Cohen's class of time-frequency distributions (TFDs). This is accomplished by decomposing the kernel of the distribution in terms of the set of analysis windows to obtain short time Fourier transforms (STFTs). The STFTs obtained using these analysis windows are used to form spectrograms which are then linearly combined with proper weights to form the desired TFD. A set of orthogonal analysis windows which also have the scaling property proves to be very effective, requiring only 1 + log2(N - 1) distinct windows for an overall analysis of N + 1 points, where N = 2n, with n a positive integer. Application of this theory offers very fast computation of TFDs, since very few analysis windows needed and fast, recursive STFT algorithms can be used. Additionally, it is shown that a minimal set of specially derived orthonormal windows can represent most TFDs, including Reduced Interference Distributions (RIDs) with only three distinct windows plus an impulse window. Finally, the Minimal Window RID (MW-RID) which achieves RID properties with only one distinct window and an impulse window is presented.

关键词： signal processing

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Minimum-phase LU factorization preconditioner for Toeplitz matrices

Minimum-phase LU factorization preconditioner for Toeplitz m...

引用

advanced signal processing algorithms, architectures, and implementations ii

作者： Ku, Ta-Kang Kuo, C.-C.J. Univ. of Southern California Los Angeles CA USA

ISBN: (纸本)0819406945

A new preconditioner is proposed for the solution of an N × N Toeplitz system TNx = b, where TN can be symmetric indefinite or nonsymmetric, by preconditioned iterative methods. The preconditioner FN is obtained based on factorizing the generating function T(z) into the product of two terms corresponding, respectively, to minimum-phase causal and anticausal systems and therefore called the minimum-phase LU (MPLU) factorization preconditioner. Due to the minimum-phase property, F N-1 is bounded. For rational Toeplitz TN with generating function T(z) = A(z-1)/B(z-1) + C(z)/D(z), where A(z), B(z), C(z), and D(z) are polynomials of orders p1, q1, p2, and q2, we show that the eigenvalues of FN-1TN are repeated exactly at 1 except at most α F outliers, where αF depends on p1, q1, p2, q2, and the number approximately ega of the roots of T(z) = A(z-1)D(z) + B(z-1)C(z) outside the unit circle. A preconditioner KN in circulant form generalized from the symmetric case is also presented for comparison.

关键词： signal processing

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